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- W2078903616 abstract "We study Leith’s model of turbulence represented by a nonlinear degenerate Q1 diffusion equation (Leith 1967 Phys. Fluids 10 1409–16, Connaughton and Nazarenko 2004 Phys. Rev. Lett. 92 044501–506). The model is constructed such that in the case of vanishing viscosity, there are two steady-state solutions: the Kolmogorov spectrum that corresponds to the cascade state and a thermodynamic equilibrium distribution. Using group analysis, we have obtained integral equations which describe all essentially different invariant Q2 solutions of the Leith equation with or without viscosity. The integral equations defining these solutions reveal new possibilities for analytical and numerical studies. In these equations, the presence of arbitrary constants allows one to solve them for different boundary conditions. We have proved existence and uniqueness for such boundary value problems." @default.
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- W2078903616 date "2014-04-17" @default.
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- W2078903616 title "Invariant solutions for the nonlinear diffusion model of turbulence" @default.
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- W2078903616 doi "https://doi.org/10.1088/1751-8113/47/18/185501" @default.
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