Breakdown of Frozen Motion of Vorticity Field and Vorticity Reconnection

Abstract

The perpendicular components to vorticity of the Laplacian of vorticity multiplied by the kinematic viscosity, ν(∇²ω)_⊥, represents the rate of breakdown due to viscous effects of the frozen motion of vortex lines with fluid particles, whereas the parallel component, ν(∇²ω)_⁄⁄, represents the deviation of the stretching rates of vortex and fluid line elements. The spatial distributions of high-value regions of these two components and vorticity are compared in detail in several analytical and numerical flows. It is found that ν(∇²ω)_⁄⁄ takes large negative values typically inside high-vorticity regions. On the other hand, ν|(∇²ω)_⊥| is large where the high-vorticity regions are interacting, which suggests that ν(∇²ω)_⊥ may serve as a good measure of the degree of vorticity reconnection.