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