  Nonlinear 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 length scales that are
respectively bigger than ion gyro frequency and smaller than ion gyro radius.
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.
