Dual cascades in quantum turbulence

P.D. MININNI

Niza

Conferencia; Universal features of hydrodynamical, optical and wave turbulence; 2019

CNRS

Dual cascades are observed in classical turbulent flows when their equations of motion conserve more than just one ideal invariant. The dual direct cascade of energy and of helicity in three-dimensional (3D) hydrodynamics, and the coexistence of an inverse cascade of energy and a direct cascade of enstrophy in two-dimensional (2D) hydrodynamic turbulence are two examples. In this talk I will present evidence of the presence of dual cascades in quantum turbulence described by the Gross-Pitaevskii equation. In 3D helical quantum turbulence a dual cascade of energy and of helicity can develop, in good agreement with the classical phenomenology of Brissaud, Frisch, Leorat, Lesieur and Mazure. But perhaps more surprisingly, under certain conditions in quantum turbulence an inverse cascade of energy can coexist with a direct cascade. For thin 3D domains, of for quasi-2D flows in cubic domains, a critical transition separates a 3D regime with a direct cascade of energy from a 2D regime with an inverse cascade of energy and a small transfer of energy to small scales.