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

The development of meanders along a Front and subsequent eddy formation res ults in the exchange of water-mass properties across the front. This is an important phenomenon, both for continental shelf and basin-scale thermodyna mics. In this study, pre are concerned with the authenticity of growing bar oclinic waves over bottom slope topography in commonly-used primitive equat ion models, as they are such a widely used tool for understanding the dynam ics 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 (198 6) isopycnal model. We focus on the linear stage of instability and on the effects of topography, with isobaths running parallel to the front. Initial ly, a quasi-geostrophic (QG), subsurface front is used as a basic state for baroclinic instability in the 2 models. A series of experiments with topog raphy are performed, introducing successively steeper topography parallel t o 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 i sopycnal model, which employ different numerical schemes for advection in t he thickness equation, are run for the flat-bottomed experiments. We demons trate how this choice of numerical scheme can affect baroclinic wave activi ty. Linear growth rate curves are plotted for each model experiment. The fa stest-growing baroclinic wave in a flat channel, is shorter in the Bryan-Co x model than that predicted by QG theory, QG numerical model results, and t he Bleck-Boudra isopycnal primitive equation model. This feature is a conse quence of the vertical discretization used in this model. The magnitude of the linear growth rates is Significantly smaller in the Bleck-Boudra isopyc nal model than in the Bryan-Cox model and the QG simulation, because of imp licit diffusion inherent in the numerical scheme used by this model. The ex periments with topography show that this implicit diffusion becomes most ac tive in more stable environments. The modifying effects of topography expec ted from QC results are found in both primitive equation models: for topogr aphy 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 e quation 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 topograp hy are performed The results from these simulations show how ageostrophic e ffects act to stabilize baroclinic waves, but do not change the way that to pography modifies them. Similar, numerically-induced, features were found i n all the experiments with the ageostrophic, outcropping front, as was foun d with the subsurface front. By focusing on the linear growth of baroclinic waves, this investigation has pinpointed some artificial tendencies inhere nt in the 2 primitive equation models, which modellers will find useful whe n interpreting the results of their simulations. The important lesson for o ceanographers is to remember, that although waves in the numerical models a re physically well-behaved, the wave characteristics may have been modified by numerical errors, and therefore to exercise care in interpretating the results.