Skip to Main content Skip to Navigation
Journal articles

Accuracy requirements to test the applicability of the random cascade model to supersonic turbulence

Abstract : A model, which is widely used for inertial rang statistics of supersonic turbulence in the context of molecular clouds and star formation, expresses (measurable) relative scaling exponents Zp of two-point velocity statistics as a function of two parameters, β and Δ. The model relates them to the dimension D of the most dissipative structures, D = 3 - Δ/(1 - β). While this description has proved most successful for incompressible turbulence (β = Δ = 2/3, and D = 1), its applicability in the highly compressible regime remains debated. For this regime, theoretical arguments suggest D = 2 and Δ = 2/3, or Δ = 1. Best estimates based on 3D periodic box simulations of supersonic isothermal turbulence yield Δ = 0.71 and D = 1.9, with uncertainty ranges of Δ ∈ [0.67,0.78] and D ∈ [2.04,1.60]. With these 5-10% uncertainty ranges just marginally including the theoretical values of Δ = 2/3 and D = 2, doubts remain whether the model indeed applies and, if it applies, for what values of β and Δ. We use a Monte Carlo approach to mimic actual simulation data and examine what factors are most relevant for the fit quality. We estimate that 0.1% (0.05%) accurate Zp, with p = 1,...,5, should allow for 2% (1%) accurate estimates of β and Δ in the highly compressible regime, but not in the mildly compressible regime. We argue that simulation-based Zp with such accuracy are within reach of today's computer resources. If this kind of data does not allow for the expected high quality fit of β and Δ, then this may indicate the inapplicability of the model for the simulation data. In fact, other models than the one we examine here have been suggested.
Complete list of metadata
Contributor : Nathalie POTHIER Connect in order to contact the contributor
Submitted on : Friday, July 1, 2022 - 10:50:59 AM
Last modification on : Friday, August 5, 2022 - 3:37:49 PM


Publisher files allowed on an open archive




Doris Folini, Rolf Walder. Accuracy requirements to test the applicability of the random cascade model to supersonic turbulence. Astronomy and Astrophysics - A&A, EDP Sciences, 2016, 587, ⟨10.1051/0004-6361/201527148⟩. ⟨insu-03710583⟩



Record views


Files downloads