Non-hydrostatic modeling of exchange flows across complex geometries

Flows between ocean and marginal sea basins are often connected by narrow channels and shallow sills. In this study, we address the effect of lateral and vertical geometric constrictions on mixing and hydraulic control. We conduct a set of numerical experiments of the lock-exchange problem in the presence of lateral and vertical contractions. Large eddy simulations (LES) are carried out using the high-order non-hydrostatic spectral element model Nek5000. A spanwise-averaged 2D non-hydrostatic model, denoted SAM, is also employed. Comparison between 2D and 3D models are conducted on the basis of the shape of the density interface and the time evolution of the background potential energy that quantifies the cumulative effects of the stratified mixing in the system. LES indicates that an S-shaped channel induces the highest amount of mixing possibly due to the additional shears caused by the centrifugal force. Vertical and horizontal constrictions enhance mixing by the trapping and breaking of the internal waves in between the obstacles. On the other hand, vertical and horizontal constrictions overlapping with each other restrain the rate of the exchange flow, reduce vertical shears and the mixing. The lowest mixing is encountered in a {n-ary logical or}-shaped channel. It is also found that SAM appears to be accurate in identifying the hydraulic control points due to both horizontal and vertical constrictions. A good agreement is found between SAM and inviscid two-layer theory regarding the steady-state location of the density interface. However SAM overestimates mixing with respect to LES since overturning eddies tend to merge in 2D, while they break down into smaller scales in 3D. SAM is then further tested a realistic application to model the flow in the Bosphorus Strait. Here, the main challenges of using SAM revolved around a non-trivial reduction of 3D geometry to a 2D mapping function, and excessive diffusion with simple closures. The realism of SAM improves significantly using a comprehensive turbulence closure of Very Large Eddy Simulation, VLES. In conclusion, exchange flows in narrow straits pose significant computational challenges due to the details of domain geometry and their impact on mixing. SAM with the VLES turbulence closure appears to be an attractive modeling tool for a first-order assessment of dynamical problems involving mixing and hydraulic effects.