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_*, 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}, where k_{*,n} is the wavenumber corresponding to k_* in the particle-number-transfer range