Stability of Equatorial Modes in a Simplified Coupled Ocean-Atmosphere Model

Abstract

The stability, periodicity, and horizontal structure of equatorial modes in a coupled ocean-atmosphere model, simplified by the assumption that zonal wind stress anomalies are proportional to sea surface temperature anomalies lagged by a zonal phase difference, are examined analytically in an unbounded basin. The gravest coupled Rossby and Kelvin modes coexist with additional westward and eastward slow modes whose phase speeds are smaller than the former. Two of these four modes, one propagating westward and the other eastward, are destabilized in each case depending upon the model parameters. For some particular parameter choices. coupled Rossby and Kelvin modes merge with westward and eastward slow modes, respectively. For other parameters, however. they separate and remain distinct from the slow modes. For all of these modes the primary modifications by coupling relative to uncoupled oceanic equatorial waves are a decrease in phase speed and an increase in meridional scale. Among the model parameter effects, those of the zonal phase lag between the wind stress and SST anomalies and the coefficients of thermal and mechanical damping are the most interesting. Positive and negative phase lags represent the wind stress anomalies located to the west and east of the SST anomalies, respectively. The frequency of all modes is symmetric about zero phase lag, whereas the growth rate is antisymmetric about zero phase lag relative to the uncoupled damping rate. Wind stress anomalies to the west of SST anomalies favor slow mode growth and coupled Rossby and Kelvin mode decay. Dissipation for the slow modes and the coupled Rossby and Kelvin modes is controlled differently. For the slow modes the dissipation is mainly thermal, whereas for coupled Rossby and Kelvin modes the dissipation is mainly mechanical.