Geodesic
Nonconservative Cascades in a Shell Model of Turbulence
Russian journal of nonlinear dynamics, Tome 19 (2023) no. 3, pp. 321-331

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Developed turbulent flows in which the intervention of external forces is fundamentally important at scales where the inertial range should exist are quite common. Then the cascade processes are not conservative any more and, therefore, it is necessary to adequately describe the external forces acting in the whole range of scales. If the work of these forces has a power law scaling, then one can assume that the integral of motion changes and the preserving value becomes a quadratic quantity, which includes the dependence on the scale. We develop this idea within the framework of shell models of turbulence. We show that, in terms of nonconservative cascades, one can describe various situations, including (as a particular case) the Obukhov – Bolgiano scaling proposed for turbulence in a stratified medium and for helical turbulence with a helicity injection distributed along the spectrum.
Keywords: inertial range, nonconservative cascades, shell models.
Mots-clés : turbulence 
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P. Frick; A. Shestakov. Nonconservative Cascades in a Shell Model of Turbulence. Russian journal of nonlinear dynamics, Tome 19 (2023) no. 3, pp. 321-331. http://geodesic.mathdoc.fr/item/ND_2023_19_3_a2/