Mathematical Modeling of Large-Scale Turbulent Structures in Coastal Systems Based on the LES Approach

A detailed three-dimensional simulation of large vortices (LES) was performed on a parallel cluster. It provided useful 3D data on currents at various bottom geometries, in the cases of Shallow Mixing Layer (SML) and Shallow Lateral Expansion (SLE). The basic LES approach is derived directly from the Navier-Stokes equations. The paper studies the evolution of large-scale horizontal turbulence structures in shallow-water systems. We investigate how the three-dimensionality of the flow affects the quasi-two-dimensional turbulence pattern of the SLE mixing layer using numerical methods. The development of the SLE mixing layer, including the dynamics of large-scale quasi-2D coherent structures (2DCS) and their interaction with steady-state cycles has a quasi-two-dimensional character, but the influence of the third dimension is obvious. Consequently, the dynamics of three-dimensional turbulence should be taken into account in the numerical study of quasi-2D turbulence. In both cases, sequences of large-scale vortex structures are induced by a lateral shift along the mixing layer, which is caused by a difference in velocities upstream. In both cases, the transverse shift decreases with increasing distance downstream, while the momentum downstream is transferred from the high velocity side to the low velocity side due to the momentum advection of large-scale quasi-2D coherent structures. The difference in the configuration of the side walls affects the overall flow pattern.