The Dynamics of Phase Locking

Abstract

Many low-frequency phenomena such as the Madden?Julian oscillation (MJO) or the El Niño?Southern Oscillation (ENSO) exhibit rapid growth where they appear to be undergoing a phase locking with other time scales such as the annual cycle. The purpose of this paper is to illustrate an example of phase locking of two different time scales. In this instance it is shown that during such epochs of phase locking a large increase in nonlinear energy exchange occurs from one time scale to the other. This paper utilizes the ECMWF Re-Analysis (ERA-40) datasets for the year 2001 to examine this problem. This study is a sequel to a recent modeling study where the maintenance of the MJO time scale was examined from scale interactions, especially with synoptic-scale waves with ?2?7 day periods. It was shown that a pair of waves on the synoptic time scale can satisfy certain selection rules and undergo triad interactions (kinetic energy to kinetic energy exchanges) and transfer energy. This present study illustrates the fact that during epochs of phase locking such nonlinear interactions can become very large, thus portraying the importance of phase locking. These explosive exchanges are shown from two perspectives: an approach based on kinetic energy exchanges in the frequency domain and another that invokes the boundary layer dynamics in the frequency domain.