On motion of the point algebraic singularity for two-dimensional nonlinear equations of hydrodynamics
type: Item
instance of: scholarly article
title: On motion of the point algebraic singularity for two-dimensional nonlinear equations of hydrodynamics
zbMATH Open document ID: 0829.35095
DOI: 10.1007/BF02110777
author: Yanyan Li
published in: Mathematical Notes
publication date: 1995-07-10T00:00:00Z
review text: For a system of two-dimensional nonlinear equations of hydrodynamics taking into account the earth's rotation, we deduce the chain of equations which contain a number of unfixed parameters that makes it possible to obtain the link of functions which define the principal term of the asymptotic representation of the solution. The closing of the obtained chain of ordinary equations is carried out. As was assumed, the center position of the weak singularity calculated by using the asymptotic representation for a solution of the initial nonlinear system can model the typhoon motion trajectory in the atmosphere of the rotating earth. We perform numerical analysis of corresponding differential equations for investigating the trajectory motion of the weak point-type singularity. By comparing the numerical data with the trajectory motion of the real typhoon, we observe their quite good qualitative coincidence. Further, the numerical analysis shows that the trajectory motion of the singularity center depends weakly on the initial conditions, that is, in fact, the position of the singularity center can be determined by a system of equations which contains far less equations.
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76N10
Mathematics Subject Classification ID: 86A10
zbMATH DE Number: 771985
zbMATH Keywords: chain of equations
zbMATH Keywords: closing
zbMATH Keywords: position of the weak singularity
zbMATH Keywords: typhoon motion trajectory in the atmosphere
zbMATH Keywords: numerical analysis
MaRDI profile type: Publication
cites work: A new theory of shock dynamics. II: Numerical solution
cites work: Singularities of the Euler equation and hydrodynamic stability
cites work: Q3657585
full work available at URL: https://doi.org/10.1007/bf02110777
OpenAlex ID: W1967368582
description: scientific article; zbMATH DE number 771985