Turbulent spectral cascades are investigated by means of fully three-dimensional (3D) simulations of a compressible Hall-magnetohydrodynamic (H-MHD) plasma in order to understand the observed spectral break in the solar wind turbulence spectra in the regime where the characteristic length scales associated with electromagnetic fluctuations are smaller than the ion gyroradius. In this regime, the results of our 3D simulations exhibit that turbulent spectral cascades in the presence of a mean magnetic field follow an omnidirectional anisotropic inertial-range spectrum close to k(-7/3). The latter is associated with the Hall current arising from nonequal electron and ion fluid velocities in our 3D H-MHD plasma model.
Driven dissipative whistler wave turbulence in two-dimensional electron magnetohydrodynamics is investigated using very high resolution nonlinear fluid simulations. It is shown that a dual cascade phenomenon of mean magnetic potential and energy invariants is in agreement with predictions based on statistical ensemble and Kolmogorov’s theories. Turbulent length scales larger than the electron skin depth (whistler wave regime) exhibit a spectral break in the vicinity of the forcing wave number that separates the inverse and forward cascade regimes. On the other hand, length scales smaller than the electron skin depth behave like hydrodynamic eddies in which both small and large scale regimes exhibit identical turbulent spectra. In both cases, however, turbulent fluctuations follow an exact Kolmogorov-type spectra. While wave effects are strong in the whistler wave regime, they are absent entirely in the hydrodynamics regime of the driven electron magnetohydrodynamic turbulence.
Non-linear, three-dimensional, time-dependent fluid simulations of whistler wave turbulence are performed to investigate role of whistler waves in solar wind plasma turbulence in which characteristic turbulent fluctuations are characterized typically by the frequency and lengthscales that are, respectively, bigger than ion gyrofrequency and smaller than ion gyroradius. The electron inertial length is an intrinsic length-scale in whistler wave turbulence that distinguishably divides the high-frequency solar wind turbulent spectra into scales smaller and bigger than the electron inertial length. Our simulations find that the dispersive whistler modes evolve entirely differently in the two regimes. While the dispersive whistler wave effects are stronger in the large-scale regime, they do not influence the spectral cascades which are describable by a Kolmogorov-like k −7/3 spectrum. By contrast, the small-scale turbulent fluctuations exhibit a Navier-Stokes-like evolution where characteristic turbulent eddies exhibit a typical k −5/3 hydrodynamic turbulent spectrum. By virtue of equipartition between the wave velocity and magnetic fields, we quantify the role of whistler waves in the solar wind plasma fluctuations.
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