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In quasi-static MHD, experiments and numerical simulations reveal that theenergy spectrum is steeper than Kolmogorov's $k^{-5/3}$ spectrum. To explainthis observation, we construct turbulence models based on variable energy flux,which is caused by the Joule dissipation. In the first model, which isapplicable to small interaction parameters, the energy spectrum is a power law,but with a spectral exponent steeper than -5/3. In the other limit of largeinteraction parameters, the second model predicts an exponential energyspectrum and flux. The model predictions are in good agreement with thenumerical results.

Modeling quasi-static magnetohydrodynamic turbulence with variable energy flux