Inertial Motions during the Transient Adjustment of a Density Anomaly in the Equatorial Ocean with Application to the Western Pacific Warm Pool

This paper is focused on the spontaneous transient adjustment of a buoyant lens of water with uniform density, initially at rest in the vicinity of the equator. For parameters typical of the western Pacific warm pool, the adjustment is shown to generate finite-amplitude wave motions with period ∼8 days, which are not covered by the standard theory of linear equatorial waves. This mechanism may be at the origin of inertial motions at the early stages of ENSO events in the western Pacific Ocean. The lens adjustment is studied within the 11/2-layer reduced-gravity approximation on the equatorial β plane, using the high-resolution finite-volume numerical methods that are specially designed to handle outcropping isopycnals. Under the reduced-gravity approximation, a buoyant region of light water with outcropping boundaries in the vicinity of the equator is described by two parameters: the meridional-to-zonal scale aspect ratio δ and the ratio γ of the Coriolis force to the pressure force on its meridional boundary. For realistic parameters (δ ∼ 10−1; γ ∼ 1), the lens, initially at rest, spreads eastward in accord with nonrotating gravity current dynamics, whereas its westward extrusion is arrested so that the western edge splits into two anticyclonic vortices. Meanwhile finite-amplitude westward-propagating inertial wave motions develop at the interface between the spreading current and the ambient fluid. The inertial wave structure is shown to be consistent with the structure of stable wave modes predicted by linear analysis of small amplitude perturbations superimposed on a zonally symmetric equatorial current with outcropping isopycnals. A Wentzel–Kramers–Brillouin–Jeffreys ray-tracing analysis indicates that the inertial wave is emitted during the early stage of the gravity current evolution and then dispersed on the spreading current.