Yuval Ne’eman Distinguished Lectures in Geophysics, Atmosphere and Space Sciences Endowed by Raymond and Beverly Sackler
Prof. Rick Salmon, Scripps Institution of Oceanography, University of California San Diego, La Jolla, California, USA
The Analogy Between Electrodynamics and Fluid Mechanics
There is an almost exact correspondence between the Lagrangian for classical electrodynamics in two space dimensions, and the Lagrangian for a hydrostatic fluid in which the density stratification is strong enough to prevent overturning. The analogy is between the single component of the magnetic field and the fluid depth (or isopycnal separation), and between the two components of electric field and the horizontal momentum of the fluid. Potential vorticity is analogous to electric charge. The fluid Lagrangian contains additional terms that cause waves in the fluid to interact, even in the absence of vorticity. The Lagrangian for electrodynamics acquires analogous terms if the physics is extended to include photons interacting with the vacuum. Pair creation of electrons and positrons is analogous to the creation, by waves in the fluid, of vortices with opposite signs.
The fluid Lagrangian can be expressed as the sum of three parts. The first part corresponds to quasigeostrophic dynamics in the absence of inertia-gravity waves. The second part corresponds to inertia-gravity waves in the absence of quasigeostrophic flow. The third part represents a coupling between the inertial-gravity waves and quasigeostrophic motion. This formulation provides the basis for a general theory of inertia-gravity waves interacting with a quasigeostrophic mean flow.