Titre/Title : Closed-form Green’s functions for the barotropic vorticity equation: new results on Bessel functions
Contact : Bruno Voisin (équipe MEIGE)
Résumé/Abstract : In a homogeneous, rigid-lid ocean or atmosphere, large-scale vorticity waves – Rossby waves - are possible due to spatial variations of the background vorticity. These variations arise due to projection of the Earth rotation vector on the local direction of gravity. Spatial variations in a magnetic field similarly lead to plasma Rossby waves. Finding the response to forcing of such waves is facilitated by constructing the Green’s function: the response to a point source of vorticity. Here, the Green’s function is solved explicitly for two cases: (1) the spatio-temporal response of a linear vorticity equation to an instantaneous, localized torque, and (2), employing renormalization, the steady response of a nonlinear vorticity equation to a sustained localized torque. Both cases lead to remarkable and explicit results. The first on a Bessel function integral, containing counterintuitive fluid dynamical aspects; the second to the notion of an incomplete Bessel function.