# some problem about "KIM, MOIN and MOSER" 's paper

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 August 10, 2016, 20:25 some problem about "KIM, MOIN and MOSER" 's paper #1 Senior Member     p ding Join Date: Mar 2009 Posts: 404 Rep Power: 17 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

 August 11, 2016, 04:42 #2 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,062 Rep Power: 64 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.

August 11, 2016, 05:11
#3
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p ding
Join Date: Mar 2009
Posts: 404
Rep Power: 17
Quote:
 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.