Spin-superflow turbulence in spin-1 ferromagnetic spinor Bose-Einstein condensates

Spin-superflow turbulence (SST) in spin-1 ferromagnetic spinor Bose-Einstein condensates is theoretically and numerically studied by using the spin-1 spinor Gross-Pitaevskii (GP) equations. SST is turbulence in which the disturbed spin and superfluid velocity fields are coupled. Applying the Kolmogorov-type dimensional scaling analysis to the hydrodynamic equations of spin and velocity fields, we theoretically find that the -5/3 and -7/3 power laws can appear in spectra of the superflow kinetic and the spin-dependent interaction energies, respectively. Our numerical calculation of the GP equations with a phenomenological small-scale energy dissipation confirms SST with the coexistence of disturbed spin and superfluid velocity field with two power laws.