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On the double cascades of energy and enstrophy in two-dimensional turbulence. II: Approach to the KLB limit and interpretation of experimental evidence. (English) Zbl 1115.76333
Summary: 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 presence of a particular solution, and the downscale enstrophy cascade forms only under certain configurations of the dissipative terms. 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.
For Part I see E. Gkioulekas and K. K. Tung, Discrete Contin. Dyn. Syst. Ser. B 5, No. 1, 79–102 (2005; Zbl 1115.76333).

MSC:
76F02 Fundamentals of turbulence
60G60 Random fields
76F55 Statistical turbulence modeling
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