Abstract
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.
Highlights
Superfluidity in liquid helium was discovered independently by Kapitza in Moscow and Allen and Meisner in Cambridge in 1938
Following the work by Wacks and Barenghi10 who failed to take account of the superfluid viscosity that mainly arises due to the vortex reconnection dynamics at a small scale,4,8,12 in this paper, we present the numerical study of the GOY like shell model to investigate the energy spectrum and the scale by scale energy budget of superfluid turbulence
We mainly focus our discussion on low temperature (T = 0.9 K), intermediate temperature (T = 1.2 K), and high temperature (1.9 K)
Summary
Superfluidity in liquid helium was discovered independently by Kapitza in Moscow and Allen and Meisner in Cambridge in 1938. They demonstrated that 4He below a critical temperature, called the lambda transition temperature Tλ ≃ 2.17 K, makes a transition to the phase, which can be described as an intimate mixture of two fluids as proposed by Landau and Tisza, which are mutually coupled to each other. Quantum turbulence is associated with the turbulent behavior shown by superfluid helium below the lambda transition temperature (Tλ ∼ 2.17 K) due to the presence of quantized vortices..
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