Multiscaling in superfluid turbulence: A shell-model study

We examine the multiscaling behavior of the normal- and superfluid-velocity structure functions in three-dimensional superfluid turbulence by using a shell model for the three-dimensional (3D) Hall-Vinen-Bekharevich-Khalatnikov (HVBK) equations. Our 3D-HVBK shell model is based on the Gledzer-Okhitani-Yamada (GOY) shell model. We examine the dependence of the multiscaling exponents on the normal-fluid fraction and the mutual-friction coefficients. Our extensive study of the 3D-HVBK shell model shows that the multiscaling behavior of the velocity structure functions in superfluid turbulence is more complicated than it is in fluid turbulence.Comment: 12 pages, 6 figure

Particles and Fields in Superfluids: Insights from the Two-dimensional Gross-Pitaevskii Equation

We carry out extensive direct numerical simulations (DNSs) to investigate the interaction of active particles and fields in the two-dimensional (2D) Gross-Pitaevskii (GP) superfluid, in both simple and turbulent flows. The particles are active in the sense that they affect the superfluid even as they are affected by it. We tune the mass of the particles, which is an important control parameter. At the one-particle level, we show how light, neutral, and heavy particles move in the superfluid, when a constant external force acts on them; in particular, beyond a critical velocity, at which a vortex-antivortex pair is emitted, particle motion can be periodic or chaotic. We demonstrate that the interaction of a particle with vortices leads to dynamics that depends sensitively on the particle characteristics. We also demonstrate that assemblies of particles and vortices can have rich, and often turbulent spatiotemporal evolution. In particular, we consider the dynamics of the following illustrative initial configurations: (a) one particle placed in front of a translating vortex-antivortex pair; (b) two particles placed in front of a translating vortex-antivortex pair; (c) a single particle moving in the presence of counter-rotating vortex clusters; and (d) four particles in the presence of counter-rotating vortex clusters. We compare our work with earlier studies and examine its implications for recent experimental studies in superfluid Helium and Bose-Einstein condensates.Comment: 24 figure

Turbulence in the two-dimensional Fourier-truncated Gross-Pitaevskii equation

We undertake a systematic, direct numerical simulation (DNS) of the two-dimensional, Fourier-truncated, Gross-Pitaevskii equation to study the turbulent evolutions of its solutions for a variety of initial conditions and a wide range of parameters. We find that the time evolution of this system can be classified into four regimes with qualitatively different statistical properties. First, there are transients that depend on the initial conditions. In the second regime, power-law scaling regions, in the energy and the occupation-number spectra, appear and start to develop; the exponents of these power-laws and the extents of the scaling regions change with time and depended on the initial condition. In the third regime, the spectra drop rapidly for modes with wave numbers $k > k_c$ and partial thermalization takes place for modes with $k < k_c$; the self-truncation wave number $k_c(t)$ depends on the initial conditions and it grows either as a power of $t$ or as $\log t$. Finally, in the fourth regime, complete-thermalization is achieved and, if we account for finite-size effects carefully, correlation functions and spectra are consistent with their nontrivial Berezinskii-Kosterlitz-Thouless forms.Comment: 30 pages, 12 figure

Homogeneous Isotropic Superfluid Turbulence in Two Dimensions: Inverse and Forward Cascades in the Hall-Vinen-Bekharevich-Khalatnikov model

We present the first direct-numerical-simulation study of the statistical properties of two-dimensional superfluid turbulence in the Hall-Vinen-Bekharevich-Khalatnikov two-fluid model. We show that both normal-fluid and superfluid energy spectra can exhibit two power-law regimes, the first associated with an inverse cascade of energy and the second with the forward cascade of enstrophy. We quantify the mutual-friction-induced alignment of normal and superfluid velocities by obtaining probability distribution functions of the angle between them and the ratio of their moduli. Our study leads to specific suggestions for experiments

The Statistical Properties of Superfluid Turbulence in 4^4He from the Hall-Vinen-Bekharevich-Khalatnikov Model

