THE CHARACTER OF THE EQUILIBRIUM OF A HEAVY, VISCOUS, INCOMPRESSIBLE, ROTATING FLUID OF VARIABLE DENSITY

Abstract

In a previous paper, the equilibrium of a plane horizontal layer of a viscous incompressible fluid of variable density po in the vertical (z) direction, which rotates uniformly at Ω rad./sec. about an axis making an angle θ with the vertical, was examined by the usual method of studying the initial behaviour of a small disturbance. The general properties of the ensuing hydrodynamical motion for any ρ₀(z) and μ₀(z) (μ₀ being the coefficient of viscosity) were discussed. It was shown that in some circumstances, including the case θ = 0, the solution is characterized by a variational principle.