The Non-Monotonicity of Solutions in Swirling Flow.

Abstract

The existence of solutions of Batchelor's nonlinear differential equations for swirling flow induced by two parallel rotating coaxial discs of infinite size is investigated. It is found that if the discs rotate in the same direction (with one rotating and one stationary disc as a special case), then for sufficiently small kinematic viscosity of the fluid, the angular velocity of the swirling flow cannot vary monotonically in the axial direction. Should a condition of monotonic variation of the angular velocity be imposed, then a solution to the governing differential equations would not exist. A detailed step by step proof is provided.

Document Details

Document Type
Technical Report
Publication Date
Oct 01, 1975
Accession Number
ADA017963

Entities

People

  • J. B. Mcleod
  • S. V. Parter

Organizations

  • University of Wisconsin–Madison

Tags

DTIC Thesaurus Topics

  • Differential Equations
  • Eddies (Fluid Mechanics)
  • Equations
  • Flow
  • Linear Differential Equations
  • Mathematical Analysis
  • Mathematics
  • Nonlinear Differential Equations
  • Real Variables
  • Stationary
  • Viscosity

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Fluid Mechanics and Fluid Dynamics.
  • Linear Algebra