1999/08/31 by B. Semelin, N. Sánchez, N. Sanchez +1 · 35 citations
Engineering · Mathematics · Physics and Astronomy · #Classical mechanics #Compressibility #Cosmology and Gravitation Theories #Dimensionless quantity #Fluid Dynamics and Turbulent Flows #Hydrodynamic stability #Instability #Linear stability #Mathematical analysis #Mathematical physics #Mathematics #Mechanics #Physics #Reynolds number #Statistical Mechanics and Entropy #Statistical physics #Thermodynamics #Turbulence #Viscosity #astro-ph #gr-qc #hep-ph #hep-th
paper · pdf · doi:10.1103/physrevd.63.084005
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 63(8) (American Physical Society) · 17 pages, 8 figures, submitted to Phys rev D
arxiv created 2000/12/19 · openalex publication_date 2001/03/12 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
This work studies the hydrodynamics of self-gravitating, compressible, isothermal fluids. We show that the hydrodynamic-evolution equations are scale covariant in the absence of viscosity. Then, we study the evolution of the time-dependent fluctuations around singular and regular isothermal spheres. We linearize the fluid equations around such stationary solutions and develop a method based on the Laplace transform to analyze their dynamical stability. We find that the system is stable below a critical size (X\ensuremath∼9.0 in dimensionless variables) and unstable above; this criterion is the same as the one found for the thermodynamic stability in the canonical ensemble and it is associated with a center-to-border density ratio of 32.1. We prove that the value of this critical size is independent of the Reynolds number of the system. Furthermore, we give a detailed description of the series of successive dynamic instabilities that appear at larger and larger sizes following the geometric progression Xn\ensuremath∼10.7n, n=1,2,…. Then, we search for exact solutions of the hydrodynamic equations without viscosity, we provide analytic and numerical axisymmetric soliton-type solutions. The stability of exact solutions corresponding to a collapsing filament is studied by computing linear fluctuations. Radial fluctuations growing faster than the background are found for all sizes of the system. However, a critical size (X\ensuremath∼4.5) appears, separating a weakly from a strongly unstable regime.