Instability of baroclinic Rossby waves; energetics in a two-layer ocean

Abstract

Abstract The instability of a baroclinic Rossby wave in a two-layer, inviscid ocean is investigated theoretically and the results are applied to the ocean. The velocity field of the basic state (the wave) is characterized by significant horizontal and vertical shears, non-zonal currents, and unsteadiness due to its westward propagation. Truncated Fourier series are used in the perturbation analyses. Growing perturbations draw their energy from the available kinetic or potential energy of the basic wave depending upon whether the horizontal scale of the wave, L , is smaller or larger than the radius of deformation, L ρ . When the horizontal and vertical shears of the wave are comparable dynamically, L ∼ L ρ , the ratio of energy transfers from the available kinetic and potential energy is very sensitive to the ratios L / L ρ and U / C , where U is a typical current and C a typical phase speed of the wave. For L = L ρ the transfers are augmenting if U C , yet they detract from each other if U C . The beta effect makes instability characteristics of meridional currents distinctly different from those of zonal currents. Although it tends to reduce the growth rate, perturbations dominated by a zonal current can grow regardless of the beta effect. The growth rate of the most unstable perturbation increases monotonically with L for the mixed instability ( L ∼ L ρ ). The scale of the fastest growing perturbation is significantly larger than L for barotropically controlled flows ( L L ρ ), reduces to L for the mixed instability, and is slightly larger than L ρ for baroclinically controlled flows ( L > L ρ ). In a geophysical field, like the ocean, this model indicates the possibility of energy transfer to motion on the scale of the radius of deformation (40-km rational scale, or 250-km wavelength) from both smaller and larger scales. It is also suggested that away from intense currents like the Gulf Stream eddy-eddy interactions are move vigorous than are eddy-mean interactions.