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Potential vorticity redistribution by localised transient forcing in the shallow-water model

Published online by Cambridge University Press:  03 August 2018

Michael C. Haigh Open the ORCID record for Michael C. Haigh [Opens in a new window]  and
Pavel S. Berloff
Michael C. Haigh*
Affiliation:
Department of Mathematics, Imperial College London, Huxley Building, 180 Queen’s Gate, London SW7 2AZ, UK
Pavel S. Berloff
Affiliation:
Department of Mathematics, Imperial College London, Huxley Building, 180 Queen’s Gate, London SW7 2AZ, UK
*
†Email address for correspondence: [email protected]
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Abstract

This study is motivated by the need to develop stochastic parameterisations for representing the effects of mesoscale oceanic eddies in non-eddy-resolving and eddy-permitting ocean circulation models. A necessary logical step on the way to such parameterisations is the understanding of flow responses to spatially stationary and localised, time-dependent ‘plunger’ forcings intended to represent transient eddy flux divergences. Specifically, this study develops an understanding of the plunger-induced convergence of potential vorticity (PV) fluxes using the linearised single-layer shallow-water model. Time-periodic solutions are obtained and the ‘footprint’, defined as the time-mean, quasi-linear PV flux convergence, quantifies the cumulative PV redistribution induced by the plunger. Using the footprint, the equivalent eddy flux (EEF) is defined such that it succinctly quantifies the extent of the PV redistribution, and its dependencies on the forcing latitude and the background flow are examined in detail. For a uniform background flow the EEF is positive for all forcing latitudes, corresponding to net-poleward PV flux convergence, as expected by current theory of $\unicode[STIX]{x1D6FD}$-plane Rossby waves. The EEF also has a robust dependence on the direction and magnitude of a uniform background flow, which is a useful quality for the EEF to provide a basis for a parameterisation of eddy PV fluxes. We also examine the PV redistribution due to forcing on top of a Gaussian jet background flow and find that forcing proximity to the jet core is the primary factor in determining whether the jet is sharpened or broadened.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Ocean circulation Geophysical and Geological Flows: Shallow water flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 852 , 10 October 2018 , pp. 199 - 225
Copyright
© 2018 Cambridge University Press 

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