Applied Mathematics Seminar: Transition to turbulence in planar shear flows

Sébastien Gomé, (ESPCI, France)

Abstract: In planar shear flows, the route to turbulence is paved by coexisting laminar and turbulent structures. At high enough Reynolds numbers, these transitional structures spontaneously emerge as regular patterns.

Once the Reynolds number is reduced, turbulent zones become sparser and either decay to the absorbing laminar state or propagate. Using a rare-event method inspired from stochastic processes, we measure a super-exponential evolution of the mean decay or propagation times with Reynolds number, which we connect to extreme value distributions.

Laminar-turbulent patterns are associated to a strong mean flow along laminar-turbulent interfaces. Via a spectral energy analysis, we determine the mechanisms by which this mean flow is fueled, and confirm its importance in selecting a pattern wavelength.

When the large-scale circulation is numerically suppressed, the transition scenario is modified and resembles the initial analogy with Directed Percolation formulated by Pomeau.