Solitary waves of vortices
type: Item
instance of: scholarly article
title: Solitary waves of vortices
zbMATH Open document ID: 0857.76022
DOI: 10.1007/BF00643788
author: Paolo Lanzano
published in: Earth, Moon, and Planets
publication date: 1996-06-05T00:00:00Z
review text: The author studies the propagation of solitary waves of vortices within a spherical shell which constitutes the uppermost layer of a solid planet. This solid-liquid configuration rotates with constant angular velocity about a fixed axis. The fluid within the shell is inviscid, incompressible, and of a constant density. The motion imparted by the planetary rotation to this fluid mass is governed by the Laplace tidal equation from which the potential of the extraplanetary forces has been deleted. Consistent with this ocean model, the stream function of a solitary wave of vortices must satisfy a third-order partial differential equation. The author obtains solutions to this wave equation by imposing the condition that the vertical component of vorticity is functionally related to the stream function. This dependence must necessarily be of the exponential type; this solution then can be reduced to a quadrature depending on some arbitrary parameters. It is shown that one can always choose these parameters in order to approximate the integral in question by means of an analytic function; thus a representation of the stream function of a solitary wave of vortices in terms of hyperbolic functions of time and position is reached.
Mathematics Subject Classification ID: 76B47
Mathematics Subject Classification ID: 76U05
Mathematics Subject Classification ID: 85A30
Mathematics Subject Classification ID: 86A05
zbMATH DE Number: 866170
zbMATH Keywords: spherical shell
zbMATH Keywords: solid-liquid configuration
zbMATH Keywords: Laplace tidal equation
zbMATH Keywords: stream function
zbMATH Keywords: third-order partial differential equation
zbMATH Keywords: wave equation
zbMATH Keywords: quadrature
zbMATH Keywords: hyperbolic functions
reviewed by: Felix Kaplanski
MaRDI profile type: Publication
cites work: Propagation of vortices within a rotating, fluid shell
cites work: Solitary waves of vortices within a rotating, fluid shell
description: scientific article; zbMATH DE number 866170