# Reynolds number with hyper-viscosity

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

For the equation: $$\partial_t u_i + u_j \partial_j u_i=-\partial_i p+ \nu_{hyper} \Delta^H u_i$$ 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: $$Re_{hyper}=\frac{U L^{2H-1}}{\nu_{hyper}}$$