Unsteadily manipulating internal flow barriers

Abstract

Typical flows contain internal flow barriers: specialised time-moving Lagrangian entities which demarcate distinct motions. Examples include the boundary between an oceanic eddy and a nearby jet, the edge of the Antarctic circumpolar vortex or the interface between two fluids which are to be mixed together in an microfluidic assay. The ability to control the locations of these barriers in a user-specified time-varying (unsteady) way can profoundly impact fluid transport between the coherent structures which are separated by the barriers. A condition on the unsteady Eulerian velocity required to achieve this objective is explicitly derived, thereby solving an ‘inverse Lagrangian coherent structure’ problem. This is an important first step in developing flow-barrier control in realistic flows, and in providing a postprocessing tool for observational/experimental velocity data. The excellent accuracy of the method is demonstrated using the Kelvin–Stuart cats-eyes flow and the unsteady double gyre, utilising finite-time Lyapunov exponents.