Total pressure etc.
 

Dear CFD experts,

The question is a bit from mechanics:

The term (u.grad)u + grad p in momentum equation has a clear meaning of convection and gradient of kinimatic pressure.

This term can be rewritten as (curl u)x(u) + grad P, where P is now Bernoulli (or total) pressure, an invariant in Euler limit.

I wounder of any interpretation for (curl u)x(u) term from the standpoint of physics/mechanics?! x - stands for vector product.

Thank you much for any suggestions and/or references!

Maxim Olshanskii

Re: Total pressure etc.
 

(1). For incompressible, inviscid flows, with constant total pressure in the initial state, the total pressure should be constant alone the streamline throughout the flow field. (2). This says gradient of the total pressure is zero everywhere. (3). So, under this condition, those funny terms should be zero also.

Re: Total pressure etc.
 

(1)It is derived from acceleration, so it is reasonable to think that it represents some acceleration. Indeed, if you write out (curl u)x(u) in porlar coordinate, you find centripetal and Colioris accelerations in it. So, it contains information about accelerations for rotational motions (2)(curl u) is a vorticity vector. So, (curl u)x(u) is a cross-product of vorticity and velocity vector (streamline). And if vorticity vector is parallel to a streamline, this term vanishes. This seems to mean that there can be vorticity along streamlines for flows governed by Euler equations of irrotational flow type, e.g. traling vortex of a 3D wing. (3)As you perhaps know, if you integrate the equation along a streamline, this term vanishes because it is perpendicular to the streamline. And you obtain Bernoulli's theorem for irrotational flows (constant total pressure along each individual streamline)

Maybe, (2)(3) are irrelevant to your question, though.