Geodesic
Renormalization group in turbulence theory: Exactly solvable Heisenberg model
Teoretičeskaâ i matematičeskaâ fizika, Tome 115 (1998) no. 2, pp. 245-262 Cet article a éte moissonné depuis la source Math-Net.Ru

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An exactly solvable Heisenberg model describing the spectral balance conditions for the energy of a turbulent liquid is investigated in the renormalization group (RG) framework. The model has RG symmetry with the exact RG functions (the $\beta$-function and the anomalous dimension $\gamma$) found in two different renormalization schemes. The solution to the RG equations coincides with the known exact solution of the Heisenberg model and is compared with the results from the $\varepsilon$ expansion, which is the only tool for describing more complex models of developed turbulence (the formal small parameter $\varepsilon$ of the RG expansion is introduced by replacing a $\delta$-function-like pumping function in the random force correlator by a powerlike function). The results, which are valid for asymptotically small $\varepsilon$, can be extrapolated to the actual value $\varepsilon=2$, and the few first terms of the $\varepsilon$ expansion already yield a reasonable numerical estimate for the Kolmogorov constant in the turbulence energy spectrum. 
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     title = {Renormalization group in turbulence theory: {Exactly} solvable {Heisenberg} model},
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}
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L. Ts. Adzhemyan; N. V. Antonov. Renormalization group in turbulence theory: Exactly solvable Heisenberg model. Teoretičeskaâ i matematičeskaâ fizika, Tome 115 (1998) no. 2, pp. 245-262. http://geodesic.mathdoc.fr/item/TMF_1998_115_2_a6/

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