A synthetic forcing to trigger laminar-turbulent transition in parallel wall bounded flows via receptivity

Abstract

Research on laminar-turbulent transition of wall-bounded parallel flows has usually focused on controlled scenarios where transition is triggered by perturbations having simple shapes and spectra. These disturbances strongly differ from the environmental noise usually present in experimental setups or industrial applications, where uncontrolled transition is usually observed. In this paper a new method is proposed to trigger uncontrolled transition to turbulence in wall-bounded parallel flows exploiting the receptivity of the flow to a volume forcing. Using some concepts provided by linear stability and sensitivity analysis, such as the resolvent, we propose a method for constructing a volume forcing capable of inducing stochastic velocity perturbations with a prescribed energy level, eventually leading to laminar-turbulent transition as a response of the system to external noise. The method has been tested in a channel flow configuration, using direct numerical simulations of the fully nonlinear Navier-Stokes equations in the presence of the volume forcing constructed on the basis of optimal forcing functions. Subcritical transition to turbulence induced by the prescribed forcing has been investigated and compared to other transition scenarios, where deterministic perturbations are imposed for obtaining a turbulent flow. Finally, the fully developed turbulent flows induced by the proposed method has been analysed, showing that low-order statistics and energy balance equations are practically unaffected by the continuous synthetic forcing.