Equatorial dynamics in a [formula omitted] model

Abstract

A nonlinear, 2 1 2 - layer model is used to study the dynamics of wind-driven equatorial ocean circulation, including the generation of mean flows and instabilities. The model allows water to entrain into, and detrain from, the upper layer, and as a consequence the temperatures of the two active layers can vary. The model ocean basin is rectangular, extends 100° zonally, and for most solutions has open boundaries at 15°S and 15°N. All solutions are forced by a switched-on wind field that is an idealized version of the Pacific trades: the wind is westward, uniform in the meridional direction (so it has no curl), located primarily in the central and eastern oceans, and in most cases it has an amplitude of 0.5 dyn cm −2. For reasonable choices of parameters, solutions adjust to have a realistic equatorial circulation with a westward surface jet, an eastward undercurrent, and with upwelling and cool sea surface temperature in the eastern ocean. Most of the meridional circulation (81% of the transport) is part of a closed tropical circulation cell, in which water upwells in the eastern, equatorial ocean and downwells elsewhere in the basin; the rest participates in a mid-latitude circulation cell with lower-layer water entering the basin and upper-layer water leaving it through the open boundaries. Three basic types of unstable disturbances are generated in the eastern ocean: two of them are antisymmetric about the equator, one being surface-trapped with a period of about 21 days (f 1), and the other predominantly a lower-layer oscillation with periods ranging from 35 to 53 days (f 2) that causes the undercurrent to meander; the third is symmetric with a period of about 28 days (f 0) and a structure like that of a first-meridional-mode Rossby wave. The amplitudes of the disturbances are sensitive to model parameters, and as parameter values are varied systematically solutions appear to follow variations of the quasi-periodic route to turbulence, one of the common transitions to chaotic behavior. Realistic mean flows develop only when detrainment and lower-layer cooling are present in the model physics, processes that are necessary for the generation of a tropical circulation cell: without detrainment, water accumulutes in the upper layer until entrainment ceases and the model adjusts to Sverdrup balance, which is a state of rest for a wind without curl; without cooling, the temperature of the lower layer slowly rises until it approaches that of the upper layer. The mean-momentum budget for the upper layer shows that the model's Reynolds-stress terms are not a significant part of the momentum balance, having a maximum amplitude only about 19% of the wind stress. In contrast, the mean-heat budget demonstrates that eddy heating warms the cold tongue significantly, with an amplitude as large as the heating through the surface. Interestingly, the time-averaged continuity equations indicate that the instabilities tend to increase the upward tilt of the upper-layer interface toward the equator. When layer temperatures are kept fixed only a weak version of disturbance f 1 develops, indicating that the equatorial temperature front is an important aspect of instability dynamics. In fact, a frontal instability does exist in the model; it involves the conversion of mean to eddy potential energy, but it is the mean energy associated with the variable upper-layer temperature field, rather than with tilted layer interfaces, as is the case for traditional baroclinic instability. Perturbation-energy budgets suggest that frontal, barotropic and Kelvin-Helmholtz instabilities are energy sources for the disturbances, whereas traditional baroclinic instability is an energy sink. The two, fastest growing, antisymmetric, unstable-wave solutions to a linearized version of the model correspond closely to disturbances f 1 and f 2 from the nonlinear model, and perturbation-energy budgets for these waves indicate that their energy sources are primarily frontal instability and lower-layer barotropic instability, respectively.