École Nationale Supérieure de
Techniques Avancées

Résumé

In the case of a 2D infinite array of small co-rotating vortices an attractor to the evolution of all possible initial conditions has been found numerically. This attractor is a family of vortices parametrised by a/b where a is the characteristic radius of the vortex and b the distance between them. This behaviour has been found independently of the value of the Reynolds number as it can be scaled out, in a region of values from Re = 10 to Re = ∞. This family of solutions has been compared with the asymptotic solution of a small 2D vortex submitted to a weak irrotational strain for high Reynolds number, calculated by Moffatt and al, where the imposed strain in our case is the one produced by all the sorrounding vortices. In a region of values of a/b from a/b = 0 to a/b~0:2 the asymptotic theory gives a proper approximation of the inner core of the streamfunction distribution. This succesfull comparation make valid the hypothesis of high Reynolds number of the asymptotic theory down to Re = 10. Although, for a=b ~0:2 the system changes to a regime where the diffusion increases which is not captured by the asymptotic theory a numerical procedure to calculate the limit of validation of the asymptotic theory has been proposed.