The reflection of internal gravity waves at sloping boundaries leads to focusing or defocusing. In closed domains, focusing typically dominates and projects the wave energy onto 'wave attractors'. For small-amplitude internal waves, the projection of energy onto higher wave numbers by geometric focusing can be balanced by viscous dissipation at high wave numbers. Contrary to what was previously suggested, viscous dissipation in interior shear layers may not be sufficient to explain the experiments on wave attractors in the classical quasi-2D trapezoidal laboratory set-ups. Applying standard boundary layer theory, we provide an elaborate description of the viscous dissipation in the interior shear layer, as well as at the rigid boundaries. Our analysis shows that even if the thin lateral Stokes boundary layers consist of no more than 1% of the wall-to-wall distance, dissipation by lateral walls dominates at intermediate wave numbers. Our extended model for the spectrum of 3D wave attractors in equilibrium closes the gap between observations and theory by Hazewinkel et al. (2008). † Email address for correspondence: f.beckebanze@uu.nl arXiv:1707.08009v1 [physics.flu-dyn]

Quantifying the physical mechanisms responsible for the transport of sediments, nutrients and pollutants in the abyssal sea is a long-standing problem, with internal waves regularly invoked as the relevant mechanism for particle advection near the sea bottom. This study focuses on internalwave induced particle transport in the vicinity of (almost) vertical walls. We report a series of laboratory experiments revealing that particles sinking slowly through a monochromatic internal wave beam experience significant horizontal advection. Extending the theoretical analysis by Beckebanze et al. (2018a), we attribute the observed particle advection to a peculiar and previously unrecognized streaming mechanism originating at the lateral walls. This vertical boundarylayer streaming mechanism is most efficient for strongly inclined wave beams, when vertical and horizontal velocity components are of comparable magnitude. We find good agreement between our theoretical prediction and experimental results. †

We study the generation of resonantly growing 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. † Email address for correspondence: f.beckebanze@uu.nl arXiv:1805.12356v2 [physics.flu-dyn]

The Dirichlet problem for the wave equation is a classical example of a problem which is not well-posed. Nevertheless, it has been used to model internal waves oscillating sinusoidally in time, in various situations, standing internal waves amongst them. We consider internal waves in two-dimensional domains bounded above by the plane z = 0 and below by z = −d(x) for depth functions d. This paper draws attention to the Abel and Schröder functional equations as a convenient way of organizing analytical solutions. Exact internal wave solutions are constructed for a selected number of simple depth functions d.

Abstract