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Center for Nonlinear Studies |
We study freely decaying superfluid turbulence by performing high resolution numerical simulations of the Gross-Pitaevskii equation (GPE) at zero temperature. The energy spectrum confirms the presence of both a Kolmogorov scaling range for scales larger than the inter-vortex scale l, and a second inertial range at scales smaller than l. Vortex line visualizations show the existence of substructures formed by a myriad of small-scale knotted vortices. We then study finite temperature effects in a decaying turbulence. To do so, first we prepare thermal states by using the stochastic Ginzburg-Landau equation, then we combine them with the Taylor-Green initial conditions and evolve 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-superfluids and classical flows, and to further calibrate the estimations of the effective viscosity, we perform low Reynolds number simulations of the Navier-Stokes equations.
Host: Nairita Pal/Susan Kurien