Energy spectrum and energy budget of superfluid turbulence using two-fluid shell model

Using a two-fluid shell model, we numerically investigate the energy spectrum and the scale by scale energy budget for superfluid turbulence in the temperature range of T = 0.9–2.175 K. Both the normal and superfluid components exhibit the Kolmogorov-like spectrum (Ek ∼ k−5/3) in the inertial range for all the temperatures. The scale to scale energy budget analysis in the wavenumber space indicates a strong coupling between the normal and superfluid components at low temperature (T = 0.9 K), which is quite evident from the observation of balancing between the viscous dissipation and the energy transfer due to the mutual friction between the components at low temperature for the normal component. We also compute the temporal probability distribution function of the energy induced by the mutual friction to a particular component, which indicates the positive energy supply at low temperature (T = 0.9 K) and negative energy supply at high temperature (T = 1.9 K) for the normal component. The results are consistent with the previous numerical and experimental studies.