SOLUTION OF THE SOMMERFELD-SEXL CHARACTERISTIC EQUATION FOR THE STABILITY OF COUETTE FLOW

Abstract

The Sommerfeld-Sexl transcendental equation which yields the stability parameters of Couette flow is first transformed. Then by introducing the Wronski determinant it is possible to eliminate the unknown Bessel functions of imaginary argument and imaginary order, which until then prohibited the solution of the original Sommerfeld-Sexl equation. A series expansion in the wall distance with the stability parameters in polynomial form was obtained which can be solved numerically for any modes and widths of the gap. For a ratio of the inner and outer radius of 2 stability was found for the first and third mode.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Aug 01, 1964
Accession Number
AD0605831

Entities

People

  • F. Schultz-grunow

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Air Force
  • Ball Bearings
  • Bessel Functions
  • Boundaries
  • Computational Science
  • Couette Flow
  • Differential Equations
  • Equations
  • Flow
  • Navier Stokes Equations
  • Perturbation Theory
  • Perturbations
  • Reynolds Number
  • Transitions
  • Turbulence
  • Wave Propagation
  • Waves

Readers

  • Calculus or Mathematical Analysis
  • Plasma Physics.