Abstract
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.
Highlights
Pedlosky and Spall [1], the interaction of an eastward flowing current with an island situated in a simple geometry that mimicked a closed basin allowed steady solutions in which Rossby wave-like modes were excited over the whole zonal range of the domain
Whenone themight dynamics under has negligible forcing, anticipate thatconsideration the steady vorticity equation frictional dissipation and no external forcing, one might anticipate that the steady vorticity equation
Would be an appropriate governing equation over most of the domain. It follows that the would be an appropriate governing equation over most of the domain. It follows that the solution must have the form Equation (1), i.e., the total vorticity must be constant on streamlines
Summary
Pedlosky and Spall [1] (hereafter P & S), the interaction of an eastward flowing current with an island situated in a simple geometry that mimicked a closed basin allowed steady solutions in which Rossby wave-like modes were excited over the whole zonal range of the domain. The second problem has flow with the unit flux entering as a narrow jet in the northwest corner and leaving in the northeast corner In this case, the streamfunction is zero on the western, southern and eastern boundaries and is equal to on the open x interval (0, xe ). The third problem has the basin completely closed so that the streamfunction is zero on all the basin boundaries Note that, in this case, ψ = 0 is not a solution to Equation (2); that equation is a solution of the original vorticity equation only for ψ ‰ 0. Flow enters the basin at the northwest corner and exits at the southeast corner In this case, the boundary conditions are:
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