Stability of relative equilibria of three vortices

Hassan Aref

Three point vortices on the unbounded plane have relative equilibria wherein the vortices either form an equilateral triangle or are collinear. While the stability analysis of the equilateral triangle configurations is straightforward, that of the collinear relative equilibria is considerably more involved.This paper gives analysis based on explicit formulas for the three eigenvalues determining the stability, including a new formula for the angular velocity of rotation of a collinear relative equilibrium.

Phys. Fluids 21, 094101 (2009)

Fluctuations and stratification in sedimentation of dilute suspensions of spheres

Daniel Chehata Gómez, Laurence Bergougnoux, Élisabeth Guazzelli, and John Hinch

Whether stratification can control velocity fluctuations in suspensions of sedimenting spheres is tested. The initial value and early decay of the velocity fluctuations are not affected by stratification. On the other hand, in the descending front where the stratification is strong and well defined, the velocity fluctuations are inhibited according to a previously proposed scaling. In between, after the initial decay and before the arrival of the front, the local value of the stratification does not always play a role.

Phys. Fluids 21, 093304 (2009)