  In quasi-static MHD, experiments and numerical simulations reveal that the
energy spectrum is steeper than Kolmogorov's $k^{-5/3}$ spectrum. To explain
this observation, we construct turbulence models based on variable energy flux,
which is caused by the Joule dissipation. In the first model, which is
applicable 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 large
interaction parameters, the second model predicts an exponential energy
spectrum and flux. The model predictions are in good agreement with the
numerical results.
