ON THE STABILITY OF SOME FLOWS OF AN IDEAL FLUID WITH FREE SURFACES

Abstract

The stability of 4 types of 2-dimensional free-surface flows of an ideal fluid was investigated when subjected to small perturbations. The perturbations of a hollow vortex flow bounded by cylindrical walls were neutrally stable; the propagation of these perturbations is compared to the propagation of gravity waves in H2O. The impinging of a jet on a plate of finite width was also a stable configuration. A series of orifice flows had stable perturbations with the exception of an isolated unstable perturbation in flow through a Borda mouthpiece. The existence of unstable perturbations is indicated in the case of equal and opposite jets. The basic flow potential for a hollow vortex bounded by parallel plane walls is expressed in terms involving elliptical functions; the complexity of the equations made a solution intractable. The method of attack gave the upper bounds on Rl (lambda) rather than a 1-dimensional continuum of permissible eigenvalues and corresponding eigenfunctions.

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Document Details

Document Type
Technical Report
Publication Date
Dec 01, 1952
Accession Number
AD0000484

Entities

People

  • G. W. Morgan
  • Jane L. Fox

Organizations

  • Brown University

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Analytic Functions
  • Boundaries
  • Coefficients
  • Differential Equations
  • Eigenvalues
  • Equations
  • Flow
  • Fluids
  • Gravity
  • Gravity Waves
  • Hodographs
  • Power Series
  • Steady Flow
  • Steady State
  • Surface Properties
  • Two Dimensional
  • Waves

Fields of Study

  • Mathematics

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Calculus or Mathematical Analysis
  • Fluid Mechanics and Fluid Dynamics.