ON INTERMEDIATE MODELS FOR STRATIFIED FLOW

Intermediate models contain physics between that in the primitive equa tions and that in the quasigeostrophic equations. The specific objecti ve here is to investigate the absolute and relative accuracy of severa l intermediate models for stratified flow by a comparison of numerical finite-difference solutions with those of the primitive equations (PE ) and with those of the quasigeostrophic (QG) equations. The numerical experiments involve initial-value problems for the time-dependent dev elopment of an unstable baroclinic jet on an f plane in a doubly perio dic domain with flat bottom. Although the geometry is idealized, the p roblem is set up so that the dynamics should be similar to that of the baroclinic jet observed off the northern California coast in the Coas tal Transition Zone (CTZ) field program. Three numerical experiments a re conducted where the flow fields are characterized by local Rossby n umbers that range from moderately small to O(1). The unstable jet deve lops finite amplitude meanders that grow in amplitude until they pinch off to form detached eddies on either side of the jet. The instabilit y process is characterized by the transfer of potential to kinetic ene rgy accompanied by a large increase in the barotropic component of the flow. Although the initial jet velocity profiles are symmetric about the jet centerline. as the Rossby number of the jet increases the mean der growth and eddy detachment process becomes more asymmetrical about the jet axis. A meander on the positive vorticity side of the jet pin ches off first to form a relatively large anticyclonic eddy followed i n time by the detachment of a smaller cyclonic eddy on the negative vo rticity side. The intermediate models that we consider are the balance equations (BE), the balance equations based on momentum equations (BE M), the iterated geostrophic models (IG2 and IG3), the linear balance equations (LBE), the linear BEM (LBEM), and the geostrophic momentum a pproximation (GM). We also include a second-order quasigeostrophic app roximation (QG2) and a primitive equation model with semi-implicit tim e differencing (PESI). The results of the numerical experiments for mo derate Rossby number flow show that the QG, QG2, LBE, and GM models gi ve large errors and produce flow fields that have substantial qualitat ive differences from the PE. The LBEM model is somewhat better, while IG2 gives considerably smaller errors. The BE, BEM, IG3, and PESI mode ls give highly accurate approximate solutions to PE, and that result h olds also for those models applied to the O(1) Rossby number flow.