INVERSE CASCADES OF ANGULAR-MOMENTUM

Most theoretical and computational studies of turbulence in Navier-Sto kes fluids and/or guiding-centre plasmas have been carried out in the presence of spatially periodic boundary conditions. In view of the fre quently reproduced result that two-dimensional and/or MHD decaying tur bulence leads to structures comparable in length scale to a box dimens ion, it is natural to ask if periodic boundary conditions are an adequ ate representation of any physical situation. Here, me study, computat ionally, the decay of two-dimensional turbulence in a Navier-Stokes fl uid or guiding-centre plasma in the presence of circular no-slip rigid malls. The method is wholly spectral, and relies on a Galerkin approx imation by a set of functions that obey two boundary conditions at the wall radius (analogues of the Chandrasekhar-Reid functions). It is po ssible to explore Reynolds numbers up to the order of 1250, based on a n RMS velocity and a box radius. It is found that decaying turbulence is altered significantly by the no-slip boundaries. First, strong boun dary layers serve as sources of vorticity and enstrophy and enhance th e early-time energy decay rate, for a given Reynolds number, well abov e the periodic boundary condition values. More importantly, angular mo mentum turns out to be an even more slowly decaying ideal invariant th an energy, and to a considerable extent governs the dynamics of the de cay. Angular momentum must be taken into account, for example, in orde r to achieve quantitative agreeement with the predicition of maximum e ntropy, or 'most probable', states. These are predicitions of conditio ns that are established after several eddy turnover times but before t he energy has decayed away. Angular momentum mill cascade to lower azi muthal mode numbers, even if absent there initially, and the angular m omentum modal spectrum is eventually dominated by the lowest mode avai lable. When no initial angular momentum is present, no behaviour that suggests the likelihood of inverse cascades is observed.