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Effects of three-dimensionality on instability and turbulence in a frontal zone

Published online by Cambridge University Press:  04 November 2015

Eric Arobone  and
Sutanu Sarkar
Eric Arobone
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, CA 92093, USA
Sutanu Sarkar*
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, CA 92093, USA
*
†Email address for correspondence: ssarkar@ucsd.edu
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Abstract

Linear stability analysis and direct numerical simulation are used to investigate the evolution of a symmetrically unstable uniform frontal zone. Simulations in a three-dimensional computational domain capable of resolving near-symmetric currents develop strong nonlinearities without the emergence of pure symmetric instability. Linear stability analysis demonstrates that for $ft>1$ ( $f$ is the Coriolis parameter and $t$ denotes time) the flow generates strongly asymmetric structures which become nearly symmetric when $ft\gg 1$. Unlike the currents generated during pure symmetric instability, near-symmetric instability generates currents that do not align with isopycnals. This greatly modifies their energetics and evolution, leading to regions of the flow that are unstable to gravitational instability and energized by the reservoir of available potential energy. A high-resolution simulation demonstrates the flow evolution from near-symmetric currents to secondary shear-convective instabilities and finally, through tertiary instabilities, to fully three-dimensional turbulence. The effect of this sequence of instabilities is quantified through velocity and vorticity statistics as well as budgets for turbulent kinetic and potential energy. It is not until $ft\sim 10$ that the energy source for fluctuations is primarily shear, in contrast to the purely symmetric instability which draws its energy exclusively from shear production.

JFM classification

Geophysical and Geological Flows: Ocean processes Turbulent Flows: Stratified turbulence Turbulent Flows: Turbulent Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 784 , 10 December 2015 , pp. 252 - 273
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Copyright
© 2015 Cambridge University Press 

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