From Classical to Quantum Turbulence: Basic Concepts and Models
Résumé
This chapter offers an introductory guide to basic concepts and models used in Classical and Quantum Turbulence. The former implies ‘normal’ (viscous) fluids, while the latter ‘superfluids’ (inviscid quantum fluids). For classical fluids, the Navier-Stokes model is the basis of all turbulence theories, including Kolmogorov’s cornerstone theory. For quantum fluids, the Gross-Pitaevskii equation describes superfluids at ultra-low temperatures, as obtained in Bose-Einstein condensates. Superfluid turbulence, or vortex tangle turbulence, is thus modelled with this equation. In more complex quantum flows, as superfluid liquid helium, the superfluid coexists with a normal fluid. The ‘two-fluid’, model is then the basis of models for quantum turbulence developing in such systems. We present all these model equations, together with their physical implications in describing CT or QT. Particular care is devoted to explain underlying phenomena, characteristic scales and analysis tools that could be useful to build physically sound numerical simulations.