We obtain the von K\'arm\'an-Howarth relation for the stochastically forced three-dimensional Hall-Vinen-Bekharvich-Khalatnikov (3D HVBK) model of superfluid turbulence in Helium ($^4$He) by using the generating-functional approach. We combine direct numerical simulations (DNSs) and analyitcal studies to show that, in the statistically steady state of homogeneous and isotropic superfluid turbulence, in the 3D HVBK model, the probability distribution function (PDF) $P(\gamma)$, of the ratio $\gamma$ of the magnitude of the normal fluid velocity and superfluid velocity, has power-law tails that scale as $P(\gamma) \sim \gamma^3$, for $\gamma \ll 1$, and $P(\gamma) \sim \gamma^{-3}$, for $\gamma \gg 1$. Furthermore, we show that the PDF $P(\theta)$, of the angle $\theta$ between the normal-fluid velocity and superfluid velocity exhibits the following power-law behaviors: $P(\theta)\sim \theta$ for $\theta \ll \theta_*$ and $P(\theta)\sim \theta^{-4}$ for $\theta_* \ll \theta \ll 1$, where $\theta_*$ is a crossover angle that we estimate. From our DNSs we obtain energy, energy-flux, and mutual-friction-transfer spectra, and the longitudinal-structure-function exponents for the normal fluid and the superfluid, as a function of the temperature $T$, by using the experimentally determined mutual-friction coefficients for superfluid Helium $^4$He, so our results are of direct relevance to superfluid turbulence in this system.Comment: 12 pages, 3 figure

Poles, Shocks and Tygers: The Time-reversible Burgers Equation

We construct a formally time-reversible, one-dimensional forced Burgers equation by imposing a global constraint of energy conservation, wherein the constant viscosity is modified to a fluctuating state-dependent dissipation coefficient. The new system exhibits dynamical properties which bear strong similarity with those observed for the Burgers equation and can be understood using the dynamics of the poles, shocks and truncation effects such as tygers. A complex interplay of these give rise to interesting statistical regimes ranging from hydrodynamic behaviour to a completely thermalized warm phase. The end of the hydrodynamic regime is associated with the appearance of a shock in the solution and a continuous transition leading to a truncation dependent state. Beyond this, the truncation effects such as tygers and appearance of secondary discontinuity at the resonance point in the solution strongly influence the statistical properties. These disappear at the second transition, at which the global quantities exhibit a jump and attain values that are consistent with the establishment of a 'quasi-equilibrium' state characterized by energy equipartition among the Fourier modes. Our comparative analysis shows that the macroscopic statistical properties of the formally time-reversible system and the Burgers equation are equivalent in all the regimes, irrespective of the truncation effects, and this equivalence is not just limited to the hydrodynamic regime, thereby further strengthening the Gallavotti's equivalence conjecture. The properties of the system are further examined by inspecting the complex space singularities in the velocity field of the Burgers equation. Furthermore, an effective theory is proposed to describe the discontinuous transition.Comment: 25 pages, 18 figure

Multi-frequency, Multi-Epoch Study of Mrk 501: Hints for a two-component nature of the emission

Since the detection of very high energy (VHE) $\gamma$-rays from Mrk 501, its broad band emission of radiation was mostly and quite effectively modeled using one zone emission scenario. However, broadband spectral and flux variability studies enabled by the multiwavelength campaigns carried out during the recent years have revealed rather complex behavior of Mrk 501. The observed emission from Mrk 501 could be due to a complex superposition of multiple emission zones. Moreover new evidences of detection of very hard intrinsic $\gamma$-ray spectra obtained from {\it Fermi}--LAT observations have challenged the theories about origin of VHE $\gamma$-rays. Our studies based on {\it Fermi}--LAT data indicate the existence of two separate components in the spectrum, one for low energy $\gamma$-rays and the other for high energy $\gamma$-rays. Using multiwaveband data from several ground and space based instruments, in addition to HAGAR data, the spectral energy distribution of Mrk~501 is obtained for various flux states observed during 2011. In the present work, this observed broadband spectral energy distribution is reproduced with a leptonic, multi-zone Synchrotron Self-Compton model.Comment: Published in Astrophysical Journal (ApJ

Multiwavelength study of TeV Blazar Mrk421 during giant flare

Context: The nearby (z=0.031) TeV blazar Mrk421 was reported to be in a high state of flux activity since November, 2009. Aims: To investigate possible changes in the physical parameters of Mrk421 during its high state of activity using multiwavelength data. Methods: We have observed this source in bright state using High Altitude GAmma Ray (HAGAR) telescope array at energies above 250 GeV during February 13 - 19, 2010. Optical, X-ray and gamma-ray archival data are also used to obtain the SEDs and light curves. Results: Mrk421 was found to undergo one of its brightest flaring episodes on February 17, 2010 by various observations in X-rays and gamma-rays. HAGAR observations during February 13 - 19, 2010 at the energies above 250 GeV show an enhancement in the flux level, with a maximum flux of ~ 7 Crab units being detected on February 17, 2010. We present the spectral energy distributions during this flaring episode and investigate the correlation of the variability in X-ray and gamma-ray bands. Conclusions: Our multiwavelength study suggests that the flare detected during February 16 and 17, 2010 could arise due to a passing shock in the jet.Comment: 9 pages, 10 figures, Accepted for publication in Astronomy and Astrophysics (A & A