Heteroclinic connections in plane Couette flow

Details Heteroclinic connections in plane Couette flow Heteroclinic connections in plane Couette flow

2008-08-13

arxiv.org/abs/0808.1865v1

Physics

Fluid Dynamics

11 pages, 4 figures, to be submitted to Journal of Fluid Mechanics

Scientific paper

10.1017/S0022112008005065

Plane Couette flow transitions to turbulence for Re~325 even though the laminar solution with a linear profile is linearly stable for all Re (Reynolds number). One starting point for understanding this subcritical transition is the existence of invariant sets in the state space of the Navier Stokes equation, such as upper and lower branch equilibria and periodic and relative periodic solutions, that are quite distinct from the laminar solution. This article reports several heteroclinic connections between such objects and briefly describes a numerical method for locating heteroclinic connections. Computing such connections is essential for understanding the global dynamics of spatially localized structures that occur in transitional plane Couette flow. We show that the nature of streaks and streamwise rolls can change significantly along a heteroclinic connection.

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