A note on helicity conservation in Leray models of incompressible flow

作者：Hernandez Monica Morales; Rebholz Leo G^*

来源：Journal of Mathematical Analysis and Applications, 2015, 422(1): 776-781.

DOI：10.1016/j.jmaa.2014.09.014

• Leray model
• Helicity conservation
• Navier-Stokes equations
• Finite element method

We prove conservation of a regularized helicity H-L := integral(Omega) u center dot w dx for the Leray model (and its variants) of turbulent flow, where w is the solution of a Leray-regularized vorticity equation. The usual definition of helicity is H = integral(Omega) u center dot (del x u) dx, which is considered by Navier-Stokes flows, but is not a conserved quantity of the Leray model. However, if u is a Leray solution, then the difference between H and H-L is that H-L uses a regularized vorticity and H uses the curl of a regularized velocity. The results are extended to show that the standard Crank-Nicolson finite element method for Leray models conserves both discrete energy and discrete regularized helicity.

• 出版日期2015-2-1