2010/01/07 by Chris Brunt, C. M. Brunt, Christoph Federrath +3 · 5 citations
Earth and Planetary Sciences · Mathematics · Physics and Astronomy · #Astrophysics and Star Formation Studies #Atmospheric Ozone and Climate #Classical mechanics #Computational physics #Field (mathematics) #Isotropy #Mach number #Magnetohydrodynamic turbulence #Magnetohydrodynamics #Mathematics #Mechanics #Optics #Physics #Plasma #Statistical physics #Stellar, planetary, and galactic studies #Turbulence #Variance (accounting) #astro-ph.CO #astro-ph.GA
paper · pdf · doi:10.1111/j.1365-2966.2009.16215.x
8 pages, 9 figures, accepted for publication in MNRAS
arxiv created 2010/01/07 · openalex publication_date 2010/02/02 · arxiv updated 2015/05/14 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We introduce and test an expression for calculating the variance of a physical field in three dimensions using only information contained in the two-dimensional projection of the field. The method is general but assumes statistical isotropy. To test the method we apply it to numerical simulations of hydrodynamic and magnetohydrodynamic turbulence in molecular clouds, and demonstrate that it can recover the three-dimensional (3D) normalized density variance with ∼10 per cent accuracy if the assumption of isotropy is valid. We show that the assumption of isotropy breaks down at low sonic Mach number if the turbulence is sub-Alfvénic. Theoretical predictions suggest that the 3D density variance should increase proportionally to the square of the Mach number of the turbulence. Application of our method will allow this prediction to be tested observationally and therefore constrain a large body of analytic models of star formation that rely on it.