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
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
. 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
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.
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
Pedlosky, J. Fofonoff Negative Modes. Fluids 2016, 1, 13.
Pedlosky J. Fofonoff Negative Modes. Fluids. 2016; 1(2):13.
Pedlosky, Joseph. 2016. "Fofonoff Negative Modes." Fluids 1, no. 2: 13.
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