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''by Maurizio Brocchini''
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The mixing-induced transport that occurs in nearshore waters is a fundamental mechanism for all physical/biological/chemical phenomena that occur in the marine environment. The '''transport and dispersion of pollutants, nutrients and tracers in mixed nearshore water''' can have direct and indirect consequences for the marine [[ecosystem]]s. 
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==Introduction==
  
This contribution finds its motivation in the awareness that the mixing-induced transport occurring in the nearshore waters is a fundamental mechanism underlying/forcing all the physical/chemical/biological phenomena occurring in the marine environment. It is also aimed at better highlighting/exploiting the wealth of knowledge built by the EU on the marine environment (about 20 years have passed since the first EU MAST Projects). Such knowledge is not yet being used at full because of the still i) scarce understanding of complex physical phenomena like mixing-induced transport; ii) fragmented view of the specialists on the marine processes.
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The release of [[pollutant]]s from coastal and atmospheric sources heavily influences our lives in many different ways, from direct contamination of edible organisms to more indirect processes of impact and endangerment of the nearshore [[ecosystem]]s. Such influences are felt not only in proximity to the source, but also in wider regions, determined primarily by the direct physical transport in marine waters. <ref name="Lekien">Lekien F., Coulliette C., Mariano A.J., Ryan E.H., Shay L.K., Haller G. & Marsden J.E. (2005). Pollution release tied to invariant manifolds: a case study for the coast of Florida. ''Physica D'' '''210''' (1–2) 1–20.</ref> High concentration zones of [[pollutant]]s have been found along coastal regions far from the coastal source, and noticeable impacts have been detected even in deep sea regions.
  
Specific EU Projects have been funded (e.g. ''TRACMASS'' Project, MAS3-CT97-0142) and have been submitted (e.g. ''TRAPPS ''Project, EVK3-2000-22032) towards a more detailed understanding of the physical phenomena and a stronger exploitation of the specific knowledge on mixing for the sustainable management of the marine resources. However, still few experts in pollution management and remediation are fully aware of the fundamental role played by mixing in transporting chemicals, pollutants, nutrients and tracers in general.
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==Water mixing, sediment and pollutant transport==
  
==The motivations==
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It is also important to acknowledge the close link between water mixing, sediment and [[pollutant]] transport. <ref name="Förstner">Förstner U. (1987). Sediment-associated contaminants - an overview of scientific bases for developing remedial options. ''Hydrobiol.'' '''149''' (1) 221–246.</ref> For example, if the morphological evolution of the nearshore bottom is forced by wave-induced phenomena, including mixing, then the bondage between [[pollutant]]s (e.g. trace metals, among which [[mercury pollution|mercury]], major elements, various organic and inorganic chemicals, etc.) and sediments (e.g. coastal inlets run-off of polluted sands, disposal of dredged materials, etc.) closes a circle in which a feedback is established between hydro- and morpho-dynamics, the [[pollutant]]s only playing a passive role. The spatial extension of contaminated sediments and the [[pollutant]]s concentration/toxicity/bioaccumulation strongly depend on the type of injection into the marine environment: while dumping sites are, usually, well protected from the hydrodynamics actions by means of a specific coverage (e.g. ''Ocean Dumping Act'', 1972) this is not the case for the widespread run-off of water-sand mixtures from coastal inlets, the latter being largely influenced by transport phenomena. <ref name="Williamson">Williamson R.B. and Morrisey D.J. (2000). Stormwater contamination of urban estuaries. 1. Predicting the build-up of heavy metals in sediments. ''Estuaries'' '''23'''(1) 56–66.</ref> <ref name="Bloom">Bloom, N.S., Moretto, L.S. Scopece P. and Ugo P. (2004). Seasonal cycling of mercury and monomethyl mercury in the Venice Lagoon (Italy). ''Mar. Chem.'' '''91''' 85–99.</ref>
  
The release of '''pollutants''' from coastal distributed/localized and atmospheric sources heavily influences our lives in many different ways, from direct contamination of edible organisms to more indirect processes of impact and endangerment of the nearshore ecosystem. Such influences are felt not only in proximity of the sources, but also in wider regions, determined primarily by the direct physical transport due to marine waters (Lekien et al., 2005). High concentration zones of pollutants have been found along coastal regions far from coastal sources, and noticeable impact of pollutants on organisms has been detected even in deep sea regions.
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Many ecological issues strongly depend on the action of large-scale eddies. For example, these are responsible for the complex but predictable patterns of dispersion of [[phytoplankton]] <ref name="Martin">Martin A.P. (2003). Phytoplankton patchiness: the role of lateral stirring and mixing. ''Progr. Ocean.'' '''57''' 125–174.</ref> and a number of marine species during their larval stage. Hence, the recent and growing attention to '''Lagrangian transport of marine species'''. <ref name="Cowen">Cowen R. K., Kamazima Lwiza M.M., Sponaugle S., Parisa C.B. and Olson D.B. (2000). Connectivity of Marine Populations: Open or Closed? ''Science'' '''287''' 857–859.</ref> <ref name="Siegel">Siegel D.A., Kinlan B.P., Gaylord B. and Gaines S.D. (2003). Lagrangian descriptions of marine larval dispersion. ''Mar. Ecol. Progr. Ser.'' '''260''' 83–96.</ref>  It is particularly interesting that increasing acknowledgement is given of the fundamental action of complex topographic features on the flow mixing and the related transport mechanisms of organic matter. Moving fronts are found to transport plankton communities in the cross-shore direction and cause differentiation between coastal and oceanic communities. <ref name="Caldeira">Caldeira R.M.A., Groom S., Miller, P., Pilgrim D. and Nezlin N.P. (2002). Sea-surface signatures of the island mass effect phenomena around Madeira Island, Northeast Atlantic. ''Remote Sens. Envir.'' '''80''' 336–360.</ref>
  
It is also important to acknowledge the close '''link between water mixing, sediment and pollutant transport '''(Förstner, 1987). For example, if, on the one hand, the morphological evolution of the nearshore bottom is forced by wave-induced phenomena, including mixing, then on the other hand, the bondage between pollutants (e.g. trace metals, among which mercury, major elements, various organic and inorganic chemicals, etc.) and sediments (e.g. coastal inlets run-off of polluted sands, disposal of dredged materials, etc.) closes a circle in which a feedback is established between hydro- and morpho-dynamics, the pollutants only playing a passive role. The spatial extension of contaminated sediments and the pollutants’ concentration/toxicity/bioaccumulation strongly depend on the type of injection into the marine environment: while dumping sites are, usually, well protected from the hydrodynamics actions by means of a specific coverage (e.g. ''Ocean Dumping Act'', 1972) this is not the case for the widespread run-off of water-sand mixtures from coastal inlets, the latter being largely influenced by transport phenomena (e.g. Williamson et al., 2000; Bloom et al., 2004).
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==Rip currents==
  
