Peter Frick

    Korolyov st.1, 614018, Perm, Russia


    Frick P., Shestakov A.
    Nonconservative Cascades in a Shell Model of Turbulence
    2023, Vol. 19, no. 3, pp.  321-331
    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
    Frick P., Okatev R., Sokoloff D.
    Spectral Properties of Low-order Dynamo Systems
    2022, Vol. 18, no. 2, pp.  289-296
    The solar 11-year activity cycle is a famous manifestation of magnetic activity of celestial bodies. The physical nature of the solar cycle is believed to be large-scale magnetic field excitation in the form of a wave of a quasi-stationary magnetic field propagating from middle solar latitudes to the solar equator. The power spectrum of solar magnetic activity recorded in sunspot data and underlying solar dynamo action contains quite a stable oscillation known as the 11-year cycle as well as the continuous component and some additional weak peaks. We consider a loworder model for the solar dynamo. We show that in some range of governing parameters this model can reproduce spectra with pronounced dominating frequency and wide spectral peaks in the low-frequency region. The spectra obtained are qualitatively similar to the observed solar activity spectrum.
    Keywords: solar activity, solar dynamo, low-order models, spectral properties
    Citation: Frick P., Okatev R., Sokoloff D.,  Spectral Properties of Low-order Dynamo Systems, Rus. J. Nonlin. Dyn., 2022, Vol. 18, no. 2, pp.  289-296

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