Baroclinic instability of stratified shear flows in the ocean and atmosphere

Abstract

As an extension of Eady's model, two new baroclinic models are studied in this paper: Model 1 consists of a layer with constant shear surmounting a quiescent layer, and model 2 consists of a more statically stable uniform layer of constant zonal flow surmounting a layer with constant shear. In model 1 two special cases are considered, one in which the upper shear layer is more stably stratified than the lower quiescent layer (1a) and another in which the upper layer is less stably stratified than the lower layer (1b). The stability properties of model 16 and model 2 turn out to be very similar, since for the same shear, depth ratio, and static stability ratio the growth rates are the same and the wave structure of model 1b is the symmetric image of that of model 2. The wavelengths of the stability cutoff wave and the most unstable wave and the growth rate of the most unstable wave are considerably influenced by the presence of a quiescent layer in model 1a but are only moderately influenced by this quiescent layer in model 1b or by the uniform layer in model 2. The unstable wave moves eastward with a velocity slower than that of the vertically averaged mean current in the shear layer in model 1 but faster than the mean current in the shear layer in model 2. The deviation of the phase velocity from this mean current becomes larger the longer the wave. Typical parameters for an oceanic current system, such as the Gulf Stream, are applied to model 1a, and typical parameters for an atmospheric mid-latitude zonal flow are applied to model 2. The implications regarding long waves are that just as the long atmospheric waves penetrate the tropopause into the stratosphere, so the long oceanic waves penetrate the base of the thermocline to great depths, although the horizontal scales for the two systems are considerably different.