Key words: point vortices, Riemann surfaces, Green functions. We consider N point vortices s j of strengths κ j moving on a closed (compact, boundaryless, orientable) surface S with riemannian metric g. As far as we know, only the sphere or surfaces of revolution, the latter qualitatively, have been treated in the available literature. The aim of this note is to present an intrinsic geometric f...

Jupiter’s Great Red Spot (GRS) has been observed in sufficient detail that we can use it to determine properties of the jovian atmosphere that cannot otherwise be found. These properties include: the potential vorticity of the GRS and its neighboring zonal jet streams, the shear imposed on the GRS by the jet streams, and the vertical entropy gradient (i.e., Rossby deformation radius). We show t...

In this paper, we provide stability and convergence analysis for a class of finite difference schemes for unsteady incompressibleNavier-Stokes equations in vorticity-stream function formulation. The no-slip boundary condition for the velocity is converted into local vorticity boundary conditions. Thom’s formula, Wilkes’ formula, or other local formulas in the earlier literature can be used in t...

The statistical properties of the local topology of two-dimensional turbulence are investigated using an electromagnetically forced soap film. The local topology of the incompressible 2D flow is characterized by the Jacobian determinant Lambda(x,y) = 1 / 4(omega(2)-sigma(2)), where omega(x,y) is the local vorticity and sigma(x,y) is the local strain rate. For turbulent flows driven by different...

We present benchmark simulations for the 8:1 di erentially heated cavity problem, the focus of a special session at the rst MIT conference on Computational Fluid and Solid Mechanics in June 2001. The numerical scheme is a fourth-order nite di erence method based on the vorticity-stream function formulation of the Boussinesq equations. The momentum equation is discretized by a compact scheme wit...

Coarse resolution numerical ocean models must typically include a parameterisation for mesoscale turbulence. A common recipe for such parameterisations is to invoke mixing of some tracer quantity, such as potential vorticity or buoyancy. However, it is well known that eddy fluxes include large rotational components which necessarily do not lead to any mixing; eddy diffusivities diagnosed from u...