On the double cascades of energy and enstrophy in two dimensional turbulence. Part 2. Approach to the KLB limit and interpretation of experimental evidence

This paper is concerned with three interrelated issues on our proposal of double cascades intended to serve as a more realistic theory of two-dimensional turbulence. We begin by examining the approach to the KLB limit. We present improved proofs of the result by Fjortoft. We also explain why in that limit the subleading downscale energy cascade and upscale enstrophy cascade are hidden in the energy spectrum. Then we review the experimental evidence from numerical simulations concerning the realizability of the energy and enstrophy cascade. The inverse energy cascade is found to be affected by the presense of a particular solution, and the downscale enstrophy cascade is not robust. In particular, while it is possible to have either the upscale range or the downscale range with suitable choice of dissipations, the dual cascade of KLB does not appear to be realizable, not even approximately. Finally, we amplify the hypothesis that the energy spectrum of the atmosphere reflects a combined downscale cascade of energy and enstrophy. The possibility of the downscale helicity cascade is also considered.