Direct numerical simulations of turbulent flow over misaligned traveling waves

Abstract

Direct numerical simulations of turbulent flow over prescribed traveling waves in a half-channel flow setup subject to a combined streamwise and spanwise pressure gradient are performed at a friction Reynolds number of 180. The simulations undertaken in this study consider both flow-aligned (including opposing and following) and misaligned waves as we attempt to quantify the effect of wave misalignment on turbulence statistics, the pressure drag force, and the wave attenuation rate. For the simulations, we consider three characteristic wave age values corresponding to slow-, intermediate-, and fast-moving waves. Wave misalignment is taken into account by applying a spanwise pressure gradient vertical to the traveling waves, which results in a three-dimensional turbulent flow field above the moving waves. Key flow quantities such as the mean velocity, velocity variances, and momentum fluxes are found to vary with the wave parameters, confirming the findings of previous studies. In addition, our analysis shows that the mean velocity vector deviates from the applied pressure gradient with larger discrepancies being found when fast-moving waves run in an obtuse angle of 135° relative to the applied pressure gradient vector. Additionally, large deviation angles (up to 50°) between the applied pressure gradient and the shear-stress vector were found to exhibit their peak within the buffer layer in ζ+<10, whereas they rapidly reduce for ζ+>10, where ζ+ is the vertical coordinate in wall units. Finally, with the help of triple decomposition we show the dependence of the spanwise wave-coherent velocity on the dynamics of the vertical component and highlight important differences between flow-following and flow-opposing waves.