seminário

[Francisco Cribari <cribari@de.ufpe.br>]

Seminário das Pós-Graduações em Estatística e Matemática Computacional

The mystery of the 2-D ideal incompressible fluid

Alexander Shnirelman
Concordia University

Data: 22 de agosto de 2007 (quarta-feira) 
Horário: 16:00 horas
Local: Auditório do Departamento de Estatística

RESUMO

2-dimensional ideal incompressible fluid is a model describing (with
some approximation) the atmospheres of the Earth and other planets. The
talk is devoted to some paradoxical properties of the flows of such a
fluid. Suppose the fluid is set in motion, and its initial velocity
field is small-scale, i.e. it looks like a collection of small (relative
to the whole flow domain) vortices, jets, etc. As the fluid moves, the
flow picture changes. The size of the vortices grows, until there
remains just a couple of large vortices. This process of energy transfer
(from small to large scales) is called inverse cascade; it appears in
all experiments and computer simulations, and looks quite strange.
Inverse cascade is in apparent contradiction with the time reversibility
of the Euler equations (describing the fluid motion). The analysis of
this contradiction leads to some deep questions of nonlinear partial
differential equations, dynamical systems, geometry and statistical
mechanics.