Nonconservative Cascades in a Shell Model of Turbulence

    Received 28 June 2023; accepted 09 August 2023; published 20 September 2023

    2023, Vol. 19, no. 3, pp.  321-331

    Author(s): Frick P., Shestakov A.

    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: turbulence, inertial range, nonconservative cascades, shell models
    Citation: Frick P., Shestakov A., Nonconservative Cascades in a Shell Model of Turbulence, Rus. J. Nonlin. Dyn., 2023, Vol. 19, no. 3, pp.  321-331

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