Enstrophy dissipation in freely evolving two-dimensional turbulence

Abstract

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.

No figures, Letter to appear in Phys. Fluids

References in corpus (3)

• Constraints on the spectral distribution of energy and enstrophy dissipation in forced two-dimensional turbulence
• Nonlinear transfer and spectral distribution of energy in $\alpha$ turbulence
• On the dual cascade in two-dimensional turbulence

Cited by in corpus (5)

• Energy and enstrophy dissipation in steady state 2-d turbulence
• Geometric microcanonical theory of two-dimensional Truncated Euler flows
• Number of degrees of freedom of two-dimensional turbulence
• Dissipation scales and anomalous sinks in steady two-dimensional turbulence
• An upper bound for passive scalar diffusion in shear flows