Lagrangian Frozen-in Hypothesis for Vortex Stretching

Abstract

A nonlinear ordinary differential equation for peak vorticity is proposed phenomenologically for 3D inviscid flows. This typically predicts that the peak vorticity behaves approximately as \(\sqrt {A}[\sin\,\{r\sqrt {A}(t_{\ast}-t)\}]^{-1}\) and the peak strain as \(\sqrt {A}[\tan\,\{r\sqrt {A}(t_{\ast}-t)\}]^{-1}\), where r , A and t * are constants. Numerical study of 3D Euler equations performed both in physical and Langrangian marker spaces is, at early stages consistent with assumptions underlying the above predictions, giving an alternative interpretation of apparently exponential growth of vorticity. It is not known if this evolution persists, leading to a finite-time singularity.