Abstract
The closure method developed in earlier papers [J. Qian, Phys. Fluids 26, 2098 (1983); 27, 2412 (1984)] is applied to the study of the inverse energy cascade in two-dimensional turbulence. The resultant inertial-range energy spectrum is E(k)=2.58g0.244ε2/3k−5/3. Here g is a localization factor and ε is the rate of energy cascade. This result is compatible with the numerical experiments by Lilly [D. K. Lilly, Phys. Fluids Suppl. II 12, 24 (1969)], Siggia and Aref [E. D. Siggia and H. Aref, Phys. Fluids 24, 171 (1981)], and Frisch and Sulem [U. Frisch and P. L. Sulem, Phys. Fluids 27, 1921 (1984)].
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