Modeling quasi-static magnetohydrodynamic turbulence with variable energy flux

In quasi-static magnetohydrodynamics, experiments and numerical simulations reveal that the energy spectrum is steeper than Kolmogorov's k(-5/3) spectrum. To explain this observation, we construct two variable energy flux based turbulence phenomenologies. Variable energy flux is due to the Joule dissipation, which is active at all scales. In the first phenomenology, 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 phenomenology predicts an exponential energy spectrum and flux. The predictions of the phenomenologies are in good agreement with the numerical results. (C) 2015 AIP Publishing LLC.