What is hyperviscosity?
 

Hi, Do anybody know what is hyperviscosity? By the way what is its function? Any reference books or papers can be recommended. Thank You very much!!

It is a hyper viscosity ..
 

Hi THere,

The hyperviscosity that I know about is related to numerical simulations of turbulence (Direct Numerical Simulations or DNS; solving the time dependent Navier-STokes equations of the flow).

One wants to have a small viscosity that will dissipate the energy in the smal scales but not affect the larger scales. The usual viscous term in the equations (d2/dx2, etc..) dissipates energy not only in the small scales but also in the not so small scales. So on have to use what is call a hyperviscosity, which is basically a term of the form d2n/dx2n, where n=2,3,4... For n=1 one has the usual viscosity and for n larger than 1 one has a hyperviscosity. With this term one is able to dissipate the energy in smallest scale only without affecting the larger scales. If one looks at the Energy spectrum, the viscosity actually cuts off the small scale (large wave number) with a given negative slope. The hyperviscosity cuts the energy spectrum with a sharper slope (more negative) and therefore allow to resolve more wavelengths. This is very important for DNS of turbulence since one wants to resolve for the fine structure of the flow.

See for example:

Cho and Polvani, 1996, Physics of Fluids, volume 8, number 6, pages 1531-1552, The emergence of jets and vortices in freely evolving shallow water turbulence on a sphere.

Patrick

Re: Thank you Patrick Godon
 

Thank you for the useful information provided.