Physical origin of vortex stretching and twisting: Viscous or inertial forces

Abstract

In this paper, the physical origin of vortex stretching and twisting is theoretically investigated. The effects of inertial and viscous forces are mainly considered and discussed. Two key conditions, i.e., solid walls and three-dimensional (3D) disturbances, are adopted in three typical cases. Among them, the first two cases are straight and curved vortex lines at the initial time without any kind of disturbance. The third case is a straight vortex line at the initial time with introduced 3D natural disturbances. Through experimental observations, numerical simulations, and theoretical analysis in these cases, the first two cases illustrate that the straight or curved vortex lines are still straight or curved at the next time, respectively, regardless of whether solid walls are introduced. However, the third case clearly shows that once natural disturbances are introduced, the straight vortex lines near and at solid walls at the initial time are stretched and twisted mainly by viscous forces, instead of inertial forces, typically demonstrated by the 3D wake transition of a straight circular cylinder and the transition of the laminar boundary layer at a flat plate. Accordingly, based on definitions of generation and enhancement in vortex stretching and twisting, it is confirmed that the viscous forces with two key conditions are the generation mechanism, while the inertial forces alone are the enhancement mechanism.