Direct numerical simulation of turbulence in a sheared air–water flow with a deformable interface

Abstract

Direct numerical simulation has been performed to explore the turbulence near a freely deformable interface in a countercurrent air–water flow, at a shear Reynolds number $\Re_{\star}=171$. The deformations of the interface fall in the range of capillary waves of waveslope $ak=0.01$, and very small phase speed-to-friction velocity ratio, $c/u_{\star}$. The results for the gas side are compared to open-channel flow data at the same shear Reynolds number, placing emphasis upon the influence of the waves in the interfacial viscosity-affected region, and away from it in the outer core flow. Comparison shows a similarity in the distribution of the turbulence intensities near the interface, confirming that for the range of flow conditions considered, the lighter phase perceives the interface like a flexible solid surface, at least in the limit of non-breaking waves. Overall, in a time-averaged sense, the interfacial motion affects the turbulence in the near-interface region; the most pertinent effect is a general dampening of the turbulent fluctuating field which, in turn, leads to a reduction in the interfacial dissipation. Furthermore, the turbulence is found to be less anisotropic at the interface than at the wall. This is confirmed by the analysis of the pressure–rate-of-strain tensor, where the effect of interfacial motion is shown to decrease the pressure strain correlation in the direction normal to the interface and in the spanwise direction. The analysis of the turbulent kinetic energy and Reynolds stress budgets reveals that the interface deformations mainly affect the so-called boundary term involving the redistribution of energy, i.e. by the action of pressure, turbulent fluctuations and molecular viscosity, and the dissipation terms, leaving the production terms almost unchanged. The non-zero value of the turbulent kinetic energy at the interface, together with the reduced dissipation, implies that the turbulent activity persists near the interface and contributes to accelerating the turbulent transfer mechanisms. Away from the interface, the decomposition of the fluctuating velocity gradient tensor demonstrates that the fluctuating rate-of-strain and rate-of-rotation at the interface influence the flow throughout the boundary layer more vigorously. The study also reveals the streaky structure over the deformable interface to be less organized than over a rigid wall. However, the elongation of the streaks does not seem to be much affected by the interfacial motion. A simple qualitative analysis of the quasi–streamwise vortices using different eduction techniques shows that the interfacial turbulent structures do not change with a change of boundary conditions.