ALBERT

Description: The stability of eddies with three-layer stratification is examined experimentally. When the difference in density between the upper two layers is much greater (or less) than that between the lower two layers baroclinic instability on two different lengthscales (the Rossby radii associated with the upper and the lower interfaces) is possible. The vortices are created using modifications of two techniques described by Griffiths & Linden (1981) in their study of two-layer eddies. ‘Constant-flux’ eddies are generated by the release of a constant flux of buoyant fluid from a small source positioned a t the surface of a two-layer fluid. In a second variation of this experiment, the source is positioned at the interface between two layers and fluid of intermediate density is injected. As the horizontal lengthscale increases, the vortices evolve from a stable to an unstable state. It is showns that the size a t which the vortices become unstable may be significantly altered by the presence of a second interface. The results agree qualitatively with the conclusions of a linear stability analysis of quasi-geostrophic three-layer flow in a channel (Smeed 1988), but it is necessary to examine the effects of horizontal shear and Ekman dissipation to explain the experimental results. ‘Constant-volume’ eddies are produced by the release of a volume of buoyant fluid, initially contained within a cylindrical barrier, a t the surface of a two-layer fluid. After the barrier is removed, the buoyant fluid spreads a distance of the order of the Rossby radius. Similarly, vortices are created by releasing a volume of fluid of density intermediate between the initial two layers. Within a few rotation periods the vortices become unstable to disturbances similar to those observed in two-layer experiments. Qualitative agreement is found between the observed wavelength and the fastest growing mode predicted by the linear stability theory (Smeed 1988). When the disturbances reach large amplitude a change in lengthscale is often observed. © 1988, Cambridge University Press. All rights reserved.

Description: The stability of quasi-geostrophic three-layer stratified flow in a channel is examined. The mean zonal velocity Ūi is uniform within each layer (i = 1, 2, 3). Thus, as in the two-layer model of Phillips (1954), the only source of energy for growing disturbances is the potential energy stored in the sloping interfaces. Attention is focused upon the case in which ε = Δρ2/Δρ1 ≪ (Δρ1,Δρ2 are the changes in density across the upper and the lower interfaces). Two scales of instability are possible: long waves (wavenumber O(1)) associated with the upper interface and short waves (wave-number O(ε-1/2)) associated with the lower interface. It is found that short waves are unstable only when 8 (the ratio of the slope of the lower interface to that of the upper interface) is greater than one or less than zero, i.e. when the gradients of potential vorticity in the two lower layers have opposite signs. The short waves have the largest growth rates when S2ε (the ratio of the potential energy stored in the lower interface to that stored in the upper interface) ≳ 1. The results of this analysis are used in an accompanying paper to interpret some experiments with three-layer eddies. © 1988, Cambridge University Press. All rights reserved.