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

The development of meanders along a front and subsequent eddy formation results in the exchangeof water-mass properties across the front. This is an important phenomenon, both for continentalshelf and basin-scale thermodynamics. In this study, we are concerned with the authenticity ofgrowing baroclinic waves over bottom slope topography in commonly-used primitive equationmodels, as they are such a widely used tool for understanding the dynamics of the ocean. Baroclinicinstability 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 onthe 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 ofexperiments with topography are performed, introducing successively steeper topography parallelto the front. The results from the 2 models are verified by comparison with QG theory and resultsfrom a QG numerical simulation. Two versions of the isopycnal model, which employ differentnumerical 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 baroclinicwave in a flat channel is shorter in the Bryan-Cox model than that predicted by QG theory, QGnumerical model results, and the Bleck–Boudra isopycnal primitive equation model. This featureis a consequence of the vertical discretization used in this model. The magnitude of the lineargrowth rates is significantly smaller in the Bleck–Boudra isopycnal model than in the Bryan–Coxmodel and the QG simulation, because of implicit diffusion inherent in the numerical scheme usedby this model. The experiments with topography show that this implicit diffusion becomes mostactive in more stable environments. The modifying effects of topography expected from QG resultsare found in both primitive equation models: for topography of positive slope (i.e., with the sameinclination as the isopycnals), the fastest-growing wavelength increases and is damped; for topographyof negative slope, the fastest-growing wavelength decreases. The 2 primitive equationmodels are then initialized with an ageostrophic, outcropping front; and their results are comparedin the light of experience gained from the subsurface front simulations. Again, a series of experimentswith topography are performed. The results from these simulations show how ageostrophic effectsact 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, outcroppingfront, 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 equationmodels, 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 modelsare physically well-behaved, the wave characteristics may have been modified by numerical errors, and therefore to exercise care in interpretating the results.