Spectrum in the Strong Turbulence Region of Gross–Pitaevskii Turbulence

Abstract

Numerical simulations of the Gross–Pitaevskii equation which describes the dynamics of quantum fluids are performed focusing on scales larger than the healing length. Dissipation and pumping of the mass are applied in high and low wavenumber ranges, respectively, in order to achieve turbulent states. In this setting of dissipation and pumping, it is found that the mass, or the particle number, cascades from low to high wavenumbers and a constant flux of the particle number is observed in the cascading wavenumber range. The spectrum F(k) (k is the wavenumber) of the order parameter field at the turbulent state is analyzed, and it is found that the obtained F(k) is consistent with the form ∝k-1[ln(k/k0)]-1 (k is the lower-end wavenumber of the scaling range) which is derived from a closure approximation of the particle-number transfer range of strong turbulence (Yoshida and Arimitsu in J Phys A Math Theor 46(33):335501, 2013).