2020/02/20 by Eric Keto
Engineering · Environmental Science · Physics and Astronomy · #Adiabatic process #Bernoulli's principle #Classical mechanics #Flow (mathematics) #Fluid Dynamics and Turbulent Flows #Initial value problem #Isothermal process #Mechanics #Partial differential equation #Physics #Plant Water Relations and Carbon Dynamics #Rotational symmetry #Solar and Space Plasma Dynamics #Steady state (chemistry) #Thermodynamics #Transonic #astro-ph.SR #physics.flu-dyn
paper · pdf · doi:10.1093/mnras/staa529
To be published in MNRAS
arxiv created 2020/02/20 · openalex publication_date 2020/02/20 · arxiv updated 2020/03/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
ABSTRACT Bondi and Parker derived a steady-state solution for Bernoulli’s equation in spherical symmetry around a point mass for two cases, respectively, an inward accretion flow and an outward wind. Left unanswered were the stability of the steady-state solution, the solution itself of time-dependent flows, whether the time-dependent flows would evolve to the steady state, and under what conditions a transonic flow would develop. In a Hamiltonian description, we find that the steady-state solution is equivalent to the Lagrangian implying that time-dependent flows evolve to the steady state. We find that the second variation is definite in sign for isothermal and adiabatic flows, implying at least linear stability. We solve the partial differential equation for the time-dependent flow as an initial-value problem and find that a transonic flow develops under a wide range of realistic initial conditions. We present some examples of time-dependent solutions.