Many ecological issues strongly depend on the action of large-scale eddies. For example, these are responsible for the complex but predictable patterns of dispersion of phytoplankton (Martin, 2003) and of most of marine species during their larval stage. Hence, it should not surprise the recent and growing attention to '''Lagrangian transport of marine species''' (e.g. Cowen et al., 2000, Siegel et al., 2003). It is particularly interesting that increasing acknowledgement is given of the fundamental action of complex topographic features on the flow mixing and the related transport mechanisms of organic matter. Moving fronts are found to transport plankton communities in the cross-shore direction and cause differentiation between coastal and oceanic communities. (e.g. Caldeira et al., 2002).
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Recreational activities are also strongly influenced by water transport phenomena. More specifically swimming safety is seriously hampered by the horizontal water mixing induced by [[rip current]]s. <ref name="Lushine">Lushine J.B. (1991). A study of rip current drownings and related weather factors. ''Natl. Wea. Dig.'', '''16''' 13–16.</ref> [[Rip current]]s are powerful, channelled currents of water flowing away from shore. They typically extend from the shoreline, through the surf zone, and past the line of breaking waves. [[Rip current]]s can occur at any beach with breaking waves but they become especially strong in the presence of bathymetric changes of the seabed. <ref name="Kennedy">Kennedy A., Brocchini M., Soldini L. and Gutierrez E. (2006). Topographically-controlled, breaking wave-induced macrovortices. Part 2. Changing geometries. ''J. Fluid Mech.'' '''559''' 57–80.</ref> Typically people who are wading or swimming accidentally venture into the [[rip current]]s, and are pulled out to sea. It is impossible to swim or walk against these currents (if you try, you will end up swimming or walking backwards out to deep water). The United States Lifesaving Association, one of the few with detailed and available statistics, estimates that the annual number of deaths due to [[rip current]]s on U.S beaches exceeds 100. [[Rip current]]s account for over 80% of rescues performed by surf beach lifeguards ([http://www.srh.noaa.gov/ripcurrents/index.shtml http://www.srh.noaa.gov/ripcurrents/index.shtml]). In Australia, 35% of rescues and 18.5% of resuscitation cases, over a ten year period, from surf beaches were due to [[rip current]]s. <ref name="Fenner">Fenner P. (1999). Prevention of drowning: visual scanning and attention span in lifeguards. Reply to a letter. ''J. Occupat. Health and Safety-Australia and New Zealand'' '''15''' 209–210.</ref> [[Rip current]]s are also recognised as a hazard for European beaches. Particularly where submerged breakwaters have been put in place in order to protect against [[erosion]], but in fact are increasing the potential for localised [[rip current]]s(e.g. ''EU DELOS ''Project'', ''EVK-2000-22038). Coastal engineers recognize [[rip current]]s as an important element in the nearshore circulation balance, particularly during storms. Nevertheless, little information is as yet available that describes where and when these currents occur. Hence, not only fundamental insight is needed into the conditions for the generation and development of [[rip current]]s and methodology for the related [[environmental risk assessment of marine activities|risk assessment]], but strategies are also required for minimizing the hazard-related socio-economical costs.
 
 
'''Recreational activities''' are also strongly influenced by water transport phenomena. More specifically swimming safety is seriously hampered by the horizontal water mixing induced by the so-called “rip currents” (Lushine, 1991). Rip currents are powerful, channelled currents of water flowing away from shore. They typically extend from the shoreline, through the surf zone, and past the line of breaking waves. Rip currents can occur at any beach with breaking waves but they become especially strong in the presence of bathymetric changes of the seabed (Kennedy et al., 2006). Typically people who are wading or swimming accidentally venture into the rip currents, and they are pulled out to sea. It is impossible to swim or walk against these currents (if you try, you will end up swimming or walking backwards out to deep water). The United States Lifesaving Association, one of the few with detailed and available statistics, estimates that the annual number of deaths due to rip currents on U.S.A. beaches exceeds 100. Rip currents account for over 80% of rescues performed by surf beach lifeguards ([http://www.srh.noaa.gov/ripcurrents/index.shtml http://www.srh.noaa.gov/ripcurrents/index.shtml]). In Australia, 35% of rescues and 18.5% of resuscitation cases, over a ten year period, from surf beaches were due to rip currents (Fenner, 1999). The role of rip current related hazard is becoming also recognized for European beaches. These are often protected against erosion by submerged breakwaters which, however, highly increase the potential of localized rip currents (e.g. ''EU DELOS ''Project'', ''EVK-2000-22038). Coastal engineers recognize rip currents as an important element in the nearshore circulation balance, particularly during storms. Nevertheless, little information is as yet available that describes where and when these currents occur. Hence, not only fundamental insight is needed into the conditions for the generation and development of rip currents and methodology for the related risk assessment, but strategies are also required for minimizing the hazard-related socio-economical costs.
 
  
 
==Modelling the physics of nearshore water mixing==
 
==Modelling the physics of nearshore water mixing==
  
Once clarified the fundamental role of the horizontal mixing of marine waters, a brief description is proposed of the phenomenon and of the recent advances in its representation/modelling. The mixing features of oceanic flows are well documented and fairly well understood be they related to the motion of abyssal streams (e.g. the Ocean Conveyor Belt) or to the horizontal circulation at both global and meso-scale level (e.g. oceanic gyres and boundary currents). For historical reasons less effort has been put in the understanding/modeling of the mixing of the continental shelf shallower waters. However, this is the complex environment which provides a boundary between the inland, where most of the anthropogenic activities occur, and the deep water flow forcing. We here focus in particular on the most active agents of horizontal mixing i.e. the large-scale eddies of the nearshore turbulence also known as “macrovortices”.
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The mixing features of oceanic flows are well documented and fairly well understood be they related to the motion of abyssal streams (e.g. the Ocean Conveyor Belt) or to the horizontal circulation at the both global and meso-scale level (e.g. oceanic gyres and boundary currents). For historical reasons less effort has been put in the understanding/modelling of the mixing of the continental shelf shallow waters. However, this is the complex environment which provides a boundary between the inland, where most of the [[anthropogenic]] activities occur, and the deep water flow forcing. The most active agents of horizontal mixing are the large-scale eddies of the nearshore turbulence also known as “macrovortices”.
 
