ANALYSIS OF SPATIAL PATTERNS IN SECONDARY FLOWS GENERATED BY TORSIONALLY OSCILLATING SPHERES IN LINEARLY STRATIFIED FLUIDS

Measurements have been made of the cellular flow patterns observed by Folse [Phys. Fluids 6, 537 (1994)] in the secondary flow field of tors ionally oscillating spheres in stratified fluids. Shadowgraphs were ma de 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 less than or equal to omega less than or equal to 13.5 rad/s and amplitudes theta(0) less than or equal to 1 rad) in linearly stratified fluids, with Brunt-Vaisala frequencies between 0.8 rad/s less than or equal to N less than or equal to 2.1 rad/s. The spatial pattern was determined by measuring the vertical size, d, and radial position, r, for each c ell. Dimensionless cell size, d/r, was found to depend on the paramete rs (omega/N), theta(0), and the angular position on the sphere phi mea sured from the pole. A correlation of the dimensionless cell size is f ound, independent of sphere radius, given by: d(n)/(r) over bar(n) = 0 .22(omega/N)theta(0)(2) cot(<(phi)over bar>(n)), where (r) over bar(n) , and <(phi)over bar>(n), are the average radial and angular positions of the nth cell. This correlation results in a discrepancy between me asurements and expectations based on a heuristic energy argument. (C) 1998 American Institute of Physics.