Analysis of spatial patterns in secondary flows generated by torsionally oscillating spheres in linearly stratified fluids

Abstract

Measurements have been made of the cellular flow patterns observed by Folse [Phys. Fluids 6, 537 (1994)] in the secondary flow field of torsionally oscillating spheres in stratified fluids. Shadowgraphs were made of the secondary flow field of spheres, radii between 2.52 and 5.08 cm, torsionally oscillating (frequencies in the range 1.0 rad/s⩽ω⩽13.5 rad/s and amplitudes θ0⩽1 rad) in linearly stratified fluids, with Brunt–Väisälä frequencies between 0.8 rad/s⩽N⩽2.1 rad/s. The spatial pattern was determined by measuring the vertical size, d, and radial position, r, for each cell. Dimensionless cell size, d/r, was found to depend on the parameters (ω/N), θ0, and the angular position on the sphere φ measured from the pole. A correlation of the dimensionless cell size is found, independent of sphere radius, given by: dn/r̄n=0.22(ω/N)θ02 cot(φ̄n), where r̄n and φ̄n are the average radial and angular positions of the nth cell. This correlation results in a discrepancy between measurements and expectations based on a heuristic energy argument.