Finite-temperature effects in helical quantum turbulence

We perform a study of the evolution of helical quantum turbulence at different temperatures by solving numerically the Gross-Pitaevskii and the stochastic Ginzburg-Landau equations, using up to 40963 grid points with a pseudospectral method. We show that for temperatures close to the critical one, the fluid described by these equations can act as a classical viscous flow, with the decay of the incompressible kinetic energy and the helicity becoming exponential. The transition from this behavior to the one observed at zero temperature is smooth as a function of temperature. Moreover, the presence of strong thermal effects can inhibit the development of a proper turbulent cascade. We provide Ansätze for the effective viscosity and friction as a function of the temperature.Fil: Clark Di Leoni, Patricio. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina. University of Rome Tor Vergata; ItaliaFil: Mininni, Pablo Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Brachet, Marc E.. Universite Pierre et Marie Curie; Franci

Kelvin waves, mutual friction, and fluctuations in the Gross-Pitaevskii model

In this work we first briefly review some of the mutual friction effects on vortex lines and rings that were obtained in the context of the truncated Gross-Pitaevskii equation in references Krstulovic \& Brachet [Phys.~Rev.~E \textbf{83}(6), 066311 and Phys.~Rev.~B \textbf{83}132506 (2011)], with particular attention to the anomalous slowdown of rings produced by thermally excited Kelvin waves. We then study the effect of mutual friction on the relaxation and fluctuations of Kelvin waves on straight vortex lines by comparing the results of full $3D$ direct simulations of the truncated Gross-Pitaevskii equation with a simple stochastic Local-Induction-Approximation model with mutual friction and thermal noise included. This new model allows us to determine the mutual friction coefficient $\alpha$ and $\alpha'$ for the truncated Gross-Pitaevskii equation

Dynamics of partially thermalized solutions of the Burgers equation

The spectrally truncated, or finite dimensional, versions of several equations of inviscid flows display transient solutions which match their viscous counterparts, but which eventually lead to thermalized states in which energy is in equipartition between all modes. Recent advances in the study of the Burgers equation show that the thermalization process is triggered after the formation of sharp localized structures within the flow called "tygers." We show that the process of thermalization first takes place in well defined subdomains, before engulfing the whole space. Using spatio-temporal analysis on data from numerical simulations, we study propagation of tygers and find that they move at a well defined mean speed that can be obtained from energy conservation arguments.Fil: Clark Di Leoni, Patricio. University of Rome “Tor Vergata”; Italia. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Mininni, Pablo Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Brachet, Marc E.. Université Paris Diderot - Paris 7; Franci

Spatio-temporal detection of Kelvin waves in quantum turbulence simulations

We present evidence of Kelvin excitations in space-time resolved spectra of numerical simulations of quantum turbulence. Kelvin waves are transverse and circularly polarized waves that propagate along quantized vortices, for which the restitutive force is the tension of the vortex line, and which play an important role in theories of superfluid turbulence. We use the Gross-Pitaevskii equation to model quantum flows, letting an initial array of well-organized vortices develop into a turbulent bundle of intertwined vortex filaments. By achieving high spatial and temporal resolution we are able to calculate space-time resolved mass density and kinetic energy spectra. Evidence of Kelvin and sound waves is clear in both spectra. Identification of the waves allows us to extract the spatial spectrum of Kelvin waves, clarifying their role in the transfer of energ

Long-time properties of MHD turbulence and the role of symmetries

We investigate long-time properties of three-dimensional MHD turbulence in the absence of forcing and examine in particular the role played by the quadratic invariants of the system and by the symmetries of the initial configurations. We observe that, when sufficient accuracy is used, initial conditions with a high degree of symmetries, as in the absence of helicity, do not travel through parameter space over time whereas by perturbing these solutions either explicitly or implicitly using for example single precision for long times, the flows depart from their original behavior and can become either strongly helical, or have a strong alignment between the velocity and the magnetic field. When the symmetries are broken, the flows evolve towards different end states, as predicted by statistical arguments for non-dissipative systems with the addition of an energy minimization principle, as already analyzed in \cite{stribling_90} for random initial conditions using a moderate number of Fourier modes. Furthermore, the alignment properties of these flows, between velocity, vorticity, magnetic potential, induction and current, correspond to the dominance of two main regimes, one helically dominated and one in quasi-equipartition of kinetic and magnetic energy. We also contrast the scaling of the ratio of magnetic energy to kinetic energy as a function of wavenumber to the ratio of eddy turn-over time to Alfv\'en time as a function of wavenumber. We find that the former ratio is constant with an approximate equipartition for scales smaller than the largest scale of the flow whereas the ratio of time scales increases with increasing wavenumber.Comment: 14 pages, 6 figure

Gravity- and temperature-driven phase transitions in a model for collapsed axionic condensates

We show how to use the cubic-quintic Gross-Pitaevskii-Poisson equation (cq-GPPE) and the cubic-quintic Stochastic Ginzburg-Landau-Poisson equation (cq-SGLPE) to investigate the gravitational collapse of a tenuous axionic gas into a collapsed axionic condensate for both zero and finite temperature $T$. At $T=0$, we use a Gaussian Ansatz for a spherically symmetric density to obtain parameter regimes in which we might expect to find compact axionic condensates. We then go beyond this Ansatz, by using the cq-SGLPE to investigate the dependence of the axionic condensate on the gravitational strength $G$ at $T = 0$. We demonstrate that, as $G$ increases, the equilibrium configuration goes from a tenuous axionic gas, to flat sheets or $\textit{Zeldovich pancakes}$, cylindrical structures, and finally a spherical axionic condensate. By varying $G$, we show that there are first-order phase transitions, as the system goes from one of these structures to the next one; we find hysteresis loops that are associated with these transitions. We examine these states and the transitions between these states via the Fourier truncated cq-GPPE; and we also obtain the thermalized $T > 0$ states from the cq-SGLPE; the transitions between these states yield thermally driven first-order phase transitions and their associated hysteresis loops. Finally, we discuss how our cq-GPPE approach can be used to follow the spatiotemporal evolution of a rotating axionic condensate and also a rotating binary-axionic-condensate system; in particular, we demonstrate, in the former, the emergence of vortices at large angular speeds $\Omega$ and, in the latter, the rich dynamics of the mergers of the components of this binary system, which can yield vortices in the process of merging.Comment: 13 pages, 8 figure