Weakly Nonlinear Internal Wavepackets

Background

As internal waves propagate upwards in the atmosphere they grow in amplitude. This is a consequence of the law of conservation of momentum: where the air is thinner (less mass) the vertical transport of horizontal velocity must be greater. The question is how does the behaviour predicted by linear theory change when the wave-amplitude is no longer negligibly small?

The study here is limited to two-dimensional, Boussinesq, horizontally periodic waves (which are already assumed to have large amplitude). Separately we consider large amplitude effects upon horizontally and vertically localized wavepackets.

Simulations

The following simulations compare the evolution of a vertially localized wavepacket as it depends upon amplitude, relative frequency and envelope shape. The profiles to the right of the perturbation fields show the computed vertical profiles of the horizontally averaged flow.


Small amplitude Gaussian wavepackets with kz=-0.4kx and kz=-1.4kx.	Large amplitude Gaussian wavepackets with kz=-0.4kx and kz=-1.4kx.

Large amplitude narrow and wide Gaussian wavepackets with kz=-0.4kx.	Large amplitude Gaussian and plateau-shaped wavepackets with kz=-0.4kx.

The initial evolution of large-amplitude is governed by interactions between waves and the wave-induced mean flow. At late times (particularly for the plateau-shaped wavepacket) parametric subharmonic instability efficiently transports energy from large to small scales.

Links to related research

Weakly Nonlinear Internal Wavepackets,
B. R. Sutherland, J. Fluid Mech.

Internal Wave Instability: Wave-Wave vs Wave-Induced Mean Flow Interactions,
B. R. Sutherland, Phys. Fluids

Acknowledgements

This research was financially supported by grants from:

NSERC
CFCAS

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