Mean flow generation by three-dimensional non-linear internal wave beams

TL;DR

This paper develops analytic solutions for 3D internal wave beams to understand how they generate mean flows, revealing a new inviscid mechanism near oscillating boundaries supported by experimental data.

Contribution

It introduces a novel analytic framework for 3D internal wave beams, including an inviscid mean flow generation mechanism near oscillating walls, validated by laboratory experiments.

Findings

Analytic solutions accurately describe wave beam behavior.

Inviscid mean flow generation is significant near oscillating boundaries.

Theoretical results align with experimental observations.

Abstract

We study the generation of strong mean flow by weakly non-linear internal wave beams. With a perturbational expansion, we construct analytic solutions for 3D internal wave beams, exact up to first order accuracy in the viscosity parameter. We specifically focus on the subtleties of wave beam generation by oscillating boundaries, such as wave makers in laboratory set-ups. The exact solutions to the linearized equations allow us to derive an analytic expression for the mean vertical vorticity production term, which induces a horizontal mean flow. Whereas mean flow generation associated with viscous beam attenuation - known as streaming - has been described before, we are the first to also include a peculiar inviscid mean flow generation in the vicinity of the oscillating wall, resulting from line vortices at the lateral edges of the oscillating boundary. Our theoretical expression for the mean vertical vorticity production is in good agreement with earlier laboratory experiments, for which the previously unrecognized inviscid mean flow generation mechanism turns out to be significant.