“ Towards a direct route to turbulence in rotating cavities using high-order numerical approximations ”
By Dr. Eric Serre
(M2P2, CNRS-les universités Aix Marseille-Ecole Centrale, Marseille)
Thursday 19th of January 2012 – 10 :00 – Room CO 016
Towards a direct route to turbulence in rotating cavities using high-order numerical approximations
The transition to turbulence is analyzed in rotating cavities of finite radial extent. This configuration provides a simple model of technological devices such as turbo-machinery and it is also relevant to geophysical flows (Launder, Poncet, Serre. Ann. Rev. 2010). The flow stability is primarily governed by the disk boundary-layers and the waves they support that can be locally analysed by reference to theoretical results from infinite disks. New interest has been stimulated by the experimental and theoretical studies of Lingwood (1996, 1997) which showed that the onset of absolute instability in both the von Kármán and Ekman layers adjacent to a single disk occurred at a value of Reynolds number which closely corresponded to that obtained experimentally for laminar-turbulent transition. This major contribution to the turbulent breakdown process opened the possibility of a direct route towards turbulence through a global instability.
But to this day, if further studies have confirmed these local linear stability results, no general agreement exists concerning their outcome in terms of global behaviour due to the competition between nonlinear and nonparallel effects. In this work, we analyze the impulse response of the boundary layer using pseudo-spectral DNS and LES. Numerical results establish the existence of a primary subcritical bifurcation to nonlinear global mode with angular phase velocity and radial envelop coherent with the so-called elephant mode theory (Pier & Huerre JFM 2001). Moreover, this self-sustained saturated wave is itself globally unstable. A second front appears in the lee of the primary where small-scale instability develops with characteristics indicating a Floquet mode of zero azimuthal wavenumber. This secondary instability leads to a much disorganized state, defining transition to turbulence. This transition, linked to the secondary instability of a global mode, confirms for the first time on a real flow the possibility of a direct transition to turbulence through an elephant cascade, a scenario up to now only observed on the Ginzburg-Landau model (Viaud, Serre, Chomaz JFM 2011). Further work investigates alternative routes, when the initial perturbation is very low or when the azimuthal wavenumber is limited to smaller values.