Energy and enstrophy dissipation in steady state 2d turbulence

Upper bounds on the bulk energy dissipation rate epsilon and enstrophy dissipation rate chi are derived for the statistical steady state of body forced two-dimensional (2d) turbulence in aperiodic domain. For a broad class of externally imposed body forces it is shown that epsilon <= k(f)U(3)Re(-1/2)(C-1 + C2Re-1)(1/2) and chi <= k(f)(3)U(3)(C-1 + C2Re-1) where U is the root-mean-square velocity, k(f) is a wavenumber (inverse length scale) related with the forcing function, and Re = U/vk(f). The positive coefficients C-1 and C-2 are uniform in the kinematic viscosity v, 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 constant-energy-flux forces acting at finite wavenumbers. Implications of our results are discussed. (c) 2006 Elsevier B.V. All rights reserved.