The Dispersion Relation for Planetary Waves in the Presence of Mean Flow and Topography. Part II: Two-Dimensional Examples and Global Results

Peter D. Killworth National Oceanography Centre, Southampton, Southampton, United Kingdom

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Jeffrey R. Blundell National Oceanography Centre, Southampton, Southampton, United Kingdom

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Abstract

The one-dimensional examples of the dispersion relation for planetary waves under the Wentzel–Kramers–Brillouin–Jeffreys (WKBJ) assumption given in Part I are extended to two dimensions and analyzed globally. The dispersion relations are complicated, and there is a nontrivial lower bound to the frequency given by the column maximum of what would be the local Doppler shift to the frequency. This generates short waves of a much higher frequency than would be expected from traditional theory; these waves can have larger phase velocities than long waves but do not appear to have faster group velocities. The longer waves possess phase speeds in excellent agreement with recent remotely sensed data. Waves cannot propagate efficiently across ocean basins, suggesting that mechanisms other than eastern boundary generation may be playing a role in the ubiquitous nature of planetary waves.

Corresponding author address: Dr. Peter D. Killworth, National Oceanography Centre, Southampton, University of Southampton and Natural Environment Research Council, Empress Dock, Southampton SO14 3ZH, United Kingdom. Email: p.killworth@noc.soton.ac.uk

Abstract

The one-dimensional examples of the dispersion relation for planetary waves under the Wentzel–Kramers–Brillouin–Jeffreys (WKBJ) assumption given in Part I are extended to two dimensions and analyzed globally. The dispersion relations are complicated, and there is a nontrivial lower bound to the frequency given by the column maximum of what would be the local Doppler shift to the frequency. This generates short waves of a much higher frequency than would be expected from traditional theory; these waves can have larger phase velocities than long waves but do not appear to have faster group velocities. The longer waves possess phase speeds in excellent agreement with recent remotely sensed data. Waves cannot propagate efficiently across ocean basins, suggesting that mechanisms other than eastern boundary generation may be playing a role in the ubiquitous nature of planetary waves.

Corresponding author address: Dr. Peter D. Killworth, National Oceanography Centre, Southampton, University of Southampton and Natural Environment Research Council, Empress Dock, Southampton SO14 3ZH, United Kingdom. Email: p.killworth@noc.soton.ac.uk

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