A numerical model comparison of baroclinic instability in the presence of topography

Abstract

The development of meanders along a front and subsequent eddy formation results in the exchange of water-mass properties across the front. This is an important phenomenon, both for continental shelf and basin-scale thermodynamics. In this study, we are concerned with the authenticity of growing baroclinic waves over bottom slope topography in commonly-used primitive equation models, as they are such a widely used tool for understanding the dynamics of the ocean. Baroclinic instability is simulated in a cyclic channel, in 2 such models: the Bryan-Cox model (Cox, 1984) and the Bleck-Boudra (1986) isopycnal model. We focus on the linear stage of instability and on the effects of topography, with isobaths running parallel to the front. Initially, a quasi-geostrophic (QG), subsurface front is used as a basic state for baroclinic instability in the 2 models. A series of experiments with topography are performed, introducing successively steeper topography parallel to the front. The results from the 2 models are verified by comparison with QG theory and results from a QG numerical simulation. Two versions of the isopycnal model, which employ different numerical schemes for advection in the thickness equation, are run for the flat-bottomed experiments. We demonstrate how this choice of numerical scheme can affect baroclinic wave activity. Linear growth rate curves are plotted for each model experiment. The fastest-growing baroclinic wave in a flat channel is shorter in the Bryan-Cox model than that predicted by QG theory, QG numerical model results, and the Bleck-Boudra isopycnal primitive equation model. This feature is a consequence of the vertical discretization used in this model. The magnitude of the linear growth rates is significantly smaller in the Bleck-Boudra isopycnal model than in the Bryan-Cox model and the QG simulation, because of implicit diffusion inherent in the numerical scheme used by this model. The experiments with topography show that this implicit diffusion becomes most active in more stable environments. The modifying effects of topography expected from QG results are found in both primitive equation models: for topography of positive slope (i.e., with the same inclination as the isopycnals), the fastest-growing wavelength increases and is damped; for topography of negative slope, the fastest-growing wavelength decreases. The 2 primitive equation models are then initialized with an ageostrophic, outcropping front; and their results are compared in the light of experience gained from the subsurface front simulations. Again, a series of experiments with topography are performed. The results from these simulations show how ageostrophic effects act to stabilize baroclinic waves, but do not change the way that topography modifies them. Similar, numerically-induced, features were found in all the experiments with the ageostrophic, outcropping front, as was found with the subsurface front. By focusing on the linear growth of baroclinic waves, this investigation has pinpointed some artificial tendencies inherent in the 2 primitive equation models, which modellers will find useful when interpreting the results of their simulations. The important lesson for oceanographers is to remember, that although waves in the numerical models are physically well-behaved, the wave characteristics may have been modified by numerical errors, and therefore to exercise care in interpretating the results.