Unstable and Damped Equatorial Modes in Simple Coupled Ocean-Atmosphere Models

Abstract

Free equatorial modes for several simple coupled ocean-atmosphere models are determined. They are found to include unstable and damped modes of large zonal scale and long period. The influence of ocean thermo-dynamics on unstable modal behavior is systematically explored. The Model I ocean features a local thermal equilibrium. In Model II, linearized temperature advection is the sole ocean thermal process. The Model III ocean features both advective and local thermal processes, while that of Model IV features only local thermal processes. The ocean and atmosphere are each represented by linear shallow water equations on the equatorial ?-plane, and are linked by traditional couplings. A finite difference method with variable resolution is used to find eigenvalues and eigenvectors of the coupled systems. Key results are checked via a series method. Ocean modes are influenced most strongly by coupling, and are damped or destabilized depending on the configuration of induced atmospheric motion relative to oceanic velocities. In Model I, the oceanic Kelvin wave is destabilized while oceanic Rossby waves are damped by the coupling. In contrast, the gravest oceanic Rossby wave is destabilized while the Kelvin wave is damped in Model II. In Model III, coupling facilitates a slowly propagating unstable mode, which has structure intermediate between the Model I unstable Kelvin wave and the Model II unstable Rossby wave. A slow, unstable mode is also present in Model IV, but the growth rate is much reduced in the absence of ocean temperature advection. Growth rates of unstable modes are dependent on a variety of model coefficients. Further experiments include arbitrary shifting and meridional restriction of the atmospheric heating field. The latter experiment provides support for a conjecture concerning the seasonal timing of El Niño. The results are applied to the equatorial Pacific; climatological background states do not permit unstable modes that seem relevant to El Niño onset. Unstable modes permitted by a background state based on conditions observed prior to an actual El Niño are discussed.