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Turbulence structures in shallow free-surface mixing layers
Tukker, J. (1997). Turbulence structures in shallow free-surface mixing layers. Communications on Hydraulic and Geotechnical Engineering, 97-2. Delft University of Technology. Faculty of Civil Engineering: Delft. xv, 118 pp.
Part of: Communications on Hydraulic and Geotechnical Engineering. Delft University of Technology. Department of Civil Engineering: Delft. ISSN 0169-6548, more

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Keywords
    Shallow water; Structures; Surface mixed layer; Turbulence

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  • Tukker, J.

Abstract
    In shallow water the transverse spreading of a turbulent mixing layer is suppressed downstream due to the shallowness of the flow. This is accompanied by a suppression of transverse mixing and turbulent transport of momentum and matter. The same phenomenon was observed in wake flows behind islands in shallow seas. The main purpose of this study is to gain insight into the mechanisms which are responsible for the suppression of the spreading rate of a mixing layer in shallow water.
    The highly anisotropic turbulence in a shallow mixing layer is characterised by the presence of two separate turbulent length scales. The large length scale is related to largescale turbulence structures caused by the transverse shear, and is of order of magnitude of the width of the mixing layer. The small length scale is related to the bottom-induced turbulence, and is of order of magnitude of the water depth. A characteristic property of a shallow mixing layer is that the layer width is (much) larger than the water depth. Experimental research was executed in a wide glass-bottom shallow-water channel. In the channel a mixing layer develops behind a splitter plate between a fast and a slow stream. The flow can be considered as a model of a river confluence. Far downstream from the splitter plate the width of the mixing layer becomes (much) larger than the water depth. The downstream evolution of the mean flow was measured in four flow cases with different inlet conditions. Detailed turbulence measurements were executed in a particular flow case by means of a 3D-Laser Doppler Anemometry system.
    The experiments show that the spreading rate of the mixing layer is suppressed due to two causes. The first cause is the downstream decrease of the velocity difference across the mixing layer, due to the influence of the bottom friction on the non-uniform mean flow. The second cause is the influence of the bottom friction on the horizontal large-scale turbulence structures generated by the transverse shear, resulting in a suppression of the growth rate of these structures.
    A 1D model was developed based on transverse integration of shallow-water equations.
    This model divides a cross-section in three regions: the mixing layer, the fast stream and the slow stream. The aim of this model is to calculate the downstream evolution of the mean flow of a shallow mixing layer in a open channel. In this model the spreading of the mixing layer is evaluated with the help of a semi-empirical relation depending on the local mean flow. This relation is based on stability analysis of a shallow mixing layer, and is a function of a stability number, the so-called bed-friction number, which takes into account the stabilizing influence of the bottom friction on the large-scale turbulence. A value of the initial spreading coefficient is obtained from measured spreading rates of unconfined mixing layers (Brown and Roshko, 1974). A value of the critical bed-friction number is obtained from data measured in shallow mixing layers (Chu and Babarutsi, 1988). In view of the simplicity the model predicts well the downstream evolution of three of the four flow cases considered in this study.
    The turbulence data obtained with LDA demonstrate the co-existence of two different characteristic turbulent scales in a shallow mixing layer. The measurements dearly show that the large-scale eddies have a quasi-two-dimensional structure due to the restricted depth. The dimensions of these large-scale turbulence structures are order of magnitude of the layer width, and are larger than the water depth. Because of the presence of separate scales, the turbulent exchanges in the horizontal directions can be divided into a contribution of the large-scale turbulence structures and of the turbulence due to the bottom friction. The first contribution is related to the local velocity difference across the mixing layer, while the latter is related to the bottom shear stress in a similar way as in uniform shallow-water flows. The quasi-2D turbulence structures interact with the bottom-induced turbulence and consequently kinetic energy is transferred from large to small scales without interaction of intermediate scales. The influence of the bottom friction on the large-scale turbulence structures becomes important at the end of the middle field and in the far field of shallow mixing layers where the spreading rate is suppressed. One-dimensional power spectra of turbulence show a peak in the low-frequency part which is related to the quasi-2D structures. The frequency of the peak centre agrees well with the most-amplified disturbance frequency corresponding to Kelvin-Helmholtz-instability. The growth rate of these turbulence structures is suppressed by the bottom friction, resulting in a suppression of the spreading rate.
    A suitable numerical technique to model highly anisotropic turbulence in shallow mixing layer is Large Eddy Simulation. The presence of separate scales gives the opportunity of the application of 2D-LES with a subgrid model taking into account the mutual interactions between the quasi-2D turbulence structures and the bottom-induced turbulence.

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