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Abstract
Abstract. A linearized version of the quasi-geostrophic model (QGM) with an explicit Ekman layer and observed static stability parameter and profile of the African easterly jet (AEJ), is used to study the instability properties of the environment of the West African wave disturbances. It is found that the growth rate, the propagation velocity and the structure of the African easterly waves (AEW) can be well simulated. Two different lower boundary conditions are applied. One assumes a lack of vertical gradient of perturbation stream function and the other assumes zero wind perturbation at the surface. The first case gives more realistic results since in the absence of horizontal diffusion, growth rate, phase speed and period have values of 0.5 day−1, 10.83 m s−1 and 3.1 day, respectively. The zero wind perturbation at the surface case leads to values of these parameters that are 50 percent lower. The analysis of the sensitivity to diffusion shows that the magnitude of the growth rate decreases with this parameter. Modelled total relative vorticity has its low level maximum around 900 hPa under no-slip, and 700 hPa under free slip condition.
Highlights
It is known that African easterly waves (AEW) are initiated and grow mostly over land (Burpee, 1972, 1974; Reed et al, 1977; Mass, 1979; Kwon, 1989; Chang, 1993; Thorncroft and Hoskins, 1994a; Lenouo et al, 2005; Parker et al, 2005; Hall et al, 2006)
We have established here that the lower boundary damping condition is fundamental to the growth rate of the normalmode of AEW
For an explicit classical Ekman layer where the lower boundary condition assumes ω=0 and there is no vertical gradient of perturbation stream function (ε=1), structure and growth rates are closer to those usually obtained, whereas they are significantly reduced when a no-slip condition (ε=0) is used
Summary
Quasi-geostrophic models (hereafter QGM) are among the most important approximate formulations for describing the dynamics of easterly waves arising from the mechanism of barotropic-baroclinic instability, as observations suggest (Hall et al, 2006). The effect of an Ekman layer on baroclinic instability has been studied by specifying Ekman pumping as a lower boundary condition in models seeking exponentially growing normal modes by Farrell (1985, 1989) and Staley (1993) They found large reductions in growth rates (sometimes vanishing altogether), at short wavelengths. The growth rates when slip (meaning zero vertical gradient of stream function just above the surface) or no-slip (meaning zero wind perturbation at the surface) boundary conditions are applied in the surface boundary layer, were analysed by Staley (1993) He found that the large cross-isobaric flow of the classic Ekman solution overestimates the damping by a factor of roughly 2.
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