Dual cascade and dissipation mechanisms in helical quantum turbulence

Leoni, Patricio Clark Di; Mininni, Pablo D.; Brachet, Marc

doi:10.1103/physreva.95.053636

Cited by 45 publications

(71 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This difference might be due to the fact that the present simulations are freely decaying, and have no force acting to sustain turbulence. The existence of two simultaneous inertial ranges separated by a bottleneck was also observed before in high resolution simulations using dif-ferent initial conditions [28], but was not visible in the N = 512 DNS of a TG flow in [24] possibly as a result of the limited spatial resolution in that study. To further illustrate these ranges, and the scale separation involved, in Fig.…”

Section: A High Resolution Gpe Runs At T =supporting

confidence: 65%

Quantitative estimation of effective viscosity in quantum turbulence

et al. 2019

Self Cite

View full text Add to dashboard Cite

We study freely decaying quantum turbulence by performing high resolution numerical simulations of the Gross-Pitaevskii equation (GPE) in the Taylor-Green geometry. We use resolutions ranging from 1024 3 to 4096 3 grid points. The energy spectrum confirms the presence of both a Kolmogorov scaling range for scales larger than the intervortex scale , and a second inertial range for scales smaller than . Vortex line visualizations show the existence of substructures formed by a myriad of small-scale knotted vortices. Next, we study finite temperature effects in the decay of quantum turbulence by using the stochastic Ginzburg-Landau equation to generate thermal states, and then by evolving a combination of these thermal states with the Taylor-Green initial conditions using the GPE. We extract the mean free path out of these simulations by measuring the spectral broadening in the Bogoliubov dispersion relation obtained from spatio-temporal spectra, and use it to quantify the effective viscosity as a function of the temperature. Finally, in order to compare the decay of high temperature quantum and that of classical flows, and to further calibrate the estimations of viscosity from the mean free path in the GPE simulations, we perform low Reynolds number simulations of the Navier-Stokes equations. * Electronic address: research.vishwanath@gmail.com † Electronic address: mininni@df.uba.ar ‡ Electronic address: krstulovic@oca.eu § Electronic address: patricio.clark@roma2.infn.it ¶ Electronic address: brachet@physique.ens.fr

show abstract

Section: A High Resolution Gpe Runs At T =supporting

confidence: 65%

Quantitative estimation of effective viscosity in quantum turbulence

et al. 2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…Such a study has been carried out in the literature using the local formulation of the GP equation (Eq. 10) [29,47], that we repeat here for the nonlocal version. Decomposing the conserved total energy as the sum of various components, we identify the part associated to kinetic energy as being the average (over space and time, the time integration starting at t rec until the end of the simulation) of the norm square of the vector √ ρv, a vector field being itself decomposed into a divergence-free part (i.e.…”

Section: Numerical Investigation Of Reconnection Of a Set Of Initmentioning

confidence: 99%

Structure, dynamics, and reconnection of vortices in a nonlocal model of superfluids

2018

View full text Add to dashboard Cite

We study the reconnection of vortices in a quantum fluid with a roton minimum, by numerically solving the Gross-Pitaevskii (GP) equations. A non-local interaction potential is introduced to mimic the experimental dispersion relation of superfluid 4 He. We begin by choosing a functional shape of the interaction potential that allows to reproduce in an approximative way the so-called roton minimum observed in experiments, without leading to spurious local crystallization events. We then follow and track the phenomenon of reconnection starting from a set of two perpendicular vortices. A precise and quantitative study of various quantities characterizing the evolution of this phenomenon is proposed: this includes the evolution of statistics of several hydrodynamical quantities of interest, and the geometrical description of a observed helical wave packet that propagates along the vortex cores. Those geometrical properties are systematically compared to the predictions of the Local Induction Approximation (LIA), showing similarities and differences. The introduction of the roton minimum in the model does not change the macroscopic properties of the reconnection event but the microscopic structure of the vortices differs. Structures are generated at the roton scale and helical waves are evidenced along the vortices. However, contrary to what is expected in classical viscous or inviscid incompressible flows, the numerical simulations do not evidence the generation of structures at smaller or larger scales than the typical atomic size.

show abstract

“…At zero or near zero temperatures the GPE, for which quantized vortices are exact solutions which can reconnect with no extra ad-hoc assumptions, is a very succesful model for BECs [19]. Moreover, a hydrodynamic analogy can be easily obtained from the GPE by means of the Madelung transformation, and it has been shown that at the larger scales its turbulent solutions match those of classical turbulence [20,21]. There are various ways of generalizing the GPE for studying finite-temperature effects [22].…”

Section: Introductionmentioning

confidence: 99%

“…The usual picture of quantum turbulence (see, for example, [1]) goes by the following: while at the larger scales the nonlinear energy transfer in quantum flows is mediated by the interaction between vortices and reconnection processes [45], and the turbulent flow resembles that of a classical fluid, at scales smaller than the mean intervortex length Kelvin waves are believed to be the ones responsible for the energy transfer, thus generating Kelvin wave turbulence [13,44,[46][47][48]. Nonlinear interaction of Kelvin waves leads to the creation of phonons [49], which are finally responsible for the depletion of incompressible kinetic energy in quantum turbulence [21,50]. Additionally, recently it was shown that at zero temperature helical quantum turbulence (i.e., for flows with non-zero largescale helicity) develops a dual cascade of energy and of helicity reminiscent of the dual cascade observed in classical helical flows, and that the emission of phonons also result in the depletion of helicity [21].…”

Section: Introductionmentioning

confidence: 99%

“…Nonlinear interaction of Kelvin waves leads to the creation of phonons [49], which are finally responsible for the depletion of incompressible kinetic energy in quantum turbulence [21,50]. Additionally, recently it was shown that at zero temperature helical quantum turbulence (i.e., for flows with non-zero largescale helicity) develops a dual cascade of energy and of helicity reminiscent of the dual cascade observed in classical helical flows, and that the emission of phonons also result in the depletion of helicity [21]. The presence of such a dual cascade, where both energy and helicity are being transferred from the larger to the smaller scales to be finally dissipated, has a strong impact in the evolution and decay of turbulence.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Finite-temperature effects in helical quantum turbulence

2018

Self Cite

View full text Add to dashboard Cite

We perform a study on the evolution of helical quantum turbulence at different temperatures by solving numerically the Gross-Pitaevskii and the Stochastic Ginzburg-Landau equations, using up to 4096 3 grid points with a pseudospectral method. We show that for temperatures close to the critical 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 anzats for the effective viscosity and friction as a function of the temperature.

show abstract

Dual cascade and dissipation mechanisms in helical quantum turbulence

Cited by 45 publications

References 41 publications

Quantitative estimation of effective viscosity in quantum turbulence

Quantitative estimation of effective viscosity in quantum turbulence

Structure, dynamics, and reconnection of vortices in a nonlocal model of superfluids

Finite-temperature effects in helical quantum turbulence

Contact Info

Product

Resources

About