A GENERALIZATION OF BERNOULLI THEOREM

The conservation of potential vorticity Q can be expressed as partial derivative(rhoQ)/partial derivative t + del . J = 0, where J denotes t he total flux of potential vorticity. It is shown that J is related un der statistically steady conditions to the Bernoulli function B by J = del theta X del B, where theta is the potential temperature. This rel ation is valid even in the nonhydrostatic limit and in the presence of arbitrary nonconservative forces (such as internal friction) and heat ing rates. In essence, it can be interpreted as a generalization of Be rnoulli's theorem to the frictional and diabatic regime. The classical Bernoulli theorem-valid for inviscid adiabatic and steady flows-state s that the intersections of surfaces of constant potential temperature and constant Bernoulli function yield streamlines. In the presence of frictional and diabatic effects, these intersections yield the flux l ines along which potential vorticity is transported.