Energy redistribution dynamics in coupled Couette–Poiseuille flows using large-Eddy simulation

Abstract

The problem of turbulent Couette flow driven by a statistically steady external wind is studied in the framework of spatially filtered Navier–Stokes equations. The phenomenon of wind-driven flow of water is represented by a layer of air modeled as Poiseuille flow (air sub-domain), coupled to a layer of water modeled as Couette flow (water sub-domain). We focus on changes in the statistics in either the air or the water sub-domain, due to the coupling with the other sub-domain. We also highlight dynamic flow structures forming near the air-water interface. Simulations based on different Reynolds numbers in the air and the water sub-domains are compared to computationally less demanding simulations with equal Reynolds numbers. Results of these simulations indicate strong similarities, i.e., the flow is well approximated by simulating air and water at the same Reynolds numbers. Further analysis shows that the flow in the water domain shares important features with classical Couette flows. The horizontal turbulent mixing renders a thinner boundary layer in the water sub-domain. Moreover, an increased intermittency in the flow velocities is observed, which may be linked to so-called splat events near the air-water interface. These splats characterize the interaction of coherent structures across the interface, being stronger in the water phase. An analysis of the pressure-strain correlation near the air-water interface on the water side shows that such splats are responsible for redistributing energy from the streamwise and spanwise directions, to the vertical direction. This behavior, although qualitatively similar to wall-bounded flows, differ mainly on the fact that most of the energy drained comes from the streamwise direction: in wall-bounded the main contributor is the spanwise direction. The boundary layers near the air-water interface show inclined vortical structures. Unlike in coupled Couette–Couette flow, the peak in the Reynolds stress is displaced from the channel’s center into the buffer region of the water sub-domain.