Nonlinearities in Low-Frequency Equatorial Waves

Abstract

The nonlinear response to low-latitude, temporally periodic forcing centered on the equator is studied. Comparisons are made with a linear solution containing no advections; for both solutions the model consists of a spectral, equatorial ?-plane shallow-water system. The imposed forcing period is 40 or 16 days, designed to simulate respectively the global-scale atmospheric oscillation and the 10?20 day monsoonal oscillation. Forcing zonal wavenumbers are M = 1 or 2 (40-day period) and M = 5 (16-day period). Results for all cases show that advection does not greatly influence the time evolution of the long-term response, although particular features at a given time may be noticeably affected. For the M = 1 (propagating forcing) experiments, the primary changes are in the geopotential field off the equator (consistent with gradient wind effects), and in the low-latitude zonal wind u. The low-latitude wind influences help cause significant displacement of divergence from forcing in the nonlinear, as opposed to linear, runs. In the real atmosphere, such displacement could provide a mechanism for nonsteady propagation of convection. For standing wave M = 2 forcing, no eastward propagation is observed in either the linear or nonlinear solutions, in contrast with the actual 40-day oscillation. Therefore, advection does not appear to be a determining factor in explaining the eastward movement. Advective effects for propagating M = 5 forcing are mostly similar to those of corresponding M = 1 cases, the main exception being in the divergence field where no phase shift relative to forcing is seen. Thus, the nonlinearly produced divergence shift appears to be scale-dependent.