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Turbulence is a dominant feature operating in gaseous flows across nearly allscales in astrophysical environments. Accordingly, accurately estimating thestatistical properties of such flows is necessary for developing acomprehensive understanding of turbulence. We develop and employ a hierarchicalBayesian fitting method to estimate the parameters describing the scalingrelationships of the velocity power spectra of supersonic turbulence. Wedemonstrate the accuracy and other advantages of this technique compared withordinary linear regression methods. Using synthetic power spectra, we show thatthe Bayesian method provides accurate parameter and error estimates. Commonlyused normal linear regression methods can provide estimates that fail torecover the underlying slopes, up to 70% of the instances, even whenconsidering the 2std.dev. uncertainties. Additionally, we apply the Bayesianmethods to analyse the statistical properties of compressible turbulence in 3Dnumerical simulations. We model driven, isothermal, turbulence with rms Machnumbers in the highly supersonic regime M~15. We study the influence of purelysolenoidal (divergence-free) and purely compressive (curl-free) forcing on thescaling exponent of the power spectrum. In simulations with solenoidal forcingand 1024^3 resolution, our results indicate that there is no extended inertialrange with a constant scaling exponent. The bottleneck effect results in acurved power spectrum at all wave numbers and is more pronounced in thetransversal modes compared with the longitudinal modes. Therefore, this effectis stronger in stationary turbulent flows driven by solenoidal forcing comparedto the compressive one. The longitudinal spectrum driven with compressiveforcing is the only spectrum with constant scaling exponent z=-1.94 +- 0.01,corresponding to slightly shallower slopes than the Burger's prediction.

Hierarchical Bayesian analysis of the velocity power spectrum in supersonic turbulence