Intense nonlinear migrations of the Pacific warm pool

An upper bound for the nonlinear eastward propagation rate of the Pacific warm pool is derived analytically using an inertial two-and-a-half-layer model on a β plane. The model is based on the familiar idea that, in most years, the eastward migration tendency is arrested by the drag imposed on the ocean by the westward trade winds. During El Nino years, however, when the wind partially (or completely) relaxes, the pool is freed to move toward the east. The upper bound that we focus on corresponds to a rapid migration associated with a complete relaxation of the westward winds. Nonlinear analytical solutions to the above state are constructed by integrating the (inviscid) horizontal momentum equations over a control volume in a coordinate system moving steadily toward the east. A balance between the eastward flow-force (i.e., the momentum flux resulting from the eastward density gradient) and the opposing westward form-drag (exerted by the westward flowing intermediate fluid diving under the pool) is examined. It involves integrated pressure forces, integrated inertia and the integrated Coriolis forces. In the limit of a control volume with an infinitesimal north–south extent, no recirculation (i.e., no lateral exchange of mass between the fraction of the pool occupying the immediate vicinity of the equator and regions immediately to the north and south), and no cross-equatorial flows, the governing equations reduce to the equations that govern the nonrotating (i.e., β≡0) intrusion of warm water into a resting two-layer system. This essentially means that the Coriolis force does not have any zonal component along the equator. For such conditions, the nonlinear eastward speed is found to be [2g(Δρ1/ρ)H1]1/2 [1−(H2/H1)]3/2, where Δρ1 is the density difference between the pool and the intermediate water underneath (i.e., the so-called intermediate layer), H1 the undisturbed thickness of the intermediate layer ahead of the pool, and H2 is the intermediate layer thickness under the pool. Typical values for the Pacific give a bounding propagation rate of 50–60 cm s−1, which is in good agreement with the observed migration rate during both the 1982–83 El Nino and the 1997 El Nino, the only ones in history that are known to result from an almost complete relaxation of the winds.