Well-posedness in the generalized sense for the incompressible Navier-Stokes equation

1991 ◽  
Vol 6 (2) ◽  
pp. 101-127 ◽  
Author(s):  
B. Christer V. Johansson
Keyword(s):  
Stokes Equation ◽  
Navier Stokes ◽  
Well Posedness ◽  
Navier Stokes Equation ◽  
Incompressible Navier Stokes Equation

Casimir cascades in two-dimensional turbulence

2013 ◽  
Vol 729 ◽  
pp. 364-376 ◽  
Author(s):  
John C. Bowman
Keyword(s):  
Stokes Equation ◽  
Navier Stokes ◽  
Fourth Power ◽  
Two Dimensional ◽  
Vorticity Field ◽  
Navier Stokes Equation ◽  
Small Scales ◽  
Open Question ◽  
Incompressible Navier Stokes Equation

AbstractIn addition to conserving energy and enstrophy, the nonlinear terms of the two-dimensional incompressible Navier–Stokes equation are well known to conserve the global integral of any continuously differentiable function of the scalar vorticity field. However, the phenomenological role of these additional inviscid invariants, including the issue as to whether they cascade to large or small scales, is an open question. In this work, well-resolved implicitly dealiased pseudospectral simulations suggest that the fourth power of the vorticity cascades to small scales.

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