Statistics – Computation
Scientific paper
Jan 1992
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992em%26p...56...75l&link_type=abstract
Earth, Moon, and Planets (ISSN 0167-9295), vol. 56, no. 1, Jan. 1992, p. 75-82.
Statistics
Computation
1
Hydrodynamic Equations, Incompressible Fluids, Planetary Atmospheres, Rotating Fluids, Vortices, Vorticity Equations, Angular Momentum, Bessel Functions, Computational Fluid Dynamics, Partial Differential Equations, Planetary Rotation, Solitary Waves, Traveling Waves
Scientific paper
A spherical, solid planet surrounded by a thin layer of an incompressible, inviscid fluid is considered. The planet rotates with constant angular velocity. Within the constraints of the geostrophic approximation of hydrodynamics, the equation that governs the motion of a vortex tube within this rotating ocean is determined and turns out to be a nonlinear partial differential equation of the third order for the stream function of the motion. The existence is examined of particular solutions to the vorticity equation that represent traveling waves of permanent form but decaying at infinity. A particular solution is obtained in terms of I1 and K1, the modified Bessel functions of order one. The question whether these localized vortices that move like solitary waves could even be solitons depends on their behavior during and after collision with each other and has not yet been resolved.
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