The free surface on a simple fluid between cylinders undergoing torsional oscillations: Part I: Theory, part II: Experiments
Abstract
Joseph (1976) developed an algorithm based on the theory of domain perturbations for the computations of unsteady motions of a simple fluid. The solution is expressed in powers of the amplitude of the unsteady data and the stresses (expanded into a Frechet series) are represented as multiple integrals which are reduced to canonical form appropriate to problems of rheological fluid mechanics. This paper applies Joseph's algorithm to find the shape of a free surface on a simple fluid between cylinders undergoing torsional vibrations. It is assumed that the angular frequency of the inner cylinder varies sinusoidally with time. Experiments designed to oscillate a circular rod sinusoidally about its axis were used to test the predictions of theory.
 Publication:

Archive for Rational Mechanics and Analysis
 Pub Date:
 December 1976
 DOI:
 10.1007/BF00248269
 Bibcode:
 1976ArRMA..62..323J
 Keywords:

 Cylindrical Bodies;
 Free Boundaries;
 Oscillating Flow;
 Surface Properties;
 Torsion;
 Algorithms;
 Canonical Forms;
 Kinematics;
 Perturbation Theory;
 Rods;
 Series Expansion;
 Shear Properties;
 Fluid Mechanics and Heat Transfer;
 Neural Network;
 Free Surface;
 Complex System;
 Nonlinear Dynamics;
 Electromagnetism