Enstrophy dissipation in freely evolving two-dimensional turbulence

Details Enstrophy dissipation in freely evolving two-dimensional turbulence Enstrophy dissipation in freely evolving two-dimensional turbulence

2005-06-23

arxiv.org/abs/nlin/0506049v1

Nonlinear Sciences

Chaotic Dynamics

No figures, Letter to appear in Phys. Fluids

Scientific paper

10.1063/1.2001687

Freely decaying two-dimensional Navier--Stokes turbulence is studied. The conservation of vorticity by advective nonlinearities renders a class of Casimirs that decays under viscous effects. A rigorous constraint on the palinstrophy production by nonlinear transfer is derived, and an upper bound for the enstrophy dissipation is obtained. This bound depends only on the decaying Casimirs, thus allowing the enstrophy dissipation to be bounded from above in terms of initial data of the flows. An upper bound for the enstrophy dissipation wavenumber is derived and the new result is compared with the classical dissipation wavenumber.

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