Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

Is it possible to evaluate a Reynolds number when viscosity operator is substituted by hyper-viscosity operator at the power H (Laplacien to the power H) in the incompressible Navier-Stokes equations ?

share|improve this question
1  
Have you tried non-dimensionalizing the equations to see what the equivalent parameter, if any, would be? –  tpg2114 Feb 17 '12 at 3:35
    
@tpg2114 no, I should have, thanks for your comment. –  aberration Feb 17 '12 at 16:01
    
No problem. Teach a man to fish :) –  tpg2114 Feb 17 '12 at 16:02

1 Answer 1

up vote 1 down vote accepted

For the equation: \begin{equation} \partial_t u_i + u_j \partial_j u_i=-\partial_i p+ \nu_{hyper} \Delta^H u_i \end{equation} with $u$ the velocity in $m.s^{-1}$ and is characteristic order $U$, $p$ the pressure in $m^{2}.s^{-2}$, $\nu$ the hyper-viscosity in $m^{2H}.s^{-1}$. The characteristic length scale is note $L$ in $m$.

Following the non-dimensionalizing, the number Reynolds like is: \begin{equation} Re_{hyper}=\frac{U L^{2H-1}}{\nu_{hyper}} \end{equation}

share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.