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Fluids 2016, 1(2), 13;

Fofonoff Negative Modes

Woods Hole Oceanographic Institution, Woods Hole, MA 02543, USA
Academic Editor: Pavel S. Berloff
Received: 15 February 2016 / Revised: 6 April 2016 / Accepted: 11 April 2016 / Published: 15 April 2016
(This article belongs to the Collection Geophysical Fluid Dynamics)
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The classic solution of Fofonoff to the problem of free inertial flow in a closed basin is extended to the case where the potential vorticity, q, is linearly proportional to the streamfunction, with a negative definite constant, K 2 . Such a relation arises naturally in the presence of an eastward flow, instead of Fofonoff’s westward zonal flow on the β plane. The resulting solutions can be wavelike if K 2 = β L 2 / U π 2 exceeds the critical value of 1 where U is the magnitude of the eastward flow and L is the characteristic meridional scale of the motion. Solutions are presented with various boundary conditions on the basin boundaries, and conditions for which the solutions suffer a resonance are also obtained. It is suggested that oceanic circulations with eastward flows naturally excite these Fofonoff negative modes. The possibility of resonance and instability adds additional physical complexity to the modes. View Full-Text
Keywords: Fofonoff modes; Rossby waves; resonance Fofonoff modes; Rossby waves; resonance

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Pedlosky, J. Fofonoff Negative Modes. Fluids 2016, 1, 13.

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