From weak to strong turbulence: a traveling wave tour
Speaker: Francesco Fedele
Affiliation: Georgia Institute of Technology, Atlanta, USA
Time: 4:00PM
Date: Monday, July 15th 2013
Location: Merrion Room, Ground Floor, NexusUCD, University College Dublin. Blocks 9 & 10, Belfield Office Park
Abstract:
The weak wave turbulence of Zakharov unveiled the dynamics of ocean waves as that of a sea of nonlinearly interacting dispersive elementary waves. Their dispersive properties and energy cascade can be observed and measured in the ocean. In this regard, I will discuss recent experiments off the Venice coast that exploit a Variational Wave Acquisition Stereo System (VWASS) to study the space-time dynamics of sea waves. The delicate balance of dispersion and nonlinearities may yield the formation of solitons or traveling waves. These are introduced in the context of the Euler equations and the associated third order compact Zakharov equation. Traveling waves exist also in the strong turbulence of the Navier-Stokes (NS) equations. Indeed, for bounded geometries I will show that the NS equations can be reduced to generalized Camassa-Holm equations. From a dynamical system perspective, in phase space the associated vector field supports an invariant group orbit manifold, which corresponds in physical space to smooth and singular axisymmetric vortexons. The relevance of these coherent structures to transition to turbulence in non-breaking waves is finally discussed.
Tea/coffee will be provided. All are welcome - please pass on to anyone else you think may be interested
Series: Applied and Computational Mathematics Seminar Series
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