A local model for the spherical collapse/expansion problem

ABSTRACT Spherical flows are a classic problem in astrophysics which typically studied from global perspective. However, much like with accretion discs, there likely many instabilities and small scale phenomena would be easier to study local For this purpose, we develop model for spherically contracting/expanding gas cloud, the spirit of shearing box, β-plane, expanding box models have had extensive use studies planets, stellar winds, respectively. The consists a, spatially homogeneous, periodic time varying aspect ratio, along factor (analogous that FRW/Newtonian cosmology) relating coordinates physical problem. We derive number symmetries conservation laws exhibited by model. Some these reflect modified dependant geometry, while others analogues energy, density, vorticity also generically increase(/decrease) as consequence collapse(/expansion). non-linear solutions, including analogue uniform density zonal flows, grow angular momentum conservation. Our is closely related accelerated Tenerani & Velli an extension isotropic considered Robertson Goldreich.