APPLIED MATHEMATICS SEMINAR

Speaker: Professor David Gurarie
Mathematics Department
Case Western Reserve University

Title : Inviscid 2D fluids, statistical equilibria, sinh-Poisson equation and 'vortex solitons'

[[||boldDate: Thursday, December 9
Time: 11 a.m.
Room: Red Centre 4082]]

Inverse cascade drives 2D-fluids (Eulerian or Navier-Stokes) to a large scale organized flow, through 'vortex merger' mechanism. The resulting quasi-equilibrium often appears as 'vortex dipole'. Such states were predicted long ago by 'statistical'(entropy) theories of 2D
turbulence, both for the 'vortex gas' dynamics (Onsager 48), and later for continuos vorticity.

Furthermore, statistical theories predict special
'stream-vorticity' relationship of the resulting stationary flows, which include among others the so-called sinh-Poisson equation. The latter has
close relation to some known Integrable Models, and allows a variety of exact analytic solutions. We loosely call them 'vortex solitons'.While
several families of 'solitons' were found over the past few years, their stability properties, hence 'physical realization' remained largely open.

The talk will review statistical theories for 2D Eulirean fluids, sinh-Poisson equation and its 'soliton' solutions. Then we shall
examine their dynamic stability using a semi-Largangian advective code developed by the author, and demonstrate it for several case studies.