Geometrization of vortex and spiral flows in an ideal homogeneous fluid
type: Item
instance of: scholarly article
title: Geometrization of vortex and spiral flows in an ideal homogeneous fluid
zbMATH Open document ID: 1051.76011
author: A. V. Kistovich
author: Yu. D. Chashechkin
published in: Regular and Chaotic Dynamics
publication date: 2004-09-07T00:00:00Z
review text: The authors present a theoretical study of steady vortex motion of homogeneous ideal heavy fluid with a free surface by methods of differential geometry. The main idea is based on suggestion that the velocity field is formed by geodesic flows on some surfaces. For steady flows, integral flow lines are geodesics on second-order surfaces being parameterized and located in the space occupied by the fluid. In this case both Euler and continuity equations are transformed into equations for inner geometry parameters. Conditions on external parameters are derived from boundary conditions of the problem. An investigation of properties of generalized Rankine vortex that is a vertical vortex flow contacting with the free surface is done. In addition to the classical Rankine vortex, these vortices are characterized by finite integral invariants. The constructed set of explicit solutions depends on a unique parameter, which can be determined experimentally through measurements of depth and shape of a near-surface hole produced by the vortex.
Mathematics Subject Classification ID: 76B47
Mathematics Subject Classification ID: 53Z05
zbMATH DE Number: 2097406
zbMATH Keywords: zero helicity flow
zbMATH Keywords: generalized Rankine vortex
zbMATH Keywords: differential geometry
zbMATH Keywords: geodesics
MaRDI profile type: Publication
DOI: 10.1070/RD2004V009N01ABEH000261
description: scientific article; zbMATH DE number 2097406