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Salmon, R.  2014.  Analogous formulation of electrodynamics and two-dimensional fluid dynamics. Journal of Fluid Mechanics. 761   10.1017/jfm.2014.642   AbstractWebsite

A single, simply stated approximation transforms the equations for a two-dimensional perfect fluid into a form that is closely analogous to Maxwell's equations in classical electrodynamics. All the fluid conservation laws are retained in some form. Waves in the fluid interact only with vorticity and not with themselves. The vorticity is analogous to electric charge density, and point vortices are the analogues of point charges. The dynamics is equivalent to an action principle in which a set of fields and the locations of the point vortices are varied independently. We recover classical, incompressible, point vortex dynamics as a limiting case. Our full formulation represents the generalization of point vortex dynamics to the case of compressible flow.

Dellar, PJ, Salmon R.  2005.  Shallow water equations with a complete Coriolis force and topography. Physics of Fluids. 17   10.1063/1.21156747   AbstractWebsite

This paper derives a set of two-dimensional equations describing a thin inviscid fluid layer flowing over topography in a frame rotating about an arbitrary axis. These equations retain various terms involving the locally horizontal components of the angular velocity vector that are discarded in the usual shallow water equations. The obliquely rotating shallow water equations are derived both by averaging the three-dimensional equations and from an averaged Lagrangian describing columnar motion using Hamilton's principle. They share the same conservation properties as the usual shallow water equations, for the same energy and modified forms of the momentum and potential vorticity. They may also be expressed in noncanonical Hamiltonian form using the usual shallow water Hamiltonian and Poisson bracket. The conserved potential vorticity takes the standard shallow water form, but with the vertical component of the rotation vector replaced by the component locally normal to the surface midway between the upper and lower boundaries. (c) 2005 American Institute of Physics.

Bogden, PS, Davis RE, Salmon R.  1993.  The North-Atlantic Circulation - Combining Simplified Dynamics with Hydrographic Data. Journal of Marine Research. 51:1-52.   10.1357/0022240933223855   AbstractWebsite

We estimate the time-averaged velocity field in the North Atlantic from observations of density, wind stress and bottom topography. The flow is assumed geostrophic, with prescribed Ekman pumping at the surface, and no normal component at the bottom. These data and dynamics determine velocity to within an arbitrary function of (Coriolis parameter)/(ocean depth), which we call the ''dynamical free mode.'' The free mode is selected to minimize mixing of potential density at mid-depth. This tracer-conservation criterion serves as a relatively weak constraint on the calculation. Estimates of vertical velocity are particularly sensitive to variations in the free mode and to errors in density. In contrast, horizontal velocities are relatively robust. Below the thermocline, we predict a strong O(1 cm/sec) westward flow across the entire North Atlantic, in a narrow range of latitude between 25N and 32N. This feature supports the qualitative (and controversial) conjecture by Wust (1935) of flow along the ''Mediterranean Salt Tongue.'' Along continental margins and at the Mid-Atlantic Ridge, predicted bottom velocity points along isobaths, with shallow water to the right. These flows agree with many long-term current measurements and with notions of the circulation based on tracer distributions. The results conflict with previous oceanographic-inverse models, which predict mid-depth flows an order of magnitude smaller and often in opposite directions. These discrepancies may he attributable to our relatively strong enforcement of the bottom boundary condition. This involves the plausible, although tenuous, assertion that the flow ''feels'' only the large-scale features of the bottom topography. Our objective is to investigate the consequences of using this hypothesis to estimate the North Atlantic circulation.