The Moving Flame Experiment
Stern, Melvin E.
- Publisher: Co-Action Publishing
(issn: 1600-0870, eissn: 0280-6495)
arxiv: Physics::Fluid Dynamics
When a flame is rotated around the outside bottom rim of a cylindrical pan of water initially at rest, D. Fultz has observed that the fluid acquires a net vertical component of angular momentum opposite to the rotation of the heat source. We have repeated this experiment in a cylindrical annulus in order to restrict the radial motions and have found that the same phenomenon occurs. Using a simple model based on the latter experiment we investigate the mechanism by which a fluid can acquire and maintain this momentum, considering that friction is the only force which can exert a net torque about the vertical. The effects of the heat source are replaced by a forced temperature field which has sinusoidal variations in the circumferential direction and which rotates about the vertical axis at a constant rate. The correlation between vertical and horizontal velocity components in the equilibrium state has been computed from the linearized two-dimensional vorticity equation. It is shown that when the viscosity is small or when the speed of the heat source is large there is a convergence of horizontal momentum towards the center of the channel which is balanced by the viscous stress of the induced mean motion. The total momentum of the fluid is computed from the conservation principle and is found to vary inversely as the square root of the molecular viscosity and inversely as the 5/2 power of the speed of the heat source.DOI: 10.1111/j.2153-3490.1959.tb00018.x