Propagation of vortices within a rotating, fluid shell

✍ Scribed by Paolo Lanzano

• Publisher: Springer Netherlands
• Year: 1992
• Tongue: English
• Weight: 787 KB
• Volume: 58
• Category: Article
• ISSN: 1573-0794
• DOI: 10.1007/bf00058072

✦ Synopsis

We consider a spherical, solid planet surrounded by a thin layer of an incompressible, inviscid fluid. The planet rotates with constant angular velocity

We study the vortex motion within this rotating ocean. For this purpose, we obtain a linearized version of the Navier-Stokes equation and adopt it as our ocean model; next, we prove analytically that a certain function of vorticity is an invariant of motion.

Using this ocean mode1 and this invariant property of vorticity, we are able to establish a genera1 equation governing the motion of vortices within a fluid shell: it is a nonlinear partial differential equation of the third order for the stream function of motion.

We finally examine some particular solutions of this vorticity equation that represent solitary waves of permanent form and decay within a finite distance. These solutions have been represented in terms of quadratic, exponential, and hyperbolic functions.

The question whether these vortices that propagate as solitary waves could be solitons depends on their behavior when they collide with each other; this has not yet been resolved.