  We use continuous wavelet transform techniques to construct the global and
environment-dependent wavelet statistics, such as energy spectrum and kurtosis,
to study the fluctuation and intermittency of the turbulent motion in the
cosmic fluid velocity field with the IllustrisTNG simulation data. We find that
the peak scales of the energy spectrum and the spectral ratio define two
characteristic scales, which can be regarded as the integral scale and the
dissipation scale of turbulence, respectively, so that the energy spectrum can
be divided into the energy-containing range, the inertial range and the
dissipation range of turbulence. The wavelet kurtosis is an increasing function
of the wavenumber $k$, first grows rapidly then slowly with $k$, indicating
that the cosmic fluid becomes increasingly intermittent with $k$. In the
energy-containing range, the energy spectrum increases significantly from $z =
2$ to $1$, but remains almost unchanged from $z = 1$ to $0$. We find that both
the environment-dependent spectrum and kurtosis are similar to the global ones,
and the magnitude of the spectrum is smallest in the lowest-density and largest
in the highest-density environment, suggesting that the cosmic fluid is more
turbulent in a high-density than in a low-density environment. In the inertial
range, the energy spectrum's exponent is steeper than both the Kolmogorov and
Burgers exponents, indicating more efficient energy transfer compared to
Kolmogorov or Burgers turbulence.