 
The importance for shallow flows of horizontal, large-scale eddies (macrovortices hereinafter) has been widely reported for coastal flows (e.g. Oltman-Shay et al., 1989; Peregrine, 1998; Brocchini et al. 2002). Large-scale, horizontal mixing of coastal flows is mostly promoted by macrovortices which are generated because of a spatially-non-uniform breaking of the incoming waves (e.g. Peregrine 1998; Brocchini et al.,&nbsp; 2004). Although such differential breaking may be induced by various reasons (irregularity of the incoming field, wave-wave interaction, etc.) the major cause of persistent breaking unevenness is due to topography. This is often characterized by longshore, isolated (natural bumps or manmade submerged breakwaters) or almost-continuous features (bars or arrays of submerged breakwaters) over which uniform wave fronts break with large lateral gradients. Hence, macrovortices can be shed which alter both the hydrodynamics and the morphodynamics (Steijn et al., 1998; Brocchini et al., 2004). A recent classification of vortex generation in shallow coastal environments distinguished among three types (Jirka, 2001; Jirka & Uijttewal, 2004):
 
  
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The importance for shallow flows of horizontal, large-scale eddies (macrovortices hereinafter) has been widely reported for coastal flows. <ref name="Oltman-Shay">Oltman-Shay J., Howd P. A. and Berkemeier W.A. (1989). Shear instabilities of the mean longshore current: field observations. ''J. Geophys. Res. – Ocean'' '''94''' 18031–18042.</ref> <ref name="Peregrine">Peregrine D.H. (1998). Surf zone currents. ''Theoret. Comput. Fluid Dyn.'' '''10''' 295–309.</ref> <ref name="Brocchini">Brocchini M., Mancinelli A., Soldini L. and Bernetti R. (2002). Structure-generated macrovortices and their evolution in very shallow depths. ''Proc. 28th Intl Conf. Coast. Engng'' '''1''' 772–783.</ref> Large-scale, horizontal mixing of coastal flows is mostly promoted by macrovortices which are generated because of a spatially-non-uniform breaking of the incoming waves. <ref name="Peregrine">Peregrine D.H. (1998). Surf zone currents. ''Theoret. Comput. Fluid Dyn.'' '''10''' 295–309.</ref> <ref name="Brocchini.">Brocchini M., Kennedy A. B., Soldini L. and Mancinelli A. (2004). Topographically controlled, breaking-wave-induced macrovortices. Part 1. Widely separated breakwaters. ''J. Fluid Mech.'' '''507''' 289–307.</ref> Although such differential breaking may be induced by various reasons (irregularity of the incoming field, wave-wave interaction, etc.) the major cause of persistent breaking unevenness is due to topography. This is often characterized by longshore, isolated (natural bumps or manmade submerged breakwaters) or almost-continuous features (bars or arrays of submerged breakwaters) over which uniform wave fronts break with large lateral gradients. Hence, macrovortices can alter both the hydrodynamics and the morphodynamics. <ref name="Steijn">Steijn R., Roelvink D., Rakhorst D., Ribberink J. and van Overeem J. (1998). North Coast of Texel: a comparison between reality and prediction. ''Proc. 26th Intl Conf. Coast. Engng.'' '''2''' 2281–2293.</ref> <ref name="Brocchini.">Brocchini M., Kennedy A. B., Soldini L. and Mancinelli A. (2004). Topographically controlled, breaking-wave-induced macrovortices. Part 1. Widely separated breakwaters. ''J. Fluid Mech.'' '''507''' 289–307.</ref> A recent classification of vortex generation in shallow coastal environments distinguished three types: <ref name="Jirika">Jirka G.H. (2001). Large scale flow structures and mixing processes in shallow flows. ''J. Hydr. Res.'', '''39'''(6) 567–573.</ref> <ref name="Jirka.">Jirka G.H. and Uijttewaal W. (Ed.s) (2004). ''Shallow Flows''. A.A.Balkema Publishers, Rotterdam.</ref>
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# Topographic forcing (from islands, headlands, jetties or groynes),
 
# Topographic forcing (from islands, headlands, jetties or groynes),
 
# Transverse shear instabilities (jet flows from lagoons or rivers, mixing layers, wakes), and
 
# Transverse shear instabilities (jet flows from lagoons or rivers, mixing layers, wakes), and
 
# Secondary instabilities of the base flow (internal vortex interactions).
 
# Secondary instabilities of the base flow (internal vortex interactions).
  
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{{Gallery
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|title=
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|width=200|height=125 |lines=2
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|align=center
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|Image:Broc_mixing1.jpg|
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  alt1=
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  |link1=
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|Fig. 1a Modelled water surface elevation of storm event
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|Image:Broc_mixing3.jpg|
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  alt2=
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  |link2=
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|Fig. 1b Strong beach erosion as a result of storm event
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|Image:Broc_mixing2.jpg|
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  alt3=
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  |link3=
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|Fig. 1c Quantitative description of macrovortices
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|Image:Broc_mixing4.jpg|
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  alt4=
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  |link4=
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|Fig. 1d Transport of passive tracers, as a result of macrovortices
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}}
  
{| align="center" style="width:100%; height:200px"
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Brocchini et al. (2004<ref name="Brocchini.">Brocchini M., Kennedy A. B., Soldini L. and Mancinelli A. (2004). Topographically controlled, breaking-wave-induced macrovortices. Part 1. Widely separated breakwaters. ''J. Fluid Mech.'' '''507''' 289–307.</ref>) proposed an analytical approach for vorticity generation mechanisms induced by isolated topographic features and the related general hydrodynamic behaviour, with particular attention to vortex trajectories and shedding periods (see figure 1). Subsequently Kennedy et al. (2006<ref name="Kennedy">Kennedy A., Brocchini M., Soldini L. and Gutierrez E. (2006). Topographically-controlled, breaking wave-induced macrovortices. Part 2. Changing geometries. ''J. Fluid Mech.'' '''559''' 57–80.</ref>) analysed the transition of startup macrovortices from isolated topographic features to nearby obstacles ([[rip current]] topographies, see figure 1) using computations and laboratory experiments. Both studies provide insight into the fundamental deterministic features of macrovortex evolution. The series of studies on shallow-water mixing is completed by a third study by Piattella et al. (2006<ref name="Piattella">Piattella A., Brocchini M. and Mancinelli A. (2006). Topographically-controlled, breaking wave-induced macrovortices. Part 3. The mixing features. ''J. Fluid Mech.'' '''559''' 81–106.</ref>) which characterizes the mixing features of macrovortices in terms of the statistical properties of the flow they induce, in conjunction with waves, in the nearshore region. The analysis gives both important theoretical results on the mixing spatial patterns and temporal regimes and practical evaluations of eddy diffusivities to be used in Fickian-type closures. Convection-diffusion equations for scalars all need turbulent diffusivities, generally known through a constitutive relationship of Fickian-type. Such a closure is largely dominated by the presence of large-scale coherent features like macrovortices and is typical of the flow conditions at hand. Examples of closures for coastal flows can be found in Inman et al. (1971<ref name="Inman">Inman D.L., Tait R.J. and Nordstrom C.E. (1971). Mixing in the surf zone. ''J. Geophys. Res. – Oceans'' '''76''' 3493–3514.</ref>), Larson & Kraus (1991<ref name="Larson">Larson M. and Kraus N. C. (1991). Numerical model of longshore current for bar and trough beaches. ''J. Waterway, Port, Coast., Ocean Engng '''''117''' 326–347.</ref>) and in Takewaka et al. (2003<ref name="Takewaka">Takewaka S., Misaki S. and Nakamura T. (2003). Dye diffusion experiment in a longshore current field. ''Coast. Engng. J.'' '''45''', 471–487.</ref>).
 
 
|- align="center"
 
 
 
| [[Image:Broc_mixing1.jpg]]
 
 
 
| [[Image:Broc_mixing2.jpg]]
 
 
 
|- align="center"
 
 
 
| [[Image:Broc_mixing3.jpg]]
 
 
 
| [[Image:Broc_mixing4.jpg]]
 
 
 
|+ ''Figure 1 - Illustration of the influence of macrovortices in the nearshore. The top-left panel shows the modelled water surface elevation of the storm event which led to the strong beach erosion of the bottom-left panel. The top-right panel gives a quantitative description of the macrovortices forcing the transport of passive tracers of the bottom-right panel.''
 
