Discrete and Continuous Symmetries of Stratified Flows Past a Sphere

Abstract

This study presents the detailed experimental results of fine structures and dynamics in a stratified flow past a sphere, which is towed with constant velocity in a transparent basin. We developed experimental procedures based on the complete solutions of the truncated fundamental fluid equations. These complete solutions describe the waves and fine accompanying ligaments, as well as the vortices and other flow structures. To visualize the flow, a variety of classical schlieren and electrolytic precipitation procedures were used. Ligaments appear in the schlieren images of the flow as fine interfaces and fibers. They strengthen the influence of the relatively weak density gradient in a continuously stratified fluid (CSF). The symmetry in the wake is discrete at small Froude numbers with the domination of buoyancy effects. At increased velocity and high Froude numbers, when the inertial and non-linear effects turn out to be significant, an axial symmetry becomes continuous.

Symmetry and Symmetry-Breaking in Fluid Dynamics

“…Three papers [7][8][9] bring the lens of symmetry/symmetry-breaking to somewhat more specialized problems. The magnetohydrodynamic turbulence in the Earth's core, the dynamo problem, is the subject of a paper by Krzysztof Mizerski [7] from the Polish Academy of Science.…”

“…The asymmetry is caused not by the geometry of the mixing zone, but by the unequal fuel and oxidizer Lewis numbers. The third paper in this group, a review article by Yuli Chashechkin [9] from the Russian Academy of Science, concerns stratified flow past a sphere, which has been visualized using the schlieren method. The images reveal the presence of very fine ligaments that, at higher velocities, introduce asymmetric features to the flow in the wake.…”