Shallow mixing interfaces between parallel streams of unequal densities

Abstract

As opposed to the case of shallow mixing layers forming between parallel streams of unequal velocities and equal densities, the spatial development of the mixing interface (MI) between two parallel streams of unequal velocities and sufficiently large density contrast is controlled by the formation of a spatially developing, lock-exchange-like flow in transverse planes. Buoyancy effects are driven by the presence of a vertical density interface near the splitter plate. Eddy-resolving numerical simulations conducted in a wide and very long channel are used to investigate the mean flow structure and the effects of the lock-exchange-like flow and the associated coherent structures on mixing and the capacity of the flow to entrain sediment from the channel bed. When the two streams have unequal densities, quasi-two-dimensional Kelvin–Helmholtz (KH) vortices still form near the MI origin, but their coherence is lost over a much shorter distance compared with the case with no density contrast, and their cores are severely stretched in the transverse direction. A main cell of recirculating (cross-) flow forms in the mean flow, in between the fronts of the near-bed intrusion of heavier fluid and the free-surface intrusion of lighter fluid. The instantaneous flow fields contain streamwise-oriented vortical cells along the interface separating the regions containing heavier and lighter fluids. These vortical cells play an important role in enhancing mixing, similar to the KH billows forming in a classical lock-exchange flow. The regions of highest turbulence amplification are situated next to the boundaries of the main recirculating cell. Once the oscillating fronts of the intrusions get sufficiently close to the channel sidewalls, streamwise cells of secondary flow form near the channel boundaries. For cases with a strong density contrast, the free-surface mixing pattern is not a good indicator of mixing between the two streams. For the same flow velocities in the incoming channels, the two streams mix faster with increasing density difference between the two streams. This is because, as opposed to the KH vortices, coherent structures induced by the formation of the lock-exchange-like flow maintain their coherence and capacity to induce mixing at very large distances from the splitter plate. Meanwhile, the redistribution of the streamwise momentum leading to uniform, fully developed flow over the whole cross-section is delayed by buoyancy effects. Away from the splitter plate, the region with the highest sediment entrainment potential is situated next to the edge of the main recirculation cell on the high-speed side of the channel. For the same flow velocities in the incoming channels, the sediment entrainment capacity of the flow is much larger in the simulations conducted with density contrast between the incoming streams and peaks for the case when the faster stream contains the denser fluid.