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

Abstract

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, ReL, based on the Obukhov turbulent length‐scale and the friction velocity, such that the transition from turbulent to laminar regime occurs at ReL ≈ 102. 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, ReL = 102, 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.

Stably stratified airflow over a waved water surface. Part 1: Stationary turbulence regime

“…We propose for these wave‐induced motions observed near the waved surface the name ‘pre‐turbulent motions’. This regime is only briefly discussed in the present article and investigated in detail in our follow‐up article (Druzhinin et al , , Part 2).…”

“…Figure 3). We consider this newly recognised regime in more detail in the follow-up article (Druzhinin et al, 2015).…”

“…The intensity of such fluctuations monotonically decreases with increasing bulk Richardson number. This supercritically stratified flow regime is studied in details in our follow‐up study (Druzhinin et al (), Part 2). Below we consider only stationary turbulent flow regimes.…”

“…Sullivan and McWilliams, ). Degeneration of turbulence at larger Ri and the problem of transition between turbulent and laminar regimes is considered in our follow‐up study (Druzhinin et al , , Part 2).…”

Research in dynamic meteorology in Russia in 2015–2018

“…В то же время вертикальные профили средней скорости и температуры сохраняют автомодельную форму, предсказанную теорией Монина-Обухова, независимо от наклона волны. В [150] выполнено DNS устойчиво стратифицированных потоков над плоской и волнистой поверхностями для широкого диапазона чисел Рейнольдса Re L и Ричардсона и обнаружено, что один и тот же порог, Re L = 10 2 , сохраняется на обеих поверхностях. Однако, когда наклон поверхностной волны достаточно крутой, сверхкритическое стратифицированное течение включает вызванные волной «пред-турбулентные» структуры потока, наиболее выраженные вблизи волнистой поверхности воды.…”