Abstract
The stability properties of a baroclinic zonal current on the β plane are studied using a three-layer quasigeostrophic model. The model is Lie-Poisson Hamiltonian as neither forcing nor dissipation are considered. The associated integrals of motion (energy, zonal momentum, and vorticity-related Casimirs) are used in Arnold's method to evaluate formal and nonlinear (or Lyapunov) stability conditions. Six parameters entirely determine the solutions of the stability problem. The latter including: one nondimensional wavenumber of the perturbation; one stratification parameter; two Charney numbers, one planetary and one topographic (due to the geostrophic slope of the lower interface in the basic state); and two aspect ratio parameters which relate to the thicknesses of the layers in the reference state. Hydrographic data are employed to evaluate numerically the inferred stability properties in order to study the significance of baroclinic instability in a region mainly influenced by the Atlantic North Equatorial Current (NEC). The data suggest that the NEC is spectrally unstable, reflecting that the current is far too wide for a Hamiltonian (pseudo energy-momentum integral) to be negative definite. The nature of the instability is studied by virtue of the resonant interplay of vorticity-related and Rossby-like elementary modes. Growth rates and wavelengths of the most destabilizing perturbations compare well within reasonable bounds with the few in situ observations reported in the literature. A reduced-gravity two-layer model is shown to be incapable of accounting for the instability, suggesting that ocean interior effects are important in the stability properties of the NEC.