Inertial-range structure of Gross-Pitaevskii turbulence within a spectral closure approximation

The inertial-range structure of turbulence obeying the Gross-Pitaevskii equation, the equation of motion for quantum fluids, is analyzed by means of a spectral closure approximation. It is revealed that, for the energy-transfer range, the spectrum of the order parameter field ψ obeys k−2 law for k < k* and k−1 law for k > k*, where k* is the wavenumber where the characteristic timescales associated with linear and nonlinear terms are of the same order. It is also shown that, for the particle-number-transfer range, the spectrum obeys k−1 law for k < k*, n and k−1 3 law for k > k*, n, where k*, n is the wavenumber corresponding to k* in the particle-number-transfer range.