On geometry of the Lagrangian description of ideal fluids

Details On geometry of the Lagrangian description of ideal fluids On geometry of the Lagrangian description of ideal fluids

2008-03-10

arxiv.org/abs/0803.1452v2

Physics

Mathematical Physics

Scientific paper

The Euler equation for an inviscid, incompressible fluid in a three-dimensional domain M implies that the vorticity is a frozen-in field. This can be used to construct a symplectic structure on RxM. The normalized vorticity and the suspended velocity fields are Hamiltonian with the function t and the Bernoulli function, respectively. The symplectic structure incorporates the helicity conservation law as an identity. The infinitesimal dilation for the symplectic two-form can be interpreted as a current vector for the helicity. The symplectic dilation implies the existence of contact hypersurfaces. In particular, these include contact structures on the space of streamlines and the Bernoulli surfaces. The symplectic structure on RxM can be realized as symplectisations of these through the Euler equation.

Affiliated with

Also associated with

No associations

Rating

On geometry of the Lagrangian description of ideal fluids does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with On geometry of the Lagrangian description of ideal fluids, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and On geometry of the Lagrangian description of ideal fluids will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-379224