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Direct numerical simulation of a breaking inertia–gravity wave

Published online by Cambridge University Press:  28 March 2013

S. Remmler ,
M. D. Fruman  and
S. Hickel
S. Remmler
Affiliation:
Institute of Aerodynamics and Fluid Mechanics, Technische Universität München, D-85747 Garching bei München, Germany
M. D. Fruman
Affiliation:
Institute for Atmospheric and Environmental Sciences, Goethe-Universität Frankfurt, D-60438 Frankfurt am Main, Germany
S. Hickel*
Affiliation:
Institute of Aerodynamics and Fluid Mechanics, Technische Universität München, D-85747 Garching bei München, Germany
*
†Email address for correspondence: sh@tum.de
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Abstract

We have performed fully resolved three-dimensional numerical simulations of a statically unstable monochromatic inertia–gravity wave using the Boussinesq equations on an $f$-plane with constant stratification. The chosen parameters represent a gravity wave with almost vertical direction of propagation and a wavelength of 3 km breaking in the middle atmosphere. We initialized the simulation with a statically unstable gravity wave perturbed by its leading transverse normal mode and the leading instability modes of the time-dependent wave breaking in a two-dimensional space. The wave was simulated for approximately 16 h, which is twice the wave period. After the first breaking triggered by the imposed perturbation, two secondary breaking events are observed. Similarities and differences between the three-dimensional and previous two-dimensional solutions of the problem and effects of domain size and initial perturbations are discussed.

JFM classification

Geophysical and Geological Flows: Atmospheric flows Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Stratified flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 722 , 10 May 2013 , pp. 424 - 436
Copyright
©2013 Cambridge University Press

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