A viscous compressible flow theory on the interaction between moving bodies and flow field in the (ω, ϑ) framework

Abstract

Reflecting on the dynamic process in fluid motion suggests that the basic root of fluid dynamics is actually on the spatial variation of the vorticity ω, dilatation ϑ, and of pressure p, rather than υ, p themselves. This leads to the "(ω, ϑ) framework". With this framework, vorticity and dilatation dynamics stand at the center of fluid dynamic theory, in which the interaction of solid body and vorticity-dilatation field is of crucial importance. Based on the momentum equation, a general theory on this interaction for three-dimensional, viscous and compressible flow is outlined. The theory consists of the generation of vorticity and dilatation from solid surface, and the reaction on solid body by the produced vorticity-dilatation field. Much deeper insight into the physical mechanisms of the interaction is gained. Some existing formulas are considerably extended to the most general case and unified as a whole.