A Theoretical Model of Long Rossby Waves in the Southern Ocean and Their Interaction with Bottom Topography
Department of Physics, University of Oxford, Oxford OX1 3PU, UK
Academic Editor: Pavel S. Berloff
Received: 25 April 2016 / Revised: 19 May 2016 / Accepted: 24 May 2016 / Published: 27 May 2016
An analytical model of long Rossby waves is developed for a continuously-stratified, planetary geostrophic ocean in the presence of arbitrary bottom topography under the assumption that the potential vorticity is a linear function of buoyancy. The remaining dynamics are controlled by equations for material conservation of buoyancy along the sea surface and the sea floor. The mean, steady-state surface circulation follows characteristics that are intermediate to f
contours, where f
is the Coriolis parameter and H
is the ocean depth; for realistic stratification and weak bottom currents, these characteristics are mostly zonal with weak deflections over the major topographic features. Equations are derived for linear long Rossby waves about this mean state. These are qualitatively similar to the long Rossby wave equations for a two-layer ocean, linearised about a state of rest, except that the surface characteristics in the wave equation, which dominate the propagation, follow precisely the same path as the mean surface flow. In addition to this topographic steering, it is shown that a weighted integral of the Rossby propagation term vanishes over any area enclosed by an
contour, which has been shown in the two-layer model to lead to Rossby waves “jumping” across the
contour. Finally, a nonlinear Rossby wave equation is derived as a specialisation of the result previously obtained by Rick Salmon. This consists of intrinsic westward propagation at the classical long Rossby speed, modified to account for the finite ocean depth, and a Doppler shift by the depth-mean flow. The latter dominates within the Antarctic Circumpolar Current, consistent with observed eastward propagation of sea surface height anomalies.
This is an open access article distributed under the Creative Commons Attribution License
which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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MDPI and ACS Style
Marshall, D.P. A Theoretical Model of Long Rossby Waves in the Southern Ocean and Their Interaction with Bottom Topography. Fluids 2016, 1, 17.
Marshall DP. A Theoretical Model of Long Rossby Waves in the Southern Ocean and Their Interaction with Bottom Topography. Fluids. 2016; 1(2):17.
Marshall, David P. 2016. "A Theoretical Model of Long Rossby Waves in the Southern Ocean and Their Interaction with Bottom Topography." Fluids 1, no. 2: 17.
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