Tracking disturbances in transitional and turbulent flows: Coherent structures

Abstract

Tracking transitional and turbulent flows requires methods other than the classical techniques, which capture coherent structures via locating pressure minima, after the disturbance field has evolved to late-transitional and turbulent flow stages. Keeping it in mind, transition to turbulence of zero pressure gradient flow is studied, following two routes of excitation, by solving the three-dimensional Navier-Stokes equation in derived variable formulation, with vorticity as one of the dependent variables. For such flows, disturbance structures should be traced from the receptivity to the coherent structure stage for the fully developed turbulent flow. The coherent structures in turbulent flows are identified by the Q- and λ2-criteria, based on the occurrence of pressure minima at the vortex cores. In the proposed study here, the zero pressure gradient boundary layer is excited (i) at the wall with a monochromatic source and (ii) causing transition to turbulence, by a convecting vortex in the free stream. The main aim here is to trace the incipient disturbances from the onset to the turbulent state in terms of physical quantities, such as the disturbance mechanical energy introduced by Sengupta et al. ["Vortex-induced instability of an incompressible wall-bounded shear layer," J. Fluid Mech. 493, 277-286 (2003)] and disturbance enstrophy transport equation, as proposed by Sengupta et al. ["An enstrophy-based linear and nonlinear receptivity theory," Phys. Fluids 30(5), 054106 (2018)]. Such methods are capable of tracing disturbance structures from the onset to the evolved stage. We compare these methods with Q- and λ2-criteria to trace disturbance evolution.