Disentangling temperature and Reynolds number effects in quantum turbulence

Area of Science:

• Fluid Dynamics
• Quantum Mechanics
• Condensed Matter Physics

Background:

• Understanding quantum turbulence in superfluid 4He requires analyzing viscous and frictional dissipation.
• The Hall-Vinen-Bekharevich-Khalatnikov (HVBK) model describes mutual friction between normal fluid and superfluid components.

Purpose of the Study:

• To derive a scale-by-scale energy budget for quantum turbulence.
• To investigate the role of mutual friction in energy dissipation and cascade dynamics.
• To define an effective Reynolds number for two-fluid turbulence and clarify the influence of temperature and Reynolds number on intermittency.

Main Methods:

• Developed a coarse-grained two-fluid model.
• Derived a scale-by-scale energy budget.
• Performed direct numerical simulations (DNS) within the HVBK model framework.
• Analyzed experimental and numerical data.

Main Results:

• Mutual friction facilitates momentum exchange and joint energy cascade between fluids despite viscosity differences.
• Frictional dissipation is small and localized at far-dissipative scales.
• An effective Reynolds number for two-fluid turbulence was defined.
• A relationship between normalized vortex spacing and Reynolds number was established, supported by data.
• Intermittency variations are attributed to Reynolds number effects, not temperature changes.

Conclusions:

• The study clarifies the interplay of viscous and frictional dissipation in quantum turbulence.
• The defined effective Reynolds number provides a new tool for analyzing two-fluid turbulence.
• The findings resolve the debate on intermittency, attributing it to Reynolds number effects.