 
 
|}
 
  
Very recently Brocchini et al. (2004) proposed an analytical approach for vorticity generation mechanisms induced by isolated topographic features and the related general hydrodynamic behaviour, with particular attention to vortex trajectories and shedding periods (see also figure 1). Subsequently Kennedy et al. (2006) analysed the transition of startup macrovortices from isolated topographic features to nearby obstacles (rip current topographies, see also figure 1) using computations and laboratory experiments. Both studies provide insight into the fundamental deterministic features of macrovortex evolution. The series of studies on shallow-water mixing is completed by a third work (Piattella et al., 2006) which characterizes the mixing features of macrovortices in terms of the statistical properties of the flow they induce, in conjunction with waves, in the nearshore region. The analysis gives both important theoretical results on the mixing spatial patterns and temporal regimes and practical evaluations of eddy diffusivities to be used in Fickian-type closures. Convection-diffusion equations for scalars all need turbulent diffusivities, generally known through a constitutive relationship of Fickian-type. Such a closure is largely dominated by the presence of large-scale coherent features like macrovortices and is typical of the flow conditions at hand. Examples of closures for coastal flows can be found in Inman et al. (1971), Larson & Kraus (1991) and in Takewaka et al. (2003).
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===2D turbulence===
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The chosen approach of deriving methods from the analysis of 2D turbulence is justified by the fact that results coming from recent experimental studies of shallow-water turbulence suggest that such turbulence, generated in shallow jets <ref name="Dracos">Dracos T., Giger M. and Jirka G.H. (1992). Plane turbulent jets in a bounded fluid layer. ''J. Fluid Mech.'' '''241''' 587–614.</ref>, wakes <ref name="Chen">Chen D. and Jirka G.H. (1995). Experimental study of plane turbulent wake in a shallow water layer. ''Fluid Dyn. Res.'' '''16''' 11–41.</ref> and mixing layers <ref name="Uijttewaal">Uijttewaal W.S.J. and Booij R. (2000). Effect of shallowness on the development of free-surface mixing layers. ''Phys. Fluids'' '''12''' 392–402.</ref>, is characterized by spectral properties typical of 2D turbulence. In this respect it is also auspicable to model the transport properties of shallow-water macrovortices in analogy to those due to coherent barotropic vortices of 2D turbulence. <ref name="Provenzale">Provenzale A. (1999). Transport by coherent barotropic vortices. ''Annu. Rev. Fluid Mech.'' '''31''' 55–93.</ref>
  
The chosen approach of deriving methods from the analysis of 2D turbulence is justified by the fact that results coming from recent experimental studies of shallow-water turbulence suggest that such turbulence, generated in shallow jets (Dracos et al. 1992), wakes (Chen & Jirka 1995) and mixing layers (Uijttewaal & Booij 2000), is characterized by spectral properties typical of 2D turbulence. In this respect it is also auspicable to model the transport properties of shallow-water macrovortices in analogy to those due to coherent barotropic vortices of 2D turbulence (Provenzale 1999).
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In a 2D turbulent flow characterized by large-scale coherent structures the evolution of tracers and the flow dynamics are so intimately connected that knowledge of the former (e.g. diffusivity) may give a predictive key for the latter (e.g. energy spectrum), and vice versa. This approach, has been employed to investigate atmospheric <ref name="Richardson">Richardson L. F. (1926). Atmospheric diffusion shown on a distance neighbor graph. ''Proc. R. Soc. Lond.'' '''A110''' 709–737.</ref> <ref name="Er-El">Er-El J. and Peskin R. (1981). Relative diffusion of constant-level balloons in the Southern hemisphere. ''J. Atmos. Sci.'' '''38''' 2264–2274.</ref> and oceanic <ref name="LaCasce">LaCasce J.H. and Bower A. (2000). Relative dispersion in the subsurface North Atlantic. ''J. Mar. Res.'' '''58''' 863–894.</ref> <ref name="LaCasce.">LaCasce J.H. and Ohlmann C. (2003). Relative dispersion in the surface of the Gulf of Mexico. ''J. Mar. Res.'' '''61''' 285–312.</ref> flows and is now becoming of interest for nearshore dynamics. <ref name="Fong">Fong D.A. and Stacey M.T. (2003). Horizontal dispersion of a near-bed coastal plume. ''J. Fluid Mech.'' '''489''' 239–267.</ref> This is also connected with the recent developments made in the monitoring of coastal waters by means of video techniques.<ref name="Lippman">Lippman T.C. and Holman R.A. (1989). Quantification of sand bar morphology: a video technique based on wave dissipation. ''J. Geophys. Res. – Oceans'' '''94''' 995–1101.</ref> With such equipment floats/dye released near the shore can be monitored for times/area large enough to provide the fundamental data for any [[dispersion]] analysis. For example, the recent work of Takewaka et al. (2003<ref name="Takewaka">Takewaka S., Misaki S. and Nakamura T. (2003). Dye diffusion experiment in a longshore current field. ''Coast. Engng. J.'' '''45''' 471–487.</ref>) shows how it is possible to apply the mentioned approach to compute dispersive parameters of dye patches released near the breaking region. In this perspective, and with the aim of using information coming from prototype-scale and laboratory-scale experiments, we attempt at creating a theoretical framework useful for the interpretation of statistics of passive tracers released in coastal areas.
  
