An unsteady extension of Bernoulli's theorem.

Abstract

An unsteady extension of Bernoulli's theorem is presented. For steady flows, the derivative of the Bernoulli function in the normal direction perpendicular both to the streamline and the gradient of potential temperature becomes equal to the product of the flow speed and the binormal component of absolute vorticity. Even for unsteady flows, the same formula holds except that the absolute vorticity is replaced by the sum of the absolute vorticity and the local rotation rate of velocity.