Speaker
Lukas Konstandin
(Institut für Theoretische Astrophysik, Heidelberg)
Description
Observations reveal that supersonic turbulence is prevalent in star forming clouds. The density and velocity field within these clouds indicate complex, chaotic, and filamentary structures, where turbulent motions interact with shocks. Therefore, understanding the properties of turbulence is a prerequisite for developing a comprehensive theory of star formation in the ISM. We study a set of three-dimensional numerical simulations of driven, isothermal, turbulence with r.m.s.~Mach numbers ranging from the subsonic to the highly supersonic regime. We focus our analysis on spectral behaviour of the decomposed velocity field into transversal $\nabla \cdot u_s=0$ and longitudinal $\nabla \times u_c=0$ modes. These components have different effects, leading to vortex structures for $u_s$ and shocks and rarefactions for $u_c$, where only the longitudinal mode is directly coupled to the gravitational field. The two components are themselves coupled and exchange energy. We find that the asymmetric transfer of energy from transversal to longitudinal component, and vice versa, introduces a forcing dependence to the total and decomposed power spectra. We measure the local scaling exponents of the power spectra with a hierarchical Bayesian method, which has the advantage that statistical and systematic uncertainties are treated self consistently. The scaling exponents are in agreement with a Burgers spectrum with a scaling exponent of $-2$ for the longitudinal modes and a pure compressive forcing field. The scaling exponents of the transversal spectrum driven with a pure solenoidal forcing field are in agreement with the Kolmogorov prediction of $-5/3$ in a limited inertial range. This discrepant behaviour shows the complexity of the problem and indicates that various processes affect the power spectrum.
Author
Lukas Konstandin
(Institut für Theoretische Astrophysik, Heidelberg)