Abstract
The equilibrium of a plane horizontal layer of a viscous incompressible fluid of variable density ρ0 in the vertical (z) direction, which rotates uniformly at Ω rad./sec. about an axis making an angle θ with the vertical, is examined by the usual method of studying the initial behaviour of a small disturbance. Diffusion effects are ignored. The theory is developed for any general ρo(z) and μ(z), where μo is the coefficient of viscosity, assumed to depend only on the density. It is shown that the solution is characterized by a variational principle in two cases, namely, (a) when θ = 0, and (b) if θ ≠ 0 when the motion is confined to planes perpendicular to the horizontal component of Ω. The possibility of ‘overstability’ (instability setting in as oscillatory motion) is discussed. A necessary, though not sufficient, condition is that d2μ0/dz2. Based on the variational principle elucidated in this paper, treatments of two special density configurations, ρ(z), are given in a following paper.
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