In a 2D turbulent flow characterized by large-scale coherent structures the evolution of tracers and the flow dynamics are so intimately connected that knowledge of the former (e.g. diffusivity) may give a predictive key for the latter (e.g. energy spectrum), and, obviously, viceversa. This approach, which has been usefully employed to investigate atmospheric (e.g. Richardson 1926; Er-El & Peskin 1981) and oceanic (e.g. LaCasce & Bower 2000; LaCasce & Ohlmann, 2003) flows, is now becoming of interest also for nearshore dynamics (Fong & Stacey 2003). This is also connected with the recent developments made in the monitoring of coastal waters by means of video techniques (e.g. Lippmann & Holman 1989). With such equipment floats/dye released near the shore can be monitored for times/area large enough to provide the fundamental data for any dispersion analysis. For example, the recent work of Takewaka et al. (2003) shows how it is possible to apply the mentioned approach to compute dispersive parameters of dye patches released near the breaking region. In this perspective, and with the aim of using information coming from prototype-scale and laboratory-scale experiments, we attempt at creating a theoretical framework useful for the interpretation of statistics of passive tracers released in coastal areas.
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==Conclusion==
  
Finally, inspection of ongoing research shows that promising practical results seem to come from the recent adaptation to unsteady flow conditions of techniques which make use of residence-time maps. As shown by Lipphardt et al. (2006) such adaptation leads to synoptic Lagrangian maps which provide a detailed and cheap approach for the horizontal transport of particles and the consequent residence times computation. Approaches of more basic nature are those which inspect the spatial variation of mixing through use of Direct Lyapunov Exponents (DLE). Such method has been recently used, with interesting characterizations of the flow inhomogeinities in the Norwegian Trondheim fjord, by Orre, Gjevik & LaCasce (2006). These recent studies clearly show the potentials and interest in Lagrangian methods for an increasingly detailed description of the horizontal mixing of nearshore waters and a consequent more accurate evaluation of the related transport phenomena.
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Finally, inspection of ongoing research shows that promising practical results seem to come from the recent adaptation to unsteady flow conditions of techniques which make use of residence-time maps. As shown by Lipphardt et al. (2006<ref name="Lipphardt">Lipphardt B.L. Jr., Small D., Kirwan A.D. Jr., Wiggins S., Ide K., Grosch C.E. and Paduan J.D. (2006). Synoptic Lagrangian maps: application to surface transport in Monterey Bay. ''J. Mar. Res.'' '''64''' 221–247.</ref>) such adaptation leads to synoptic Lagrangian maps which provide a detailed and cheap approach for the horizontal transport of particles and the consequent [[residence time|residence times]] computation. Approaches of a more basic nature are those which inspect the spatial variation of mixing through the use of Direct Lyapunov Exponents (DLE). Such method have been recently used, with interesting characterizations of the flow inhomogeinities in the Norwegian Trondheim fjord, by Orre, Gjevik & LaCasce (2006<ref name="Orre">Orre S., Gjevik B. and LaCasce J.H. (2006). Characterization of chaotic dispersion in a coastal tidal model. ''Cont. Shelf Res.'' '''26''' 1360–1374.</ref>). These recent studies clearly show the potentials and interest in Lagrangian methods for an increasingly detailed description of the horizontal mixing of nearshore waters and consequently a more accurate evaluation of the related transport phenomena.
  
 
==References==
 
==References==
Bloom, N.S., Moretto, L.S. Scopece, P. & Ugo. P. (2004). Seasonal cycling of mercury and monomethyl mercury in the Venice Lagoon (Italy). ''Mar. Chem.'' '''91''', 85–99.
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<references/>
 
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Brocchini, M., Kennedy, A. B., Soldini, L. & Mancinelli, A. (2004). Topographically controlled, breaking-wave-induced macrovortices. Part 1. Widely separated breakwaters. ''J. Fluid Mech.'' '''507''', 289–307.
+
==See also==
 
 
Brocchini, M., Mancinelli, A., Soldini, L. & Bernetti, R. (2002). Structure-generated macrovortices and their evolution in very shallow depths. ''Proc. 28th Intl Conf. Coast. Engng'' '''1''', 772–783.
 
 
 
Caldeira, R.M.A., Groom, S., Miller, P., Pilgrim, D. & Nezlin, N.P. (2002). Sea-surface signatures of the island mass effect phenomena around Madeira Island, Northeast Atlantic. ''Remote Sens. Envir.'' '''80''', 336–360.
 
 
 
Chen, D. & Jirka, G.H. (1995). Experimental study of plane turbulent wake in a shallow water layer. ''Fluid Dyn. Res.'' '''16''', 11–41.
 
 
 
Cowen, R. K., Kamazima Lwiza, M.M., Sponaugle, S., Parisa C.B. & Olson, D.B. (2000). Connectivity of Marine Populations: Open or Closed? ''Science'' '''287''', 857–859.
 
 
 
Dracos, T., Giger, M. & Jirka, G.H. (1992). Plane turbulent jets in a bounded fluid layer. ''J. Fluid Mech.'' '''241''', 587–614.
 
 
 
Er-El, J. & Peskin, R. (1981). Relative diffusion of constant-level balloons in the Southern hemisphere. ''J. Atmos. Sci.'' '''38''', 2264–2274.
 
 
 
Fenner, P. (1999). Prevention of drowning: visual scanning and attention span in lifeguards. Reply to a letter. ''J. Occupat. Health and Safety-Australia and New Zealand'' '''15''', 209–210.
 
 
 
Fong, D.A. & Stacey, M.T. (2003). Horizontal dispersion of a near-bed coastal plume. ''J. Fluid Mech.'' '''489''', 239–267.
 
 
 
Förstner, U. (1987). Sediment-associated contaminants - an overview of scientific bases for developing remedial options. ''Hydrobiol.'' '''149(1)''', 221–246.
 
 
 
Inman, D.L., Tait, R.J. & Nordstrom, C.E. (1971). Mixing in the surf zone. ''J. Geophys. Res. – Oceans'' '''76''', 3493–3514.
 
 
 
Jirka, G.H. (2001). Large scale flow structures and mixing processes in shallow flows. ''J. Hydr. Res.'', '''39(6)''', 567–573.
 
 
 
Jirka, G.H. & Uijttewaal, W. (Ed.s) (2004). ''Shallow Flows''. A.A.Balkema Publishers, Rotterdam.
 
 
 
Kennedy, A., Brocchini, M., Soldini, L. & Gutierrez, E. (2006). Topographically-controlled, breaking wave-induced macrovortices. Part 2. Changing geometries. ''J. Fluid Mech.'' '''559''', 57–80.
 
LaCasce, J.H. & Bower, A. (2000). Relative dispersion in the subsurface North Atlantic. ''J. Mar. Res.'' '''58''', 863–894.
 
 
 
LaCasce, J.H. & Ohlmann, C. (2003). Relative dispersion in the surface of the Gulf of Mexico. ''J. Mar. Res.'' '''61''', 285–312.
 
 
 
Larson, M. & Kraus, N. C. (1991). Numerical model of longshore current for bar and trough beaches. ''J. Waterway, Port, Coast., Ocean Engng '''''117''', 326–347.
 
 
 
Lekien, F., Coulliette, C., Mariano, A.J., Ryan, E.H., Shay, L.K., Haller, G. & Marsden, J.E. (2005). Pollution release tied to invariant manifolds: a case study for the coast of Florida. ''Physica D'' '''210(1–2)''', 1–20.
 
