Three-dimensional Iroshnikov-Kraichnan turbulence in a mean magnetic field

Forced, weak MHD turbulence with guide field is shown to adopt different regimes, depending on the magnetic excess of the large forced scales. When the magnetic excess is large enough, the classical perpendicular cascade with $5/3$ scaling is obtained, while when equipartition is imposed, an isotropic $3/2$ scaling appears in all directions with respect to the mean field (\cite{2010PhRvE..82b6406G} or GM10). We show here that the $3/2$ scaling of the GM10 regime is not ruled by a small-scale cross-helicity cascade, and propose that it is a 3D extension of a perpendicular weak Iroshnikov-Kraichnan (IK) cascade. We analyze in detail the structure functions in real space and show that they closely follow the critical balance relation both in the local frame and the global frame: we show that there is no contradiction between this and the isotropic $3/2$ scaling of the spectra. We propose a scenario explaining the spectral structure of the GM10 regime, that starts with a perpendicular weak IK cascade and extends to 3D by using quasi-resonant couplings. The quasi-resonance condition happens to reduce the energy flux in the same way as is done in the weak perpendicular cascade, so leading to a $3/2$ scaling in all directions. We discuss the possible applications of these findings to solar wind turbulence.Comment: Major re-write of manuscrip

The friction factor of two-dimensional rough-boundary turbulent soap film flows

We use momentum transfer arguments to predict the friction factor $f$ in two-dimensional turbulent soap-film flows with rough boundaries (an analogue of three-dimensional pipe flow) as a function of Reynolds number Re and roughness $r$, considering separately the inverse energy cascade and the forward enstrophy cascade. At intermediate Re, we predict a Blasius-like friction factor scaling of $f\propto\textrm{Re}^{-1/2}$ in flows dominated by the enstrophy cascade, distinct from the energy cascade scaling of $\textrm{Re}^{-1/4}$. For large Re, $f \sim r$ in the enstrophy-dominated case. We use conformal map techniques to perform direct numerical simulations that are in satisfactory agreement with theory, and exhibit data collapse scaling of roughness-induced criticality, previously shown to arise in the 3D pipe data of Nikuradse.Comment: 4 pages, 3 figure

Inertial range scaling of the scalar flux spectrum in two-dimensional turbulence

Two-dimensional statistically stationary isotropic turbulence with an imposed uniform scalar gradient is investigated. Dimensional arguments are presented to predict the inertial range scaling of the turbulent scalar flux spectrum in both the inverse cascade range and the enstrophy cascade range for small and unity Schmidt numbers. The scaling predictions are checked by direct numerical simulations and good agreement is observed

A stochastic model of cascades in 2D turbulence

The dual cascade of energy and enstrophy in 2D turbulence cannot easily be understood in terms of an analog to the Richardson-Kolmogorov scenario describing the energy cascade in 3D turbulence. The coherent up- and downscale fluxes points to non-locality of interactions in spectral space, and thus the specific spatial structure of the flow could be important. Shell models, which lack spacial structure and have only local interactions in spectral space, indeed fail in reproducing the correct scaling for the inverse cascade of energy. In order to exclude the possibility that non-locality of interactions in spectral space is crucial for the dual cascade, we introduce a stochastic spectral model of the cascades which is local in spectral space and which shows the correct scaling for both the direct enstrophy - and the inverse energy cascade.Comment: 4 pages, 3 figure

Translationally invariant cumulants in energy cascade models of turbulence

In the context of random multiplicative energy cascade processes, we derive analytical expressions for translationally invariant one- and two-point cumulants in logarithmic field amplitudes. Such cumulants make it possible to distinguish between hitherto equally successful cascade generator models and hence supplement lowest-order multifractal scaling exponents and multiplier distributions.Comment: 11 pages, 3 figs, elsart.cls include