Abstract
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.
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