On the eddy-wave crossover and bottleneck effect in He III-B superfluid turbulence
Résumé
An eddy damped quasi-normal Markovian closure model coupled to a differential approximation model suggested in L’vov, Nazarenko, and Rudenko [“Gradual eddy-wave crossover in superfluidturbulence,” J. Low Temp. Phys.153, 140 (2008)10.1007/s10909-008-9844-0] is proposed to simulate the full unsteady dynamics of superfluidturbulence from large-scale hydrodynamiceddy motion to Kelvin waves that occur on quantized vortices in He III-B at very low temperature. The present model accounts for eddy-wave interactions over crossover scales, and coupling with the two existing models for the Kelvin wave cascade (L’vov and Nazarenko model [V. S L’vov and S. Nazarenko, “Spectrum of Kelvin waveturbulence in superfluids,” JETP Lett.91, 428–434 (2010)10.1134/S002136401008014X] or Kozik and Svistunov model [E. Kozik and B. Svistunov, “Kelvin wave cascade and decay of superfluidturbulence,” Phys. Rev. Lett.92, 035301 (2004)10.1103/PhysRevLett.92.035301]), are considered. Hydrodynamic kinetic energy spectrum and Kelvin waveenergy spectrum are solved separately, allowing for a deep insight into flow physics. A detailed analysis of the bottleneck phenomena is performed thanks to a systematic investigation of the crossover region and the Kelvin cascade model. It is observed that both the shape and the width of the bottleneck region are governed by the eddy-wave interaction model. It is concluded that the bottleneck is robust in the sense that it is observed in all cases, but that a detailed description escapes both present direct numerical simulation and experimental capabilities.