A REPRESENTATION OF ROTATION AND CURVATURE IN FLUID FLOWS AND CONNECTION WITH VORTICITY AND DISSIPATION,

Abstract

The report attempts to show connections between vorticity, the rotation of a line element, the curvature of a streamline, and dissipation in viscous fluid flows. A tensor of third rank is shown to determine the angular velocity of a differential element of a filament (curve) of a moving material, if the current direction of the differential element is known. The same tensor determines the curvature of streamline at a point, if the velocity of the fluid at that point is given. Dilatation does not influence the tensor. The dissipation function of an incompressible Newtonian fluid can be expressed in terms of its second order invariants. The report also includes other properties of the tensor such as algebraic properties. (Author)

Document Details

Document Type
Technical Report
Publication Date
Mar 11, 1964
Accession Number
AD0605364

Entities

People

  • Kirit Yajnik
  • Paul Lieber

Organizations

  • University of California, Berkeley

Tags

DTIC Thesaurus Topics

  • Curvature
  • Dissipation
  • Filaments
  • Flow
  • Fluid Flow
  • Geometric Forms
  • Geometry
  • Lines (Geometry)
  • Materials
  • Motion
  • Rotation

Fields of Study

  • Mathematics

Readers

  • Fluid Mechanics and Fluid Dynamics.
  • Graph Algorithms and Convex Optimization.