Onset of Turbulence from the Receptivity Stage of Fluid Flows

Abstract

The traditional viewpoint of fluid flow considers the transition to turbulence to occur by the secondary and nonlinear instability of wave packets, which have been created experimentally by localized harmonic excitation. The boundary layer has been shown theoretically to support spatiotemporal growing wave fronts by Sengupta, Rao, and Venkatasubbaiah [Phys. Rev. Lett. 96, 224504 (2006)] by a linear mechanism, which is shown here to grow continuously, causing the transition to turbulence. Here, we track spatiotemporal wave fronts to a nonlinear turbulent state by solving the full 2D Navier-Stokes equation, without any limiting assumptions. Thus, this is the only demonstration of deterministic disturbances evolving from a receptivity stage to the full turbulent flow. This is despite the prevalent competing conjectures of the event being three-dimensional and/or stochastic in nature.