A reduced model of the Madden-Julian oscillation
We have extended our virtual laboratory for internal wave motions (Int. J. Numer Meth. Fluids 2005; 47:1369-1374) to the case of rotating fluids on an equatorial beta-plane. A virtual wave-maker is introduced via a time-dependent coordinate transformation in the meridional direction, represented by two lateral boundary meanders. The technique is consistently incorporated into the numerical algorithm of the nonhydrostatic model EULAG. The modelling framework is applied in simulations of equatorial wave motions to enhance our understanding of the Madden-Julian oscillation (MJO). The simulation of a realistic MJO in global Circulation and climate models is a continuing challenge-in part, due to the failure of existing theories to explain the ubiquitous modelling difficulties of the phenomenon. Virtual laboratory experiments appear ideal complementary tools to isolate and study particular geophysical flow structures. In these laboratory-scale 'climate' simulations we observe eastward propagating low-frequency horizontal Structures consistent with Rossby solitary wave theory, representing a particular solution of the Korteweg-de Vries equation for the evolution of the wave amplitude under a given forcing. The latter extends the linear shallow water theory-commonly used to explain different modes of equatorial wave motions-to the weakly nonlinear regime. One important outcome Of Our simulations is the finding that these structures depend on strong stratification, and may be easily destroyed or weakened if substantial near-surface perturbations and associated vertical motions exist. This could play a role in the failure to simulate a realistic MJO, but it may also provide an explanation why solitary waves are not as readily observed in oceans as they are in models and theory. Ultimately, our research aims at constructing a simplified dynamical apparatus to reproduce MJO-like structures in a laboratory analogue, in the spirit of the Plumb-McEwan experiment for the quasi-biennial oscillation and vis-a-vis its numerical equivalent. Copyright (C) 2007 John Wiley & Sons, Ltd.
eulag mjo solitary wave korteweg-de vries equation generalized coordinate transformation equatorial beta-plane tank experiment