Long-time dynamics of internal wave streaming

• Published in: Journal of fluid mechanics Vol. 907
• Main Authors: Jamin, Timothée, Kataoka, Takeshi, Dauxois, Thierry, Akylas, T. R.
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 25.01.2021
• Subjects: Advection; Computational fluid dynamics; Evolution; Experiments; Flow; Gravity waves; Horizontal advection; Horizontal orientation; Internal waves; JFM Papers; Lasers; Mathematical models; Navier-Stokes equations; Potential vorticity; Quasi-steady states; Reynolds number; Saturation; Streaming; Three dimensional flow; Vorticity; Wave propagation; stratified flows; internal waves
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2020.806

The mean flow induced by a three-dimensional propagating internal gravity wave beam in a uniformly stratified fluid is studied experimentally and theoretically. Previous related work concentrated on the early stage of mean-flow generation, dominated by the phenomenon of streaming – a horizontal mean flow that grows linearly in time – due to resonant production of mean potential vorticity in the vicinity of the beam. The focus here, by contrast, is on the long-time mean-flow evolution. Experimental observations in a stratified fluid tank for times up to $t=120T_0$, where $T_0$ is the beam period, reveal that the induced mean flow undergoes three distinct stages: (i) resonant growth of streaming in the beam vicinity; (ii) saturation of streaming and onset of horizontal advection; and (iii) establishment of a quasi-steady state where the mean flow is highly elongated and stretches in the along-tank horizontal direction. To capture (i)–(iii), the theoretical model of Fan et al. (J. Fluid Mech., vol. 838, 2018, R1) is extended by accounting for the effects of horizontal advection and viscous diffusion of mean potential vorticity. The predictions of the proposed model, over the entire mean-flow evolution, are in excellent agreement with the experimental observations as well as numerical simulations based on the full Navier–Stokes equations.