Large Eddy Simulations Analysis of the Energy Spectrum Without Mutual Friction in Superfluid $$ ^{4} $$ 4 He: HVBK Model

Abstract

The reliability of the filtered on the Hall–Vinen–Bekarevich–Khalatnikov (HVBK) model without mutual friction force is now investigated via some large eddy simulations of freely decaying isotropic superfluid turbulence. The filtered HVBK model is solved using a fully pseudo-spectral method, which is an extension of the classical Rogallo’s method to the two-fluid model. Furthermore, in this paper, we analyze the evolution of various terms constituting the HVBK momentum equations using the balance equation for the energy-spectrum function. Our results are presented in both cases with and without mutual friction force. LES predictions have shown that this mutual friction decreases the energy dissipation of the normal part and the energy transfer is more significant when this force is taken into account.