A laboratory study of baroclinic instability

Abstract

Experimental and theoretical results are presented for a simple system which exhibits baroclinic instability. We consider the motion of two immiscible fluids with densities ρ ₁ and ρ ₂ contained in a cylinder rotating with angular frequency ω. The motion is driven by a contact lid rotating with frequency ω + ω. In this paper ω, ω, 2(ρ ₂ – ρ ₁)/(ρ ₂ + ρ ₁), and the geometry are such that the interface does not intersect the “ground” (e.g. an almost horizontal boundary). The motions are described by two-layer quasi-geostrophic equations which are identical, except perhaps for the presence of interfacial friction and tension, with those used in meteorology and oceanography. For small enough internal Froude number F = 4ω² L ²/(g(Δρ/ρ)H) or small enough Rossby number ε = ω/2ω the flow is steady and axisymmetric, the velocity field in each layer being determined primarily by frictional effects in top, bottom, and interfacial Ekman layers. For certain (F, ε) the flow becomes non-axisymmetric. The transition points for the case where the basic potential vorticity gradient is due to interface slope alone have been carefully measured and are in very good agreement with a linear instability theory which neglects sidewall effects. Some preliminary observations of supercritical motion, which include repeatable amplitude and wavenumber vacillation, are reported.