Multiscaling in superfluid turbulence: A shell-model study

Statistical properties of superfluid turbulence in ^{4}He from the Hall-Vinen-Bekharevich-Khalatnikov model

We obtain the von Kármán-Howarth relation for the stochastically forced three-dimensional (3D) Hall-Vinen-Bekharevich-Khalatnikov (HVBK) model of superfluid turbulence in helium (^{4}He) by using the generating-functional approach. We combine direct numerical simulations (DNSs) and analytical studies to show that, in the statistically steady state of homogeneous and isotropic superfluid turbulence, in the 3D HVBK model, the probability distribution function (PDF) P(γ), of the ratio γ of the magnitude of the normal fluid velocity and superfluid velocity, has power-law tails that scale as P(γ)∼γ^{3}, for γ≪1, and P(γ)∼γ^{-3}, for γ≫1. Furthermore, we show that the PDF P(θ) of the angle θ between the normal-fluid velocity and superfluid velocity exhibits the following power-law behaviors: P(θ)∼θ for θ≪θ_{*} and P(θ)∼θ^{-4} for θ_{*}≪θ≪1, where θ_{*} is a crossover angle that we estimate. From our DNSs we obtain energy, energy-flux, and mutual-friction-transfer spectra, as well as the longitudinal-structure-function exponents for the normal fluid and the superfluid, as a function of the temperature T, by using the experimentally determined mutual-friction coefficients for superfluid helium ^{4}He, so our results are of direct relevance to superfluid turbulence in this system.

Dynamic scaling in rotating turbulence: A shell model study

We investigate the scaling form of appropriate timescales extracted from time-dependent correlation functions in rotating turbulent flows. In particular, we obtain precise estimates of the dynamic exponents z_{p}, associated with the timescales, and their relation with the more commonly measured equal-time exponents ζ_{p}. These theoretical predictions, obtained by using the multifractal formalism, are validated through extensive numerical simulations of a shell model for such rotating flows.

Dynamic multiscaling in magnetohydrodynamic turbulence

We present a study of the multiscaling of time-dependent velocity and magnetic-field structure functions in homogeneous, isotropic magnetohydrodynamic (MHD) turbulence in three dimensions. We generalize the formalism that has been developed for analogous studies of time-dependent structure functions in fluid turbulence to MHD. By carrying out detailed numerical studies of such time-dependent structure functions in a shell model for three-dimensional MHD turbulence, we obtain both equal-time and dynamic scaling exponents.