Identification of vortex boundaries in two-dimensional incompressible flows based on the Liutex-shear interaction

Abstract

According to the Liutex-shear decomposition, vorticity can be decomposed into a rotational part, i.e., the Liutex vector, and a residual shear part. With this decomposition, the vorticity transport equation can be used to formulate a governing equation for Liutex easily for two-dimensional incompressible flows with a source term depending on the residual shear. The dynamics of Liutex-identified structures is then studied in a Taylor-Green vortex flow and a flow past a cylinder at Reynolds number of 200. It is revealed that such boundaries exist outside which the shear has trivial impact on the evolution of Liutex and inside which enhancing and weakening effects of shear on Liutex can be observed. In addition, there is a strong dissipation effect upon Liutex on these boundaries. Based on the interaction mechanism between Liutex and shear, we argue that the vortex boundaries can be identified by these highly dissipative boundaries. In contrast, traditional methods use iso-surfaces of arbitrarily selected thresholds to represent vortex boundaries. The current method of identifying vortex boundaries based on the Liutex-shear interaction has a clearer theoretical base and avoids the arbitrary selection of thresholds. Extensions to three-dimensional incompressible flows can be made in future following the same procedure but with a slightly more complex vorticity transport equation which includes the velocity gradient induced stretching or tilting term.