Scaling Exponents of Strong Turbulence in the Eddy Viscosity Approximation

A dynamic equation for velocity structure functions $S_{n}(r) = <(u(x)-u(x'))^{n}>$ in strong turbulence is derived in the one-loop (eddy viscosity) approximation. This homogemeous differential equation yields scaling exponents $ξ_{n}$ in the relations $S_{n}(r)\propto r^{ξ_{n}}$ which are in a very good agreement with experimental data.

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