 
 
Lippman, T.C. & Holman, R.A. (1989). Quantification of sand bar morphology: a video technique based on wave dissipation. ''J. Geophys. Res. – Oceans'' '''94''', 995–1101.
 
 
 
Lipphardt, B.L. Jr., Small, D., Kirwan, A.D. Jr., Wiggins, S., Ide, K., Grosch, C.E. & Paduan, J.D. (2006). Synoptic Lagrangian maps: application to surface transport in Monterey Bay. ''J. Mar. Res.'' '''64''', 221–247.
 
 
 
Lushine, J.B. (1991). A study of rip current drownings and related weather factors. ''Natl. Wea. Dig.'', '''16''', 13–16.
 
 
 
Martin, A.P. (2003). Phytoplankton patchiness: the role of lateral stirring and mixing. ''Progr. Ocean.'' '''57''', 125–174.
 
  
 
McGillicuddy, Jr., D.J., Robinson, A.R., Siegel, D.A., Jannasch, H.W., Johnson, R., Dickey, T.D. McNeil, J., Michaels A.F. & Knap, A.H. (1998). Influence of mesoscale eddies on new production in the Sargasso Sea. ''Nature'' '''394''', 263–265.
 
McGillicuddy, Jr., D.J., Robinson, A.R., Siegel, D.A., Jannasch, H.W., Johnson, R., Dickey, T.D. McNeil, J., Michaels A.F. & Knap, A.H. (1998). Influence of mesoscale eddies on new production in the Sargasso Sea. ''Nature'' '''394''', 263–265.
  
Oltman-Shay, J., Howd, P. A. & Berkemeier, W.A. (1989). Shear instabilities of the mean longshore current: field observations. ''J. Geophys. Res. – Ocean'' '''94''', 18031–18042.
 
 
Orre, S., Gjevik., B. & LaCasce J.H. (2006). Characterization of chaotic dispersion in a coastal tidal model. ''Cont. Shelf Res.'' '''26''', 1360–1374.
 
 
Peregrine, D.H. (1998). Surf zone currents. ''Theoret. Comput. Fluid Dyn.'' '''10''', 295–309.
 
 
Piattella, A., Brocchini, M. & Mancinelli, A. (2006). Topographically-controlled, breaking wave-induced macrovortices. Part 3. The mixing features. ''J. Fluid Mech.'' '''559''', 81–106.
 
 
Provenzale, A. (1999). Transport by coherent barotropic vortices. ''Annu. Rev. Fluid Mech.'' '''31''', 55–93.
 
 
Richardson, L. F. (1926). Atmospheric diffusion shown on a distance neighbor graph. ''Proc. R. Soc. Lond.'' '''A110''', 709–737.
 
  
Siegel, D.A., Kinlan, B.P., Gaylord, B. & Gaines, S.D. (2003). Lagrangian descriptions of marine larval dispersion. ''Mar. Ecol. Progr. Ser.'' '''260''', 83–96.
 
  
Steijn, R., Roelvink, D., Rakhorst, D., Ribberink, J. & van Overeem, J. (1998). North Coast of Texel: a comparison between reality and prediction. ''Proc. 26th Intl Conf. Coast. Engng.'' '''2''', 2281–2293.
+
{{author
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|AuthorID=12946
 +
|AuthorFullName=Maurizio Brocchini
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|AuthorName=MaurizioBrocchini}}
  
Takewaka, S., Misaki, S. & Nakamura, T. (2003). Dye diffusion experiment in a longshore current field. ''Coast. Engng. J.'' '''45''', 471–487.
 
  
Uijttewaal, W.S.J. & Booij, R. (2000). Effect of shallowness on the development of free-surface mixing layers. ''Phys. Fluids'' '''12''', 392–402.
 
  
Williamson, R.B. & Morrisey, D.J. (2000). Stormwater contamination of urban estuaries. 1. Predicting the build-up of heavy metals in sediments. ''Estuaries'' '''23(1)''', 56–66.
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[[Category:Theme 4]]
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[[Category:Coastal and marine pollution]]
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[[Category:Hydrological processes and water]]
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[[Category:Coastal habitats and ecosystems in transitional waters]]
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[[Category:Techniques and methods in coastal management]]

Revision as of 15:05, 19 March 2013

The mixing-induced transport that occurs in nearshore waters is a fundamental mechanism for all physical/biological/chemical phenomena that occur in the marine environment. The transport and dispersion of pollutants, nutrients and tracers in mixed nearshore water can have direct and indirect consequences for the marine ecosystems.

Introduction

The release of pollutants from coastal and atmospheric sources heavily influences our lives in many different ways, from direct contamination of edible organisms to more indirect processes of impact and endangerment of the nearshore ecosystems. Such influences are felt not only in proximity to the source, but also in wider regions, determined primarily by the direct physical transport in marine waters. [1] High concentration zones of pollutants have been found along coastal regions far from the coastal source, and noticeable impacts have been detected even in deep sea regions.

Water mixing, sediment and pollutant transport

It is also important to acknowledge the close link between water mixing, sediment and pollutant transport. [2] For example, if the morphological evolution of the nearshore bottom is forced by wave-induced phenomena, including mixing, then the bondage between pollutants (e.g. trace metals, among which mercury, major elements, various organic and inorganic chemicals, etc.) and sediments (e.g. coastal inlets run-off of polluted sands, disposal of dredged materials, etc.) closes a circle in which a feedback is established between hydro- and morpho-dynamics, the pollutants only playing a passive role. The spatial extension of contaminated sediments and the pollutants concentration/toxicity/bioaccumulation strongly depend on the type of injection into the marine environment: while dumping sites are, usually, well protected from the hydrodynamics actions by means of a specific coverage (e.g. Ocean Dumping Act, 1972) this is not the case for the widespread run-off of water-sand mixtures from coastal inlets, the latter being largely influenced by transport phenomena. [3] [4]

Many ecological issues strongly depend on the action of large-scale eddies. For example, these are responsible for the complex but predictable patterns of dispersion of phytoplankton [5] and a number of marine species during their larval stage. Hence, the recent and growing attention to Lagrangian transport of marine species. [6] [7] It is particularly interesting that increasing acknowledgement is given of the fundamental action of complex topographic features on the flow mixing and the related transport mechanisms of organic matter. Moving fronts are found to transport plankton communities in the cross-shore direction and cause differentiation between coastal and oceanic communities. [8]

