Restarts of bursts in turbulence in a log-minimal channel

Abstract

Recent evidence on the sustainment of wall-normal-velocity bursts in wall-bounded turbulence challenges the classical streak-dependent picture, suggesting that the problem should be approached relying on no a priori knowledge regarding other flow structures. This paper discusses the restarts of bursts in a log-minimal channel within the framework of a linearised Navier-Stokes system with forcing terms encapsulating the nonlinear effects of all other structures. Two generic issues are addressed. The first concerns the conditions for burst-restart-like solutions for the forced linearised system itself. We formulate optimisation problems to understand the 'minimal requirements' for burst restarting. The solutions illustrate three conceptual periods in a typical restarting process, distinguished by the behaviour of spanwise vorticity structures: breakup, counter-rotating catch-up, and co-rotating catch-up. External forces promote this process by breaking up forward-inclined vortices and merging co-rotating, catching-up vortices. A quantity termed linearly available energy (LAE) is accordingly proposed to parameterise the restarting process. The second issue concerns the contributory features to the observed burst restarts in real turbulence. We show that an essential role of nonlinearity in restarting a burst is to increase a decaying state's LAE to a level sufficient for the onset of the subsequent burst. Flow patterns extracted during the restarting stage exhibit breakup and merging effects, both facilitated by nonlinearity. This suggests that the two effects observed in both the linearised models and real turbulence are manifestations of real flow structures that cause burst restarts.