On the instability of inviscid, rigidly rotating immiscible fluids in zero gravity
type: Item
instance of: scholarly article
title: On the instability of inviscid, rigidly rotating immiscible fluids in zero gravity
zbMATH Open document ID: 0898.76032
author: J. Ning
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1998-11-01T00:00:00Z
review text: The paper deals with the linear instability of the rigid rotation of a two-fluid column in zero gravity against three-dimensional normal-mode perturbations. Both fluids are inviscid and incompressible, and the rotation is uniform. The surface tension coefficient at the immiscible interface is constant. The inner core fluid is surrounded by another fluid bounded by an outer impermeable right cylinder, and the radially distant fluid is of higher density than the core fluid. The nondimensionalized problem consists of the Euler and continuity equations, kinematic and dynamic conditions on the interface, the slip condition on the outer wall, a condition for the pressure on the cylinder axis, and a pressure jump relation on the interface. The basic state is the zero velocity field in each fluid and parabolic pressure distributions depending on the radial coordinate only. The perturbation problem is an eigenvalue three-point problem for a system of eight ordinary differential equations with variable coefficients defined on two adjacent segments of the real axis and containing seven real parameters. The authors derive the eigenvalue relation in terms of the modified Bessel functions of the first and second kind. Their investigation is performed by the package Mathematica and mainly deals with the maximum growth rates and with the corresponding preferred instability wavelengths. Finally, the authors consider the limiting cases of no outer fluid (or the hollow-core vortex), and of the stationary two-fluid system.
Mathematics Subject Classification ID: 76E05
Mathematics Subject Classification ID: 76U05
zbMATH DE Number: 1097771
zbMATH Keywords: incompressible Euler equations
zbMATH Keywords: outer core
zbMATH Keywords: three-dimensional normal-mode perturbations
zbMATH Keywords: surface tension coefficient
zbMATH Keywords: inner core
zbMATH Keywords: eigenvalue three-point problem
zbMATH Keywords: system of eight ordinary differential equations
zbMATH Keywords: modified Bessel functions
zbMATH Keywords: Mathematica
zbMATH Keywords: instability wavelengths
reviewed by: Adelina Georgescu
describes a project that uses: Mathematica
MaRDI profile type: Publication
full work available at URL: s000330050073
OpenAlex ID: W2048914728
DOI: 10.1007/S000330050073
description: scientific article; zbMATH DE number 1097771