Solitary Rossby Waves in the Lower Tropical Troposphere

Weakly nonlinear approximation is used to study the theoretical comportment of large-scale disturbances around the intertropical midtropospheric jet. We show here that the Korteweg de Vries (KdV) theory is appropriated to describe the structure of the streamlines around the African easterly jet (AEJ) region. The introduction of the additional velocity of the soliton C1 permits to search the stage where the configuration of the wave structures is going to emerge out of specified initial conditions and this is the direct and inverse cascade method. It was also shown that the configurations of disturbances can be influenced by this parameter so that we can look if the disturbances are in the control or not of their dispersive effects. This permits to explain the evolution of initial conditions of the Tropical Storm (TS) Debby over West Africa from 20 to 24 August 2006. 1. Introduction The Rossby waves are the most important in large-scale atmospheric flow processes [1]. For their analysis, it is usually sufficient to study the horizontal structure of waves. Most theories treating the structure of these waves are based on linear models which only take into account their dispersive behaviour. Nonlinear processes are more interesting because they can help to explain, for example, the hurricane spiral bands observed in the tropical zone [2] and energy exchanges between different modes of the waves [3]. Solitary Rossby waves in a zonal flow appear to have been discovered (analytically) by [4] and have been studied subsequently by [5–10]. All invoke Rossby’s β-plane model, in which the northerly gradient of the vertical component of the Earth’s rotation is constant. Many studies have dealt with nonlinear waves and particularly solitary waves in the atmosphere, stating with works by [11, 12]. On the theoretical level, nonlinear waves have been examined by [3] in the midatmosphere where the African easterly waves (AEWs) are propagated. In the same region, [13] showed that the Korteweg de Vries (KdV) theory is appropriate to describe the Rossby solitary waves. But the physical interpretation of the results in terms of the Rossby solitary waves is not evident and the roles that these waves could influence the structure and energy of these waves have not been examined. Moreover, [14] established that the propagation of the Rossby solitary wave has behaviour closer to those of ridges and troughs. They therefore showed that these waves can travel long distances in the northern hemisphere without a change both in speed or structure, and for any hour. The first