Large Oceanic Gyres: Lagrangian Description

Anatoly Abrashkin (HSE, Nizhny Novgorod)

Jan 20. 2020, 14:30 — 15:30

The introduction gives an overview of various approaches to the consideration of vortices on a spherical surface. It is noted that they are all formulated in Euler coordinates. We have developed a new approach based on the use of Lagrangian variables.

A hydrodynamic model of an oceanic gyre is proposed. The fluid motion is considered in the leading-order shallow-water approximation in the spherical Lagrangian coordinates. Motion of liquid particles at the spherical surfaces is studied versus latitude and longitude as unknown variables. The boundary condition at the edge of the gyre is not formulated. An approximation of the averaged latitude is introduced when the coefficients of the momentum equation are replaced by constant values corresponding to the latitude of the center of the gyre. It is shown that the resulting set of equations is similar to the equations of plane hydrodynamics. Two classes of analytical solutions describing unsteady vortices are obtained. Variants of their matching with the external flow and models of vortices with a moving center are discussed.

Separately, the conclusion of the approximation of the averaged latitude in Euler coordinates is given. The prospects of its applications to the problems of vortex dynamics are analyzed.

Further Information
Venue:
ESI Boltzmann Lecture Hall
Associated Event:
Mathematical Aspects of Geophysical Flows (Workshop)
Organizer(s):
Adrian Constantin (U of Vienna)
George Haller (ETH Zurich)