LAYER-MEAN QUANTITIES, LOCAL CONSERVATION-LAWS, AND VORTICITY

We derive local conservation laws for layer-mean quantities in two gen eral settings. When applied to Euler hows, the first of these settings yields well-known local conservation laws for quantities averaged bet ween material surfaces. The second, however, leads to new local conser vation laws for quantities involving the vorticity that are averaged b etween arbitrary surfaces. These produce the crucial vorticity conserv ation laws in shallow water models that admit nonhydrostatic and nonco lumnar motion. Moreover, they seem to lie outside the Hamiltonian para digm of fluid dynamics. The formalism generalizes to skew-symmetric ma trix fields; applications to electromagnetism are suggested.