Mesoscopic spectra in two-dimensional decaying turbulence

Two-dimensional decaying turbulence is simulated using a lattice Boltzmann model with the Bhatnagar-Gross-Krook collision operator. Auto-power spectra of the one-velocity particle distribution functions are presented. The relation between the spectrum of the kinetic energy and the spectra of the distribution functions is given. An interpretation of the non-equilibrium spectra as a measure of the dissipation in different scales is given. A peak in the spectrum of the resting particle distribution functions is observed exactly at the ultraviolet cutoff. It is shown that the peak can be associated with enhanced acoustic activity, which might be a numerical artifact or a consequence of the compressibility of the lattice Boltzmann fluid.