Energy and enstrophy dissipation in steady state 2-d turbulence

Alexandros Alexakis; Charles R. Doering

doi:10.1016/j.physleta.2006.07.048

paper

Energy and enstrophy dissipation in steady state 2-d turbulence

arXiv:physics/0605090 · doi:10.1016/j.physleta.2006.07.048

Abstract

Upper bounds on the bulk energy dissipation rate $ε$ and enstrophy dissipation rate $χ$ are derived for the statistical steady state of body forced two dimensional turbulence in a periodic domain. For a broad class of externally imposed body forces it is shown that $ε \leq k_{f} U^{3} R e^{- 1/2} (C_{1} + C_{2} R e^{- 1})^{1/2}$ and $χ \leq k_{f}^{3} U^{3} (C_{1} + C_{2} R e^{- 1})$ where $U$ is the root-mean-square velocity, $k_{f}$ is a wavenumber (inverse length scale) related with the forcing function, and $R e = U / ν k_{f}$ . The positive coefficients $C_{1}$ and $C_{2}$ are uniform in the the kinematic viscosity $ν$ , the amplitude of the driving force, and the system size. We compare these results with previously obtained bounds for body forces involving only a single length scale, or for velocity dependent a constant-energy-flux forces acting at finite wavenumbers. Implications of our results are discussed.

Submmited to Phys. Lett. A

Energy and enstrophy dissipation in steady state 2-d turbulence

Abstract

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