Large-scale Organization of Small-scale Flow: The Examples of 2D Turbulence and of Rayleigh-Benard Convection

Small-scale turbulent flows sometimes undergo a self-organization process that generates structure at much larger scale. In some instances, this event is associated with an inverse cascade of an important dynamical quantity, even though other mechanisms can be at work.
In this talk I review two different examples, namely (1) the inverse enstrophy cascade that acts in small-scale elliptic patches of two-dimensional turbulence, and (2) the clustering of same-sign thermals and plumes in Rayleigh-Benard convection at moderately large values of the Rayleigh number.

References:
A. Babiano, A. Provenzale. Coherent vortices and tracer cascades in two-dimensional turbulence. J. Fluid Mech. 574, doi: 10.1017/S0022112006004265 (2007).
A. Parodi, J. von Hardenberg, G. Passoni, A. Provenzale, E.A Spiegel. Clustering of plumes in thermal convection. Phys. Rev. Lett., 92, doi: 101103/PhysRevLett.92.194503 (2004).
J. von Hardenberg, A. Parodi, G. Passoni, A. Provenzale, E.A Spiegel. Large-scale patterns in Rayleigh-Benard convection. Physics Letters A, in press (2008).