Rip currents

Recreational activities are also strongly influenced by water transport phenomena. More specifically swimming safety is seriously hampered by the horizontal water mixing induced by rip currents. [9] Rip currents are powerful, channelled currents of water flowing away from shore. They typically extend from the shoreline, through the surf zone, and past the line of breaking waves. Rip currents can occur at any beach with breaking waves but they become especially strong in the presence of bathymetric changes of the seabed. [10] Typically people who are wading or swimming accidentally venture into the rip currents, and are pulled out to sea. It is impossible to swim or walk against these currents (if you try, you will end up swimming or walking backwards out to deep water). The United States Lifesaving Association, one of the few with detailed and available statistics, estimates that the annual number of deaths due to rip currents on U.S beaches exceeds 100. Rip currents account for over 80% of rescues performed by surf beach lifeguards (http://www.srh.noaa.gov/ripcurrents/index.shtml). In Australia, 35% of rescues and 18.5% of resuscitation cases, over a ten year period, from surf beaches were due to rip currents. [11] Rip currents are also recognised as a hazard for European beaches. Particularly where submerged breakwaters have been put in place in order to protect against erosion, but in fact are increasing the potential for localised rip currents(e.g. EU DELOS Project, EVK-2000-22038). Coastal engineers recognize rip currents as an important element in the nearshore circulation balance, particularly during storms. Nevertheless, little information is as yet available that describes where and when these currents occur. Hence, not only fundamental insight is needed into the conditions for the generation and development of rip currents and methodology for the related risk assessment, but strategies are also required for minimizing the hazard-related socio-economical costs.

Modelling the physics of nearshore water mixing

The mixing features of oceanic flows are well documented and fairly well understood be they related to the motion of abyssal streams (e.g. the Ocean Conveyor Belt) or to the horizontal circulation at the both global and meso-scale level (e.g. oceanic gyres and boundary currents). For historical reasons less effort has been put in the understanding/modelling of the mixing of the continental shelf shallow waters. However, this is the complex environment which provides a boundary between the inland, where most of the anthropogenic activities occur, and the deep water flow forcing. The most active agents of horizontal mixing are the large-scale eddies of the nearshore turbulence also known as “macrovortices”.

The importance for shallow flows of horizontal, large-scale eddies (macrovortices hereinafter) has been widely reported for coastal flows. [12] [13] [14] Large-scale, horizontal mixing of coastal flows is mostly promoted by macrovortices which are generated because of a spatially-non-uniform breaking of the incoming waves. [13] [15] Although such differential breaking may be induced by various reasons (irregularity of the incoming field, wave-wave interaction, etc.) the major cause of persistent breaking unevenness is due to topography. This is often characterized by longshore, isolated (natural bumps or manmade submerged breakwaters) or almost-continuous features (bars or arrays of submerged breakwaters) over which uniform wave fronts break with large lateral gradients. Hence, macrovortices can alter both the hydrodynamics and the morphodynamics. [16] [15] A recent classification of vortex generation in shallow coastal environments distinguished three types: [17] [18]

  1. Topographic forcing (from islands, headlands, jetties or groynes),
  2. Transverse shear instabilities (jet flows from lagoons or rivers, mixing layers, wakes), and
  3. Secondary instabilities of the base flow (internal vortex interactions).
Fig. 1a Modelled water surface elevation of storm event  
Fig. 1b Strong beach erosion as a result of storm event  
Fig. 1c Quantitative description of macrovortices  
Fig. 1d Transport of passive tracers, as a result of macrovortices  

Brocchini et al. (2004[15]) proposed an analytical approach for vorticity generation mechanisms induced by isolated topographic features and the related general hydrodynamic behaviour, with particular attention to vortex trajectories and shedding periods (see figure 1). Subsequently Kennedy et al. (2006[10]) analysed the transition of startup macrovortices from isolated topographic features to nearby obstacles (rip current topographies, see figure 1) using computations and laboratory experiments. Both studies provide insight into the fundamental deterministic features of macrovortex evolution. The series of studies on shallow-water mixing is completed by a third study by Piattella et al. (2006[19]) which characterizes the mixing features of macrovortices in terms of the statistical properties of the flow they induce, in conjunction with waves, in the nearshore region. The analysis gives both important theoretical results on the mixing spatial patterns and temporal regimes and practical evaluations of eddy diffusivities to be used in Fickian-type closures. Convection-diffusion equations for scalars all need turbulent diffusivities, generally known through a constitutive relationship of Fickian-type. Such a closure is largely dominated by the presence of large-scale coherent features like macrovortices and is typical of the flow conditions at hand. Examples of closures for coastal flows can be found in Inman et al. (1971[20]), Larson & Kraus (1991[21]) and in Takewaka et al. (2003[22]).

2D turbulence

The chosen approach of deriving methods from the analysis of 2D turbulence is justified by the fact that results coming from recent experimental studies of shallow-water turbulence suggest that such turbulence, generated in shallow jets [23], wakes [24] and mixing layers [25], is characterized by spectral properties typical of 2D turbulence. In this respect it is also auspicable to model the transport properties of shallow-water macrovortices in analogy to those due to coherent barotropic vortices of 2D turbulence. [26]

In a 2D turbulent flow characterized by large-scale coherent structures the evolution of tracers and the flow dynamics are so intimately connected that knowledge of the former (e.g. diffusivity) may give a predictive key for the latter (e.g. energy spectrum), and vice versa. This approach, has been employed to investigate atmospheric [27] [28] and oceanic [29] [30] flows and is now becoming of interest for nearshore dynamics. [31] This is also connected with the recent developments made in the monitoring of coastal waters by means of video techniques.[32] With such equipment floats/dye released near the shore can be monitored for times/area large enough to provide the fundamental data for any dispersion analysis. For example, the recent work of Takewaka et al. (2003[22]) shows how it is possible to apply the mentioned approach to compute dispersive parameters of dye patches released near the breaking region. In this perspective, and with the aim of using information coming from prototype-scale and laboratory-scale experiments, we attempt at creating a theoretical framework useful for the interpretation of statistics of passive tracers released in coastal areas.

Conclusion

Finally, inspection of ongoing research shows that promising practical results seem to come from the recent adaptation to unsteady flow conditions of techniques which make use of residence-time maps. As shown by Lipphardt et al. (2006[33]) such adaptation leads to synoptic Lagrangian maps which provide a detailed and cheap approach for the horizontal transport of particles and the consequent residence times computation. Approaches of a more basic nature are those which inspect the spatial variation of mixing through the use of Direct Lyapunov Exponents (DLE). Such method have been recently used, with interesting characterizations of the flow inhomogeinities in the Norwegian Trondheim fjord, by Orre, Gjevik & LaCasce (2006[34]). These recent studies clearly show the potentials and interest in Lagrangian methods for an increasingly detailed description of the horizontal mixing of nearshore waters and consequently a more accurate evaluation of the related transport phenomena.

