[ztdep]

Dear friends:
In the paper of KIM, MOIN and MOSER, " Turbulence statistics in fully developed channel flow at low Reynolds number" , the incompressbile N-s equations and the continuity equations were reduced to a normal component of vorticity euqation and a fourth order equation for v.

I do not understand how to obtain the fourth oder equation for v velocity?
and why we only need the normal component of vorticity euqation .

Regards

[FMDenaro]

I never worked on such formulation (and I don't like too), but it is of some interest now because the database for high Re number of Hojas, Jimenez and al. are based on such formulation (http://turbulence.ices.utexas.edu/co...anneldata.html).

I haven't done the manipulation needed but I suppose that you can derive the equations by applying the Laplacian to all the terms in the equation for the v component. The use the vorticity equation and project them over the normal component. Combining them, using the continuity equation you can eliminate the pressure term.

I hope someone who worked practically can give you more help.

[ztdep]

Originally Posted by FMDenaro

I never worked on such formulation (and I don't like too), but it is of some interest now because the database for high Re number of Hojas, Jimenez and al. are based on such formulation (http://turbulence.ices.utexas.edu/co...anneldata.html).

I haven't done the manipulation needed but I suppose that you can derive the equations by applying the Laplacian to all the terms in the equation for the v component. The use the vorticity equation and project them over the normal component. Combining them, using the continuity equation you can eliminate the pressure term.

I hope someone who worked practically can give you more help.

thank you very much for you feedback. I have understand it. we take the curl of the curl of NS equation, we can obtain the formulation.