From Rings to Smoke: the quest to uncover a mechanism of turbulence

Abstract

The equations of motion that govern the dynamics of fluid flows--the Navier-Stokes equations--were formulated nearly two centuries ago. In that time, we have made immense advancements in the ways that we understand these equations in order to characterize, analyze, and model a myriad of fluid flows. To this day, however, our understanding of how turbulent flows evolve dynamically remains limited. The challenge in understanding how turbulent flows develop arises from the complexity of the transfer of energy through the interactions of vortices over a broad range of length and time scales. These ubiquitous flows are notoriously difficult to study due to our lack of a mechanistic framework that encapsulates how vortices interact, break down, and form new generations of vortices, driving the cascade of energy down to the dissipative scale. Here we examine the violent, head-on collision of vortex rings in order to identify how the vortices break down into a transient turbulent flow. At moderate Reynolds numbers, the colliding vortices locally flatten each other and split into new, smaller generations of vortex filaments. These secondary filaments, themselves, interact with each other, flatten, and break down again in an iterative manner that is consistent with recent theoretical predictions. At higher Reynolds numbers, the colliding vortices generate a new ordered array of antiparallel secondary filaments through the onset of the elliptical instability. These secondary filaments interact, leading to the formation of even smaller tertiary filaments in the same manner as the preceding generation. We examine what role these vortex interactions play in the cascading of energy down to smaller scales in recent numerical studies of turbulence. This mechanistic framework could help shift the paradigm of viewing turbulence as a cascade of discrete instabilities through vortex interactions, rather than statistically.