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Energy Partitioning and Horizontal Dispersion in a Stratified Rotating Lake

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  • 1 Dipartimento di Ingegneria Idraulica, Marittima, Geotecnica ed Ambientale, Universitá di Padova, Padua, Italy
  • | 2 Centre for Water Research, University of Western Australia, Perth, Australia
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Abstract

The response of a stratified rotating basin to the release of a linearly tilted interface is derived. This case is compared with a uniformly forced basin in the two limits when the duration of the forcing is much greater than the period of the dominant internal waves and when it is much smaller. Energy partitioning is studied as a function of the Burger number S (relative importance of stratification versus rotation), showing the dominance of a geostrophic component over the wave field for low S. Trajectories are integrated numerically, revealing the Stokes drift of the waves to be always cyclonic. Transport properties are classified in terms of S and the Wedderburn number W (relative importance of the disturbance versus stratification). The geostrophic flow is the main source of advection, but only the waves allow particles to break the barrier to transport between the two geostrophic gyres, ultimately leading to stretching and folding. For low values of W, advection can become chaotic. Conservation of potential vorticity explains the difference in transport properties between the forced cases and the initial tilt release. A transition time between spreading dominated by turbulence and that dominated by large-scale motions is derived as a function of the initial size of a cloud. The results show that spreading is mainly due to turbulence for weak forcing, small time, and small clouds; for stronger forcing, larger time, or larger clouds the effect of large-scale motions can be dominant.

Corresponding author address: Roman Stocker, Department of Applied Mathematics, MIT, 2-339, 77 Massachusetts Ave., Cambridge, MA 02139. Email: stocker@math.mit.edu

Abstract

The response of a stratified rotating basin to the release of a linearly tilted interface is derived. This case is compared with a uniformly forced basin in the two limits when the duration of the forcing is much greater than the period of the dominant internal waves and when it is much smaller. Energy partitioning is studied as a function of the Burger number S (relative importance of stratification versus rotation), showing the dominance of a geostrophic component over the wave field for low S. Trajectories are integrated numerically, revealing the Stokes drift of the waves to be always cyclonic. Transport properties are classified in terms of S and the Wedderburn number W (relative importance of the disturbance versus stratification). The geostrophic flow is the main source of advection, but only the waves allow particles to break the barrier to transport between the two geostrophic gyres, ultimately leading to stretching and folding. For low values of W, advection can become chaotic. Conservation of potential vorticity explains the difference in transport properties between the forced cases and the initial tilt release. A transition time between spreading dominated by turbulence and that dominated by large-scale motions is derived as a function of the initial size of a cloud. The results show that spreading is mainly due to turbulence for weak forcing, small time, and small clouds; for stronger forcing, larger time, or larger clouds the effect of large-scale motions can be dominant.

Corresponding author address: Roman Stocker, Department of Applied Mathematics, MIT, 2-339, 77 Massachusetts Ave., Cambridge, MA 02139. Email: stocker@math.mit.edu

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