The interaction of turbulence with shock waves

The region downstream of the heliospheric termination shock (HTS) was expected to be turbulent [Zank, 1999], the result of upstream turbulence and disturbances (shock waves, pressure and density enhancements, structures, etc. [Story, 1997]) being transmitted across and interacting with the shock. A turbulent downstream region, the heliosheath, has indeed been observed downstream of the HTS [Burlaga et al., 2006], but the character of the turbulence is significantly different from that of the solar wind. The 48-sec averages of the downstream magnetic field analyzed by Burlaga et al. [2006] reveal that the turbulence is isotropic, and each component has a Gaussian distribution. The distribution of 1-hour averages of the magnetic field was also Gaussian in the heliosheath, unlike the log-normal distributions found in the supersonic solar wind. The Gaussian distribution indicates a scale invariance in the form of the magnetic field distribution. The second intriguing observation was that the turbulence was substantially compressible since the width of the 48-sec magnetic field averages is greater than that for the components. Clearly MHD turbulence in the inner heliosheath is significantly different from that upstream of the HTS in the supersonic solar wind. Since the character of the turbulence is different immediately downstream of the HTS, it suggests that "processing'" by the HTS plays an important role in modifying turbulent upstream fluctuations. Motivated by a need to better understand these observations and related observations at interplanetary shocks and the Earth's bow shock, the interaction of turbulence with shock waves is attracting increasing attention. We will discuss the interaction of upstream disturbances and turbulence with a shock wave both analytically and numerically.