## Free Atmospheric Planetary Waves on an Equatorial β-plane Part I: Theoretical Background and Simulation

Theoretical Simulation of Free Atmospheric Planetary Waves
on an Equatorial $\beta$-plane

+Sandro Wellyanto Lubis and Sonni Setiawan
Department of Geophysics and Meteorology, Bogor Agricultural
University, Bogor 16680, Indonesia
+now in Leipzig Institute for Meteorology, University of Leipzig,
04103 Germany

[ MATLAB – The Language of Technical Computing ]

2011

A simple theoretical model was developed to investigate behavior of equatorial planetary waves (EPW) on a motionless basic state of mean depth H on the equatorial barotropic $\beta$-plane. Based on general nondimensional linearized equations of EPW in equatorial $\beta$-plane, the amplitude of meridional wind perturbation (v’) is maximum at latitude y= $\pm$ 1 for mode n=1 and equal to zero at latitude y = ±1/2$\sqrt{2}$ for mode n=2. The symmetric meridional wind perturbation (v’) with maximum amplitude at latitude y= ± 1 and antisymmetric zonal wind perturbation (u’) are some implications that correspond to simulation of Yanai waves in which the geopotential field perturbation ($\Phi'$) is in the state of geostrophic balance at latitude -1< y <1 or –$(\beta^{-1}\sqrt{gH})^{1/2} > y > (\beta^{-1}\sqrt{gH})^{1/2}$. The simulation of Kelvin waves resulted that either zonal wind or geopotential field has symmetric amplitude and symmetric perturbation relative to Earth’s latitude. Further filtered equatorial waves mode n=1, 2, and 3 showed that there are two classes of EPW which can be classified into high frequency Poincaré modes waves and the low frequency Rossby modes waves.

Figure 1. Simulation of geopotential field and horizontal wind perturbations corresponding to Yanai waves mode n= 0 with zonal wave number (k) = 0.5, =1.0, and 1.5, respectively (left panel) and Simulation of geopotential field and horizontal wind perturbations corresponding to Kelvin waves mode n= -1 with zonal wave number (k) =0.5, =1.0, and 1.5, respectively (right panel).

Figure 2. Simulation of horizontal wind and geopotential field perturbations corresponding to equatorial Rossby waves mode n= 1, 2, and 3.

Figrure 3. Simulation of horizontal wind and geopotential field perturbations corresponding to equatorial Eastward Poincaré waves mode n= 1, 2, and 3.

Figure 4. Simulation of horizontal wind and geopotential field perturbations corresponding to equatorial Westward Poincaré waves mode n= 1, 2, and 3.

Figure 5. Simulation of surface elevation corresponding to Kelvin waves, Yanai waves, Rossby waves, eastward Poincare waves and westward Poincare waves, respectively

Acknowledgements

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Sandro and Setiawan gladly acknowledge their gratefulness to Laurel McCoy
(Atmospheric Sciences, University of Missouri-Columbia, USA), Nina
Kargapolova (Institute of Computational Mathematics and Mathematical
Geophysics, Russia), and Davesh Vashishtha (University of Delhi, India) for
their contribution on reviewing this paper. The anonymous reviewers of this
paper provided valuable suggestions, and we truly appreciate them.