The Formation of Oceanic Eddies in Symmetric and Asymmetric Jets. Part I: Early Time Evolution and Bulk Eddy Transports

Abstract

A numerical study of the life cycles of eddies formed in perturbed baroclinic jets, emphasizing the influence of spanwise asymmetry in the initial structure of the jet on the downstream evolution of the flow, is presented. In particular, attention is focused on the early time evolution of two such currents that are fully determined by their lateral/vertical cross sections of streamwise velocity and balanced temperature fields. The first jet profile is constructed so as to be representative of a typical observational cross section of the Gulf Stream off Cape Hatteras; it therefore has laterally asymmetric baroclinicity and barotropy. The second cross section consists of a jet with laterally symmetric velocity shear. Primitive equation nonseparable linear stability analyses of these two mean states are performed to determine the wavelengths, phase speeds, and growth rates of the fastest growing normal modes of temporal instability. The life cycles of the eddies that develop on these jets are investigated using a three-dimensional numerical model that employs the nonhydrostatic Boussinesq equations of motion in channel geometry with inflow/outflow streamwise boundary conditions. The wavelengths, phase speeds, and growth rates of the disturbances that develop during the early stages of flow evolution are compared to those predicted by the temporal stability analysis presented herein, and also to previous temporal and spatial stability analyses. Bulk spanwise eddy transports of heat and momentum are examined to assess the influence of asymmetry in the initial jet profile. The formation frequency and strength of warm core and cold core rings in the two simulations are compared and contrasted with observations of eddy formation in the Gulf Stream system. In a companion paper we explore the detailed dynamical mechanisms through which individual coherent vortical structures form and more fully analyze the associated horizontal and vertical mixing of heat and potential vorticity.