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Existence, stability and formation of baroclinic tripoles in quasi-geostrophic flows

Published online by Cambridge University Press:  11 November 2015

Jean N. Reinaud  and
Xavier Carton
Jean N. Reinaud*
Affiliation:
Mathematical Institute, University of St Andrews, North Haugh, St Andrews KY16 9SS, UK
Xavier Carton
Affiliation:
Laboratoire de Physique des Océans, UFR Sciences, UBO/UEB, 6, Avenue le Gorgeu, 29200 Brest, France
*
†Email address for correspondence: jean@mcs.st-and.ac.uk
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Abstract

Hetons are baroclinic vortices able to transport tracers or species, which have been observed at sea. This paper studies the offset collision of two identical hetons, often resulting in the formation of a baroclinic tripole, in a continuously stratified quasi-geostrophic model. This process is of interest since it (temporarily or definitely) stops the transport of tracers contained in the hetons. First, the structure, stationarity and nonlinear stability of baroclinic tripoles composed of an upper core and two lower (symmetric) satellites are studied analytically for point vortices and numerically for finite-area vortices. The condition for stationarity of the point vortices is obtained and it is proven that the baroclinic point tripoles are neutral. Finite-volume stationary tripoles exist with marginal states having very elongated (figure-of-eight shaped) upper cores. In the case of vertically distant upper and lower cores, the latter can nearly join near the centre of the plane. These steady states are compared with their two-layer counterparts. Then, the nonlinear evolution of the steady states shows when they are often neutral (showing an oscillatory evolution); when they are unstable, they can either split into two hetons (by breaking of the upper core) or form a single heton (by merger of the lower satellites). These evolutions reflect the linearly unstable modes which can grow on the vorticity poles. Very tall tripoles can break up vertically due to the vertical shear mutually induced by the poles. Finally, the formation of such baroclinic tripoles from the offset collision of two identical hetons is investigated numerically. This formation occurs for hetons offset by less than the internal separation between their poles. The velocity shear during the interaction can lead to substantial filamentation by the upper core, thus forming small upper satellites, vertically aligned with the lower ones. Finally, in the case of close and flat poles, this shear (or the baroclinic instability of the tripole) can be strong enough that the formed baroclinic tripole is short-lived and that hetons eventually emerge from the collision and drift away.

JFM classification

Geophysical and Geological Flows: Quasi-geostrophic flows Vortex Flows: Vortex instability Vortex Flows: Vortex interactions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 785 , 25 December 2015 , pp. 1 - 30
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© 2015 Cambridge University Press 

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