Stably stratified air-flow over a waved water surface. Part 2: Wave-induced pre-turbulent motions

摘要

Recent experimental and direct numerical simulation (DNS) studies have discovered that stably stratified boundary-layer turbulence over a flat surface is characterized by the critical Reynolds number, Re-L, based on the Obukhov turbulent length-scale and the friction velocity, such that the transition from turbulent to laminar regime occurs at Re-L approximate to 10(2). We have performed DNS of stably stratified flows over both flat and waved surfaces for a wide range of bulk Reynolds numbers and Richardson numbers and revealed that the same threshold, Re-L = 10(2), holds true over waved surfaces. However, when the surface wave slope is sufficiently steep, the supercritically stratified flow involves wave-induced, pre-turbulent' flow patterns, most pronounced in the vicinity of the waved water surface. In the present article, we study basic properties of these motions through DNS and propose a theoretical model of their generation via secondary parametric resonance instability of two-dimensional disturbances induced in the air-flow by the surface waves.