  Spin-superflow turbulence (SST) in spin-1 ferromagnetic spinor Bose-Einstein
condensates is theoretically and numerically studied by using the 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 appear in
spectra of the superflow kinetic and the spin-dependent interaction energy,
respectively. Our numerical calculation of the GP equations confirms SST with
the coexistence of disturbed spin and superfluid velocity field with two power
laws.
