Objective material barriers to the transport of momentum and vorticity

Abstract: I discuss a recent theory for material surfaces that maximally inhibit the diffusive transport of a dynamically active (i.e., velocity-dependent) vector field, such as the linear momentum, the angular momentum or the vorticity, in three-dimensional unsteady flows. These diffusion barriers provide physics-based, observer-independent boundaries of dynamically active coherent structures. Instantaneous limits of these Lagrangian diffusion barriers mark objective Eulerian barriers to short-term active transport. I show how active diffusion barriers can be identified with active versions of Lagrangian coherent structure (LCS) diagnostics. In comparison to their passive counterparts, however, active LCS diagnostics require no significant fluid particle separation and hence provide substantially higher-resolved Lagrangian and Eulerian coherent structure boundaries from shorter velocity data sets. I illustrate these results on two-dimensional turbulence and three-dimensional wall-bounded turbulence.

mathematical physicsdifferential geometrydynamical systemssymplectic geometrychaotic dynamicsexactly solvable and integrable systemsfluid dynamicsquantum physics

Audience: researchers in the topic

Geometry, Dynamics and Mechanics Seminar

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