Comparison of mesoscale meanders and eddies simulated by quasi‐geostrophic and primitive equation models: A case study

Abstract

A comparison is made between meanders and eddies simulated by a two‐layer, quasi‐geostrophic numerical model and those simulated by a Bryan‐Cox type primitive equation model at various values of the Rossby number. The model geometry and parameter settings are based on a previous study of the Norwegian Coastal Current by Ikeda et al. (1989). The aim is to identify the dynamical effects of increasing the Rossby number and to assess the performance of the quasi‐gestrophic (QG) model when applied to meandering currents which are outside its formal range of validity. The growth rates of meanders in the primitive equation (PE) model are particularly sensitive to the vertical resolution used; this sensitivity is strongest at short wavelengths, and suggests that very fine vertical resolution may be needed in the Bryan‐Cox model for accurate simulation of meander growth. The QG model simulates the phase speed of meanders in the PE model well but overestimates the growth rate at moderate Rossby number (by about 25% when the Rossby number is 0.69). As the Rossby number is increased, the asymmetry of the primitive equation vorticity equation comes increasingly into play, and at finite meander amplitude this results in small, intense cyclones and large, weak anticyclones. This effect, which is absent in the quasi‐geostrophic model, can lead to significant changes in the potential vorticity field (and hence, by implication, in the concentration fields of other tracers). The principal trends in the solutions as the Rossby number is increased are as follows: (1) the disturbance becomes less energetic (in a dimensionless sense) at all stages of its life cycle; (2) the effects of the disturbance become increasingly trapped near the position of the original frontal jet; and (3) cross‐frontal transport, particularly offshore transport of coastal water, is inhibited as coastal water is wrapped around the intense cyclones. Our results provide guidance in interpreting the results of Ikeda et al. and those of other eddy models.