Geometry, Dissipation, Cooling, and the Dynamical Evolution of Wind-Blown Bubbles

Bubbles driven by energy and mass injection from small scales are ubiquitous in astrophysical fluid systems and essential to feedback across multiple scales. In particular, O stars in young clusters produce high velocity winds that create hot bubbles in the surrounding gas. We demonstrate that the dynamical evolution of these bubbles is critically dependent upon the geometry of their interfaces with their surroundings and the nature of heat transport across these interfaces. These factors together determine the amount of energy that can be lost from the interior through cooling at the interface, which in turn determines the ability of the bubble to do work on its surroundings. We further demonstrate that the scales relevant to physical dissipation across this interface are extremely difficult to resolve in global numerical simulations of bubbles for parameter values of interest. This means the dissipation driving evolution of these bubbles in numerical simulations is often of a numerical nature. We describe the physical and numerical principles that determine the level of dissipation in these simulations; we use this, along with a fractal model for the geometry of the interfaces, to explain differences in convergence behavior between hydrodynamical and magneto-hydrodynamical simulations presented here. We additionally derive an expression for momentum as a function of bubble radius expected when the relevant dissipative scales are resolved and show that it still results in efficiently-cooled solutions as postulated in previous work.