On the eddy-wave crossover and bottleneck effect in He III-B superfluid turbulence

Abstract

Universal spectrum in the infrared range of two-dimensional turbulent flows Phys. Fluids 26, 025105 (2014); 10.1063/1.4864103Eddy damped quasinormal Markovian simulations of superfluid turbulence in helium II An eddy damped quasi-normal Markovian closure model coupled to a differential approximation model suggested in L'vov, Nazarenko, and Rudenko ["Gradual eddywave crossover in superfluid turbulence," J. Low Temp. Phys. 153, 140 (2008)] is proposed to simulate the full unsteady dynamics of superfluid turbulence from largescale hydrodynamic eddy 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 wave turbulence in superfluids," JETP Lett. 91, 428-434 (2010)] or Kozik and Svistunov model [E. Kozik and B. Svistunov, "Kelvin wave cascade and decay of superfluid turbulence," Phys. Rev. Lett. 92, 035301 (2004)]), are considered. Hydrodynamic kinetic energy spectrum and Kelvin wave energy 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. C 2012 American Institute of Physics. [http://dx.

Nested polyhedra model of turbulence

“…[3] for weak magnetohydrodynamic turbulence). It is also commonly used in isotropic cascade modeling using closures, such as the eddy-damped quasinormal Markovian approximation [4][5][6] and differential approximation models [7][8][9]. Cascade models that use a logarithmic discretization, or shell models (see, for example, Ref.…”

Logarithmic discretization and systematic derivation of shell models in two-dimensional turbulence

“…It is also employed in closure calculations such as computations with the direct interaction approximation or the eddy damped quasi-normal Markovian closure [2? , 3], differential approximation models [4][5][6], where isotropy and local interaction assumptions lead to the transformation of the integro-differential equation in k- Figure 1. A cartoon of all possible triads with k and p fixed, such that k > p. Note that the minimum and maximum values that q can take are qmin = k − p and qmax = k + p. Note that if instead k < p, the minimum value would be qmin = p − k.…”