Structure Function Scaling in Compressible Super-Alfvenic MHD Turbulence
Abstract
Supersonic turbulent flows of magnetized gas are believed to play an important role in the dynamics of star-forming clouds in galaxies. Understanding statistical properties of such flows is crucial for developing a theory of star formation. In this letter we propose a unified approach for obtaining the velocity scaling in compressible and super--Alfv\'enic turbulence, valid for arbitrary sonic Mach number, . We demonstrate with numerical simulations that the scaling can be described with the She--L\'ev\eque formalism, where only one parameter, interpreted as the Hausdorff dimension of the most intense dissipative structures, needs to be varied as a function of . Our results thus provide a method for obtaining the velocity scaling in interstellar clouds once their Mach numbers have been inferred from observations.
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