Turbulence revealed by wavelet transform: power spectrum and intermittency for the velocity field of the cosmic baryonic fluid

Abstract: 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 scale of the energy spectrum define a characteristic scale, which can be regarded as the integral scale of turbulence, and the Nyquist wavenumber can be regarded as the dissipation scale. With these two characteristic scales, 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.