Nonlocal Phenomenology for anisotropic MHD turbulence

A non-local cascade model for anisotropic MHD turbulence in the presence of a guiding magnetic field is proposed. The model takes into account that (a) energy cascades in an anisotropic manner and as a result a different estimate for the cascade rate in the direction parallel and perpendicular to the guiding field is made. (b) the interactions that result in the cascade are between different scales. Eddies with wave numbers $k_\|$ and $k_\perp$ interact with eddies with wave numbers $q_\|,q_\perp$ such that a resonance condition between the wave numbers $q_\|,q_\perp$ and $k_\|,k_\perp$ holds. As a consequence energy from the eddy with wave numbers $k_\|$ and $k_\perp$ cascades due to interactions with eddies located in the resonant manifold whose wavenumbers are determined by: $q_\|\simeq \epsilon^{{1}/{3}}k_\perp^{2/3}/B$, $q_\perp=k_\perp$ and energy will cascade along the lines $k_\|\sim C+k_\perp^{2/3} \epsilon^{1/3}/B_0$. For a uniform energy injection rate in the parallel direction the resulting energy spectrum is $E(k_\|,k_\perp)\simeq \epsilon^{2/3}k_\|^{-1}k_\perp^{-5/3}$. For a general forcing however the model suggests a non-universal behavior. The connections with previous models, numerical simulations and weak turbulence theory are discussed.Comment: Submited to Astophys. Let

Condensates in rotating turbulent flows

Using a large number of numerical simulations we examine the steady state of rotating turbulent flows in triple periodic domains, varying the Rossby number $Ro$ (that measures the inverse rotation rate) and the Reynolds number $Re$ (that measures the strength of turbulence). The examined flows are sustained by either a helical or a non-helical Roberts force, that is invariant along the axis of rotation. The forcing acts at a wavenumber $k_f$ such that $k_fL=4$, where $2\pi L$ is the size of the domain. Different flow behaviours were obtained as the parameters are varied. Above a critical rotation rate the flow becomes quasi two dimensional and transfers energy to the largest scales of the system forming large coherent structures known as condensates. We examine the behaviour of these condensates and their scaling properties close and away from this critical rotation rate. Close to the the critical rotation rate the system transitions super-critically to the condensate state displaying a bimodal behaviour oscillating randomly between an incoherent-turbulent state and a condensate state. Away from the critical rotation rate, it is shown that two distinct mechanisms can saturate the growth of the large scale energy. The first mechanism is due to viscous forces and is similar to the saturation mechanism observed for the inverse cascade in two-dimensional flows. The second mechanism is independent of viscosity and relies on the breaking of the two-dimensionalization condition of the rotating flow. The two mechanisms predict different scaling with respect to the control parameters of the system (Rossby and Reynolds), which are tested with the present results of the numerical simulations. A phase space diagram in the $Re,Ro$ parameter plane is sketched

The Lorentz force effect on the On-Off dynamo intermittency

An investigation of the dynamo instability close to the threshold produced by an ABC forced flow is presented. We focus on the on-off intermittency behavior of the dynamo and the counter-effect of the Lorentz force in the non-linear stage of the dynamo. The Lorentz force drastically alters the statistics of the turbulent fluctuations of the flow and reduces their amplitude. As a result much longer burst (on-phases) are observed than what is expected based on the amplitude of the fluctuations in the kinematic regime of the dynamo. For large Reynolds numbers, the duration time of the ``On'' phase follows a power law distribution, while for smaller Reynolds numbers the Lorentz force completely kills the noise and the system transits from a chaotic state into a ``laminar'' time periodic flow. The behavior of the On-Off intermittency as the Reynolds number is increased is also examined. The connections with dynamo experiments and theoretical modeling are discussed.Comment: 8 page