A preliminary study of the detection of geomorphological features over northeast Africa by satellite radiation measurements in the visible and infrared

Detecting geomorphological features over Northeast Africa by Nimbus 2 visible and infrared radiation measurement

Inverse cascades in turbulence and the case of rotating flows

We first summarize briefly several properties concerning the dynamics of two-dimensional (2D) turbulence, with an emphasis on the inverse cascade of energy to the largest accessible scale of the system. In order to study a similar phenomenon in three-dimensional (3D) turbulence undergoing strong solid-body rotation, we test a previously developed Large Eddy Simulation (LES) model against a high-resolution direct numerical simulation of rotating turbulence on a grid of $3072^3$ points. We then describe new numerical results on the inverse energy cascade in rotating flows using this LES model and contrast the case of 2D versus 3D forcing, as well as non-helical forcing (i.e., with weak overall alignment between velocity and vorticity) versus the fully helical Beltrami case, both for deterministic and random forcing. The different scaling of the inverse energy cascade can be attributed to the dimensionality of the forcing, with, in general, either a $k_{\perp}^{-3}$ or a $k_{\perp}^{-5/3}$ energy spectrum of slow modes at large scales, perpendicular referring to the direction of rotation. We finally invoke the role of shear in the case of a strongly anisotropic deterministic forcing, using the so-called ABC flow.Comment: 10 pages, 3 figure

Conformal invariance in three-dimensional rotating turbulence

We examine three--dimensional turbulent flows in the presence of solid-body rotation and helical forcing in the framework of stochastic Schramm-L\"owner evolution curves (SLE). The data stems from a run on a grid of $1536^3$ points, with Reynolds and Rossby numbers of respectively 5100 and 0.06. We average the parallel component of the vorticity in the direction parallel to that of rotation, and examine the resulting $_\textrm{z}$ field for scaling properties of its zero-value contours. We find for the first time for three-dimensional fluid turbulence evidence of nodal curves being conformal invariant, belonging to a SLE class with associated Brownian diffusivity $\kappa=3.6\pm 0.1$. SLE behavior is related to the self-similarity of the direct cascade of energy to small scales in this flow, and to the partial bi-dimensionalization of the flow because of rotation. We recover the value of $\kappa$ with a heuristic argument and show that this value is consistent with several non-trivial SLE predictions.Comment: 4 pages, 3 figures, submitted to PR

Energy spectra stemming from interactions of Alfven waves and turbulent eddies

We present a numerical analysis of an incompressible decaying magnetohydrodynamic turbulence run on a grid of 1536^3 points. The Taylor Reynolds number at the maximum of dissipation is ~1100, and the initial condition is a superposition of large scale ABC flows and random noise at small scales, with no uniform magnetic field. The initial kinetic and magnetic energies are equal, with negligible correlation. The resulting energy spectrum is a combination of two components, each moderately resolved. Isotropy obtains in the large scales, with a spectral law compatible with the Iroshnikov-Kraichnan theory stemming from the weakening of nonlinear interactions due to Alfven waves; scaling of structure functions confirms the non-Kolmogorovian nature of the flow in this range. At small scales, weak turbulence emerges with a k_{\perp}^{-2} spectrum, the perpendicular direction referring to the local quasi-uniform magnetic field.Comment: 4 pages, 4 figure

Numerical study of dynamo action at low magnetic Prandtl numbers

We present a three--pronged numerical approach to the dynamo problem at low magnetic Prandtl numbers $P_M$. The difficulty of resolving a large range of scales is circumvented by combining Direct Numerical Simulations, a Lagrangian-averaged model, and Large-Eddy Simulations (LES). The flow is generated by the Taylor-Green forcing; it combines a well defined structure at large scales and turbulent fluctuations at small scales. Our main findings are: (i) dynamos are observed from $P_M=1$ down to $P_M=10^{-2}$; (ii) the critical magnetic Reynolds number increases sharply with $P_M^{-1}$ as turbulence sets in and then saturates; (iii) in the linear growth phase, the most unstable magnetic modes move to small scales as $P_M$ is decreased and a Kazantsev $k^{3/2}$ spectrum develops; then the dynamo grows at large scales and modifies the turbulent velocity fluctuations.Comment: 4 pages, 4 figure

Depletion of Nonlinearity in Magnetohydrodynamic Turbulence: Insights from Analysis and Simulations

We build on recent developments in the study of fluid turbulence [Gibbon \textit{et al.} Nonlinearity 27, 2605 (2014)] to define suitably scaled, order-$m$ moments, $D_m^{\pm}$, of $\omega^\pm= \omega \pm j$, where $\omega$ and $j$ are, respectively, the vorticity and current density in three-dimensional magnetohydrodynamics (MHD). We show by mathematical analysis, for unit magnetic Prandtl number $P_M$, how these moments can be used to identify three possible regimes for solutions of the MHD equations; these regimes are specified by inequalities for $D_m^{\pm}$ and $D_1^{\pm}$. We then compare our mathematical results with those from our direct numerical simulations (DNSs) and thus demonstrate that 3D MHD turbulence is like its fluid-turbulence counterpart insofar as all solutions, which we have investigated, remain in \textit{only one of these regimes}; this regime has depleted nonlinearity. We examine the implications of our results for the exponents $q^{\pm}$ that characterize the power-law dependences of the energy spectra $\mathcal{E}^{\pm}(k)$ on the wave number $k$, in the inertial range of scales. We also comment on (a) the generalization of our results to the case $P_M \neq 1$ and (b) the relation between $D_m^{\pm}$ and the order-$m$ moments of gradients of hydrodynamic fields, which are used in characterizing intermittency in turbulent flows.Comment: 14 pages, 3 figure