In this chapter, we deal with a comparison of quantum versus classical turbulence from two different perspectives. The first one is the hierarchy of equations for the turbulent fluctuations of the several physical variables in the system. In classical turbulence, density, velocity, and temperature may fluctuate; in quantum turbulence, also heat flux and vortex line density may independently fluctuate, because they are independent quantities. We will pay attention to the hierarchy of equations for the fast fluctuating parts of these quantities, to its suitable truncation and to the formulation of a \(K-\epsilon -L\) model generalizing the classical \(K-\epsilon \) model of classical turbulence. This allows a macroscopic treatment and understanding of some features relating both kinds of turbulence.

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Classical Versus Quantum Turbulence: Hierarchies of Fluctuations and Energy Cascades

  • Maria Stella Mongiovì,
  • David Jou,
  • Michele Sciacca

摘要

In this chapter, we deal with a comparison of quantum versus classical turbulence from two different perspectives. The first one is the hierarchy of equations for the turbulent fluctuations of the several physical variables in the system. In classical turbulence, density, velocity, and temperature may fluctuate; in quantum turbulence, also heat flux and vortex line density may independently fluctuate, because they are independent quantities. We will pay attention to the hierarchy of equations for the fast fluctuating parts of these quantities, to its suitable truncation and to the formulation of a \(K-\epsilon -L\) model generalizing the classical \(K-\epsilon \) model of classical turbulence. This allows a macroscopic treatment and understanding of some features relating both kinds of turbulence.