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Stratified turbulence dominated by vortical motion

Published online by Cambridge University Press:  11 October 2004

MICHAEL L. WAITE
Affiliation:
McGill University, 805 rue Sherbrooke ouest, Montréal, QC H3A 2K6, [email protected]
PETER BARTELLO
Affiliation:
McGill University, 805 rue Sherbrooke ouest, Montréal, QC H3A 2K6, [email protected]

Abstract

We present numerical simulations of stably stratified, vortically forced turbulence at a wide range of Froude numbers. Large-scale vortical forcing was chosen to represent geophysical vortices which break down at small scales where Coriolis effects are weak. The resulting vortical energy spectra are much steeper in the horizontal direction and shallower in the vertical than typical observations in the atmosphere and ocean, as noted in previous studies. We interpret these spectra in terms of the vertical decoupling which emerges in the strongly stratified limit. We show that this decoupling breaks down at a vertical scale of $U/N$, where $N$ is the Brunt–Väisälä frequency and $U$ is a characteristic horizontal velocity, confirming previous scaling arguments. The transfer of vortical energy to wave energy is most efficient at this vertical scale; vertical spectra of wave energy are correspondingly peaked at small scales, as observed in past work. The equilibrium statistical mechanics of the inviscid unforced truncated problem qualitatively predicts the nature of the forced–dissipative solutions, and confirms the lack of an inverse cascade of vortical energy.

Type
Papers
Copyright
© 2004 Cambridge University Press

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