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
Lagrangian Methods in Fluid Mechanics
Methods loosely classified as Lagrangian are less familiar than the standard methods of Eulerian fluid mechanics, but Lagrangian methods offer significant advantages. These include the existence of a variational principle with a fluid-particle-relabeling symmetry property that corresponds to the conservation of potential vorticity. Approximations to the Lagrangian that respect this symmetry property yield dynamical equations that automatically conserve potential vorticity. Other approximations, such as averaging over wave phase, create new conservation laws, like the conservation of wave action. Despite their reputation as being difficult to solve, the Lagrangian equations have solutions that are impossible to write down in Eulerian form: In these, one obtains fluid particle locations and velocities as functions of the fluid particle labels, but the labels cannot be eliminated to give velocity as a function of location. From the Eulerian viewpoint, such solutions correspond to families of parametric solutions.