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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 ?

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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
up vote 2 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}

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