Instability and energetics in a baroclinic ocean
32° 10'N, 64°30'W
This thesis is made of two separate, but interrelated parts. In Part I the instability of a baroclinic Rossby wave in a two-layer ocean of inviscid fluid without topography, is investigated and its results are applied in 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. This configuration is more relevant to the ocean than are the steady, zonal 'meteorological' flows, which dominate the literature of baroclinic instability. Truncated Fourier series are used in perturbation analyses. The wave is found to be unstable for a wide range of the wavelength; growing perturbations draw their energy from kinetic or potential energy of the wave depending upon whether the wavelength, 2πL, is much smaller or larger than 2πLρ, respectively, where Lρ is the internal radius of deformation. When the shears are comparable dynamically, L~Lρ , the balance between the two energy transfer processes is very sensitive to the ratios L/Lρ and U/C as well, where U is a typical current speed, and C a typical phase speed of the wave. For L = Lρ they are augmenting if U < C, yet they detract from each other if U > C. The beta-effect tends to stabilize the flow, but perturbations dominated by a zonal velocity can grow irrespective of the beta-effect. It is necessary that growing perturbations are comprised of both barotropic and baroclinic modes vertically. The scale of the fastest growing perturbation is significantly larger than L for barotropically controlled flows (L < Lρ ), reduces to the wave scale L for a mixed kind (L ~ Lρ ) and is fixed slightly larger than Lρ for baroclinically controlled flows (L > Lρ ). Increasing supply of potential energy causes the normalized growth rate, αL/U, to increase monotonically as L → Lρ from below. As L increases beyond Lρ, the growth rate αLρ /U shows a slight increase, but soon approaches an asymptotic value. In a geophysical eddy field like the ocean this model shows possible pumping of energy into the radius of deformation (~ 40 km rational scale, or 250 km wavelength) from both smaller and larger scales through nonlinear interactions, which occur without interference from the beta-effect. The e-folding time scale is about 24 days if U = 5 cm/sec and L = 90 km. Also it is strongly suggested that, given the observed distribution of energy versus length scale, eddy-eddy interactions are more vigorous than eddy-mean interaction, away from intènse currents like the Gulf Stream. The flux of energy toward the deformation scale, and the interaction of barotropic and baroclinic modes, occur also in fully turbulent 'computer' oceans, and these calculations provide a theoretical basis for source of these experimental cascades. In Part II an available potential energy (APE) is defined in terms appropriate to a limited area synoptic density map (e.g., the 'MODE-I' data) and then in terms appropriate to time-series of hydrographic station at a single geographic location (e. g., the 'Panulirus' data). Instantaneously the APE shows highly variable spatial structure, horizontally as well as vertically, but the vertical profile of the average APE from 19 stations resembles the profile of vertical gradient of the reference stratification. The eddy APE takes values very similar to those of the average kinetic energy density at 500 m, 1500 m and 3000 m depth in the MODE area. In and above the thermocline the APE has roughly the same level in the MODE area (centered at 28°N, 69° 40'W) as at the Panulirus station (32° 10'N, 64° 30'W), yet in the deep water there is significantly more APE at the Panulirus station. This may in part indicate an island effect near Bermuda.
Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute and the Woods Hole Oceanographic Institution August 1975