Inhomogeneous whistler turbulence in low beta space plasmas

A nonlinear two dimensional fluid model of whistler turbulence is developed that nonlinearly couples wave magnetic field with electron density perturbations. This coupling leads essentially to finite compressibility effects in whistler turbulence model. Interestingly it is found from our simulations that despite strong compressibility effects, the density fluctuations couple only weakly to the wave magnetic field fluctuations. In a characteristic regime where large scale whistlers are predominant, the weakly coupled density fluctuations do not modify inertial range energy cascade processes. Consequently, the turbulent energy is dominated by the large scale (compared to electron inertial length) eddies and it follows a Kolmogorov-like $k^{-7/3}$ spectrum, where $k$ is a characteristic wavenumber. The weak coupling of the density fluctuations is explained on the basis of a whistler wave parameter that quantifies the contribution of density perturbations in the wave magnetic field.