Understanding vortex identifiication criteria

Abstract

In this thesis two new criteria used for instability analysis based on equations for disturbance mechanical energy (Sengupta et al.:Vortex-induced instability of an incompressible wall-bounded shear layer. Journal of Fluid Mechanics,493:277–286, 2003) and disturbance enstrophy (Sengupta et al.:An enstrophy-based linear and nonlinear receptivity theory. Physics of Fluids, 30(5):054106, 2018) are discussed and compared with commonly used Q-criterion (Hunt, Wray and Moin: Eddies, streams, and convergence zones in turbulent flows, CTR Report, Stanford Univ.,1988) and λ2-criteria (Jeong and Hussain: On the identification of a vortex, J. Fluid Mech.,285, 69-94, 1995) for vortex identification for a zero pressure gradient flow over a flat plate. The criteria used for instability analysis are derived directly from navier-stokes equation for incompressible flow without any assumptions. We show the superiority of these new criteria over the commonly used Q- and λ2-criteia in distinguishing between flow before and after the formation of a turbulent spot. criteria based on disturbance enstrophy equation is also used along with instantaneous vorticity to explain the initiation of flow transition. As the commonly used vortex identification criteria are just mathematical constructs without any clear physical meaning, an attempt is made to correlate them with rate of change of disturbance enstrophy using a point search algorithm. A similarity is observed between instantaneous vorticity and DETE for all times. Scale factors are then extracted to explain this similarity.