arXiv subjects

Raffaele Marino

Publications and source records attributed to Raffaele Marino.

62 records · Page 4Linked to original sources

arXiv2016

Advective-diffusive motion on large scales from small-scale dynamics with an internal symmetry

We consider coupled diffusions in $n$-dimensional space and on a compact manifold and the resulting effective advective-diffusive motion on large scales in space. The effective drift (advection) and effective diffusion are determined as a solvability conditions in a multi-scale analysis. As an example we consider coupled diffusions in $3$-dimensional space and on the group manifold $SO(3)$ of proper rotations, generalizing results obtained by H. Brenner (1981). We show in detail how the analysis can be conveniently be carried out using local charts and invariance arguments. As a further example we consider coupled diffusions in $2$-dimensional complex space and on the group manifold $SU(2)$. We show that although the local operators may be the same as for $SO(3)$, due to the global nature of the solvability conditions the resulting diffusion will be different, and generally more isotropic.

cond-mat.stat-mech↗

arXiv2016

Diffusion of a Brownian ellipsoid in a force field

We calculate the effective long-term convective velocity and dispersive motion of an ellipsoidal Brownian particle in three dimensions when it is subjected to a constant external force. This long-term motion results as a "net" average behavior from the particle rotation and translation on short time scales. Accordingly, we apply a systematic multi-scale technique to derive the effective equations of motion valid on long times. We verify our theoretical results by comparing them to numerical simulations.

cond-mat.stat-mech↗

arXiv2016

Entropy production of a Brownian ellipsoid in the overdamped limit

We analyze the translational and rotational motion of an ellipsoidal Brownian particle from the viewpoint of stochastic thermodynamics. The particle's Brownian motion is driven by external forces and torques and takes place in an heterogeneous thermal environment where friction coefficients and (local) temperature depend on space and time. Our analysis of the particle's stochastic thermodynamics is based on the entropy production associated with single particle trajectories. It is motivated by the recent discovery that the overdamped limit of vanishing inertia effects (as compared to viscous fricion) produces a so-called "anomalous" contribution to the entropy production, which has no counterpart in the overdamped approximation, when inertia effects are simply discarded. Here, we show that rotational Brownian motion in the overdamped limit generates an additional contribution to the "anomalous" entropy. We calculate its specific form by performing a systematic singular perturbation analysis for the generating function of the entropy production. As a side result, we also obtain the (well-known) equations of motion in the overdamped limit. We furthermore investigate the effects of particle shape and give explicit expressions of the "anomalous entropy" for prolate and oblate spheroids and for near-spherical Brownian particles.

cond-mat.stat-mech↗

arXiv2015

Interplay of waves and eddies in rotating stratified turbulence and the link with kinetic-potential energy partition

The interplay between waves and eddies in stably stratified rotating flows is investigated by means of world-class direct numerical simulations using up to $3072^3$ grid points. Strikingly, we find that the shift from vortex to wave dominated dynamics occurs at a wavenumber $k_R$ which does not depend on Reynolds number, suggesting that partition of energy between wave and vortical modes is not sensitive to the development of turbulence at the smaller scales. We also show that $k_R$ is comparable to the wavenumber at which exchanges between kinetic and potential modes stabilize at close to equipartition, emphasizing the role of potential energy, as conjectured in the atmosphere and the oceans. Moreover, $k_R$ varies as the inverse of the Froude number as explained by the scaling prediction proposed, consistent with recent observations and modeling of the Mesosphere-Lower Thermosphere and of the ocean.

physics.flu-dyn↗

arXiv2015

Waves and vortices in the inverse cascade regime of stratified turbulence with or without rotation

We study the partition of energy between waves and vortices in stratified turbulence, with or without rotation, for a variety of parameters, focusing on the behavior of the waves and vortices in the inverse cascade of energy towards the large scales. To this end, we use direct numerical simulations in a cubic box at a Reynolds number Re=1000, with the ratio between the Brunt-Väisälä frequency N and the inertial frequency f varying from 1/4 to 20, together with a purely stratified run. The Froude number, measuring the strength of the stratification, varies within the range 0.02 < Fr < 0.32. We find that the inverse cascade is dominated by the slow quasi-geostrophic modes. Their energy spectra and fluxes exhibit characteristics of an inverse cascade, even though their energy is not conserved. Surprisingly, the slow vortices still dominate when the ratio N/f increases, also in the stratified case, although less and less so. However, when N/f increases, the inverse cascade of the slow modes becomes weaker and weaker, and it vanishes in the purely stratified case. We discuss how the disappearance of the inverse cascade of energy with increasing N/f can be interpreted in terms of the waves and vortices, and identify three major effects that can explain this transition based on inviscid invariants arguments.

physics.flu-dyn↗

arXiv2014

Restricted Equilibrium and the Energy Cascade in Rotating and Stratified Flows

Most of the turbulent flows appearing in nature (e.g. geophysical and astrophysical flows) are subjected to strong rotation and stratification. These effects break the symmetries of classical, homogenous isotropic turbulence. In doing so, they introduce a natural decomposition of phase space in terms of wave modes and potential vorticity modes. The appearance of a new time scale associated to the propagation of waves, in addition to the eddy turnover time, increases the complexity of the energy transfers between the various scales; nonlinearly interacting waves may dominate at some scales while balanced motion may prevail at others. In the end, it is difficult to predict \emph{a priori} if the energy cascades downscale as in homogeneous isotropic turbulence, upscale as expected from balanced dynamics, or follows yet another phenomenology. In this paper, we suggest a theoretical approach based on equilibrium statistical mechanics for the ideal system, inspired from the restricted partition function formalism introduced in metastability studies. In this framework, we show analytically that in the presence of rotation, when the dynamics is restricted to the slow modes, the equilibrium energy spectrum features an infrared divergence characteristic of an inverse cascade regime, whereas this is not the case for purely stratified flows.

physics.flu-dyn↗

arXiv2013

On the emergence of helicity in rotating stratified turbulence

We perform numerical simulations of decaying rotating stratified turbulence and show, in the Boussinesq framework, that helicity (velocity-vorticity correlation), as observed in super-cell storms and hurricanes, is spontaneously created due to an interplay between buoyancy and rotation common to large-scale atmospheric and oceanic flows. Helicity emerges from the joint action of eddies and of inertia-gravity waves (with inertia and gravity with respective associated frequencies $f$ and $N$), and it occurs when the waves are sufficiently strong. For $N/f < 3$ the amount of helicity produced is correctly predicted by a quasi-linear balance equation. Outside this regime, and up to the highest Reynolds number obtained in this study, namely $Re\approx 10000$, helicity production is found to be persistent for $N/f$ as large as $\approx 17$, and for $ReFr^2$ and $ReRo^2 $ respectively as large as $\approx 100$ and $\approx 24000$.

physics.flu-dyn↗

arXiv2007

Observation of inertial energy cascade in interplanetary space plasma

We show in this article direct evidence for the presence of an inertial energy cascade, the most characteristic signature of hydromagnetic turbulence (MHD), in the solar wind as observed by the Ulysses spacecraft. After a brief rederivation of the equivalent of Yaglom's law for MHD turbulence, we show that a linear relation is indeed observed for the scaling of mixed third order structure functions involving Elsässer variables. This experimental result, confirming the prescription stemming from a theorem for MHD turbulence, firmly establishes the turbulent character of low-frequency velocity and magnetic field fluctuations in the solar wind plasma.

astro-ph↗