Time-Periodic Flows in Geophysical and Classical Fluid Dynamics

Abstract

Time-periodic flows form an important special class of fluid motions. This class includes, for example, the many well-known families of linear propagating waves. Recently, nonlinear time-periodic flows have received increased attention in several contexts in geophysical and classical fluid mechanics. Despite the relative simplicity of their Eulerian representation, time-periodic velocity fields can give rise to complex, aperiodic Lagrangian motion; models of this type can be useful for understanding fluid transport processes in the ocean and atmosphere. One approach to the analysis of chaotic dynamical systems, including certain models of geophysical flows, is based on the identification of a large set of unstable periodic cycles, each of which corresponds to an independent time-periodic flow. Time-periodic flows provide accessible examples in which to explore mechanisms of disturbance growth in general time-dependent flows, a problem of practical interest in numerical weather and ocean prediction. Recent advances in the theory of the transition to turbulence in classical pipe flow involve bifurcation analysis for a special class of time-periodic flows.