Pattern Formation Via Resonant Interactions in Fluid Flows

Abstract

Pattern formation is a familiar element in the laminar-transition mechanism in fluid flows. Patterns also are clearly present in the disordered states existing in fully developed turbulent flows, where they are known as “coherent structures” Pattern formation is best understood in “closed flows” the prototype being thermal convection in fluid layers heated from below, because such problems are set in closed spatial domains in physical space and are therefore simpler mathematically than “open flows” which are typically set in domains idealized to be spatially infinite Nevertheless, the experimental evidence of patterning is incontrovertible-even striking-in both closed and open flows, with the prototypical examples of the latter type being boundary layer flows or mixing layer flows. In the case of boundary layers and channel flows, the existence and importance of Tollmien-Schlichting waves has long been known. Helical waves are their analogues in rotating pipe flows. The dynamics leading to pattern formation dominate the characteristics of preturbulent flows, including the physically and technologically important transfer properties of the flow (such as heat, momentum, and mass transfer). In this presentation we describe some computational and analytical investigations of transition sequences and coherent structures in two classes of fluid flows, (i) rotating pipe flows, (ii) transitional boundary layers and channel flows.