Energy Cascade: Difference between revisions

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In a fully turbulent flow, at high Re, we have large eddies breaking up into smaller ones, and those break up as well until �finally the eddies are so small that they are dissipated by viscosity. Clearly the scale at which dissipation occurs depends on the viscosity. A poem by Lewis Fry Richardson:
In a fully turbulent flow, at high Reynolds number, we have large eddies breaking up into smaller ones, and those break up as well until finally the eddies are so small that they are dissipated by viscosity.  If the system is in a steady state, this means that at every scale energy is being received from larger scales and supplied to smaller scales at the same rate, and so by extension the energy supplied at the largest scales is the same as the energy dissipated by viscosity. Clearly the scale at which dissipation occurs depends on the viscosity.


A poem by Lewis Fry Richardson:


Big whirls have little whirls,
Big whirls have little whirls,  
 
Which feed on their velocity,  
Which feed on their velocity,
And little whirls have lesser whirls,  
 
and so on to viscosity.
And little whirls have lesser whirls,
 
and so on to viscosity.
 
 
See Kolmogorov's 5/3 law for the energy in terms of wavenumber in the inertial subrange of wavenumbers before dissipation occurs.

Latest revision as of 15:47, 4 April 2017

In a fully turbulent flow, at high Reynolds number, we have large eddies breaking up into smaller ones, and those break up as well until finally the eddies are so small that they are dissipated by viscosity. If the system is in a steady state, this means that at every scale energy is being received from larger scales and supplied to smaller scales at the same rate, and so by extension the energy supplied at the largest scales is the same as the energy dissipated by viscosity. Clearly the scale at which dissipation occurs depends on the viscosity.

A poem by Lewis Fry Richardson:

Big whirls have little whirls, 
Which feed on their velocity, 
And little whirls have lesser whirls, 
and so on to viscosity.