References

  1. Lekien F., Coulliette C., Mariano A.J., Ryan E.H., Shay L.K., Haller G. & Marsden J.E. (2005). Pollution release tied to invariant manifolds: a case study for the coast of Florida. Physica D 210 (1–2) 1–20.
  2. Förstner U. (1987). Sediment-associated contaminants - an overview of scientific bases for developing remedial options. Hydrobiol. 149 (1) 221–246.
  3. Williamson R.B. and Morrisey D.J. (2000). Stormwater contamination of urban estuaries. 1. Predicting the build-up of heavy metals in sediments. Estuaries 23(1) 56–66.
  4. Bloom, N.S., Moretto, L.S. Scopece P. and Ugo P. (2004). Seasonal cycling of mercury and monomethyl mercury in the Venice Lagoon (Italy). Mar. Chem. 91 85–99.
  5. Martin A.P. (2003). Phytoplankton patchiness: the role of lateral stirring and mixing. Progr. Ocean. 57 125–174.
  6. Cowen R. K., Kamazima Lwiza M.M., Sponaugle S., Parisa C.B. and Olson D.B. (2000). Connectivity of Marine Populations: Open or Closed? Science 287 857–859.
  7. Siegel D.A., Kinlan B.P., Gaylord B. and Gaines S.D. (2003). Lagrangian descriptions of marine larval dispersion. Mar. Ecol. Progr. Ser. 260 83–96.
  8. Caldeira R.M.A., Groom S., Miller, P., Pilgrim D. and Nezlin N.P. (2002). Sea-surface signatures of the island mass effect phenomena around Madeira Island, Northeast Atlantic. Remote Sens. Envir. 80 336–360.
  9. Lushine J.B. (1991). A study of rip current drownings and related weather factors. Natl. Wea. Dig., 16 13–16.
  10. 10.0 10.1 Kennedy A., Brocchini M., Soldini L. and Gutierrez E. (2006). Topographically-controlled, breaking wave-induced macrovortices. Part 2. Changing geometries. J. Fluid Mech. 559 57–80.
  11. Fenner P. (1999). Prevention of drowning: visual scanning and attention span in lifeguards. Reply to a letter. J. Occupat. Health and Safety-Australia and New Zealand 15 209–210.
  12. Oltman-Shay J., Howd P. A. and Berkemeier W.A. (1989). Shear instabilities of the mean longshore current: field observations. J. Geophys. Res. – Ocean 94 18031–18042.
  13. 13.0 13.1 Peregrine D.H. (1998). Surf zone currents. Theoret. Comput. Fluid Dyn. 10 295–309.
  14. Brocchini M., Mancinelli A., Soldini L. and Bernetti R. (2002). Structure-generated macrovortices and their evolution in very shallow depths. Proc. 28th Intl Conf. Coast. Engng 1 772–783.
  15. 15.0 15.1 15.2 Brocchini M., Kennedy A. B., Soldini L. and Mancinelli A. (2004). Topographically controlled, breaking-wave-induced macrovortices. Part 1. Widely separated breakwaters. J. Fluid Mech. 507 289–307.
  16. Steijn R., Roelvink D., Rakhorst D., Ribberink J. and van Overeem J. (1998). North Coast of Texel: a comparison between reality and prediction. Proc. 26th Intl Conf. Coast. Engng. 2 2281–2293.
  17. Jirka G.H. (2001). Large scale flow structures and mixing processes in shallow flows. J. Hydr. Res., 39(6) 567–573.
  18. Jirka G.H. and Uijttewaal W. (Ed.s) (2004). Shallow Flows. A.A.Balkema Publishers, Rotterdam.
  19. Piattella A., Brocchini M. and Mancinelli A. (2006). Topographically-controlled, breaking wave-induced macrovortices. Part 3. The mixing features. J. Fluid Mech. 559 81–106.
  20. Inman D.L., Tait R.J. and Nordstrom C.E. (1971). Mixing in the surf zone. J. Geophys. Res. – Oceans 76 3493–3514.
  21. Larson M. and Kraus N. C. (1991). Numerical model of longshore current for bar and trough beaches. J. Waterway, Port, Coast., Ocean Engng 117 326–347.
  22. 22.0 22.1 Takewaka S., Misaki S. and Nakamura T. (2003). Dye diffusion experiment in a longshore current field. Coast. Engng. J. 45, 471–487. Cite error: Invalid <ref> tag; name "Takewaka" defined multiple times with different content
  23. Dracos T., Giger M. and Jirka G.H. (1992). Plane turbulent jets in a bounded fluid layer. J. Fluid Mech. 241 587–614.
  24. Chen D. and Jirka G.H. (1995). Experimental study of plane turbulent wake in a shallow water layer. Fluid Dyn. Res. 16 11–41.
  25. Uijttewaal W.S.J. and Booij R. (2000). Effect of shallowness on the development of free-surface mixing layers. Phys. Fluids 12 392–402.
  26. Provenzale A. (1999). Transport by coherent barotropic vortices. Annu. Rev. Fluid Mech. 31 55–93.
  27. Richardson L. F. (1926). Atmospheric diffusion shown on a distance neighbor graph. Proc. R. Soc. Lond. A110 709–737.
  28. Er-El J. and Peskin R. (1981). Relative diffusion of constant-level balloons in the Southern hemisphere. J. Atmos. Sci. 38 2264–2274.
  29. LaCasce J.H. and Bower A. (2000). Relative dispersion in the subsurface North Atlantic. J. Mar. Res. 58 863–894.
  30. LaCasce J.H. and Ohlmann C. (2003). Relative dispersion in the surface of the Gulf of Mexico. J. Mar. Res. 61 285–312.
  31. Fong D.A. and Stacey M.T. (2003). Horizontal dispersion of a near-bed coastal plume. J. Fluid Mech. 489 239–267.
  32. Lippman T.C. and Holman R.A. (1989). Quantification of sand bar morphology: a video technique based on wave dissipation. J. Geophys. Res. – Oceans 94 995–1101.
  33. Lipphardt B.L. Jr., Small D., Kirwan A.D. Jr., Wiggins S., Ide K., Grosch C.E. and Paduan J.D. (2006). Synoptic Lagrangian maps: application to surface transport in Monterey Bay. J. Mar. Res. 64 221–247.
  34. Orre S., Gjevik B. and LaCasce J.H. (2006). Characterization of chaotic dispersion in a coastal tidal model. Cont. Shelf Res. 26 1360–1374.

See also

McGillicuddy, Jr., D.J., Robinson, A.R., Siegel, D.A., Jannasch, H.W., Johnson, R., Dickey, T.D. McNeil, J., Michaels A.F. & Knap, A.H. (1998). Influence of mesoscale eddies on new production in the Sargasso Sea. Nature 394, 263–265.


The main author of this article is Maurizio Brocchini
Please note that others may also have edited the contents of this article.

Citation: Maurizio Brocchini (2013): Transport and dispersion of pollutants, nutrients, tracers in mixed nearshore water. Available from http://www.coastalwiki.org/wiki/Transport_and_dispersion_of_pollutants,_nutrients,_tracers_in_mixed_nearshore_water [accessed on 28-03-2024]