Variations in Wave Energy and Amplitudes along the Ray Paths of Barotropic Rossby Waves in Horizontally Non-Uniform Basic Flows

Yaokun Li,Yanyan Kang,Jiping Chao

doi:10.3390/atmos12040458

Yaokun Li, Yanyan Kang + Show 1 more

Open Access

https://doi.org/10.3390/atmos12040458

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Abstract

A non-divergent barotropic model on a sphere transformed to Mercator coordinates is used to examine the variations in wave energy and amplitude along the energy dispersion paths of barotropic Rossby waves in non-uniform basic flows. Wave energy can be easily solved by specifying the divergence of the group velocity along the corresponding rays. In an analytical non-uniform basic flow that represents the basic features of the observed one at middle latitudes, waves with different periods decay accompanying the decreases in wave energy and amplitude and the increase in the total wavenumber. This implies that the waves are trapped and the energy is eventually absorbed by the basic flow. For the observed non-uniform basic flow that can represent the basic features of the non-divergent wind field at 200 hPa, the situation is more complicated. The significant increase in wave energy can be caused by either the convergence of wave energy or the barotropic energy absorption from the basic flow or both of them. A significant increase in amplitude can also be observed if the total wavenumber varies moderately. This means waves can significantly develop. Waves may decay if both wave energy and amplitude decrease. Waves may propagate without significant developing or decaying to realize a long distance propagation. The propagating waves are mainly caused by oscillating wave energy as well as amplitude.

Highlights

Carl Gustaf Rossby’s discovery in the 1930s of a special class of waves that owe their existence to the spherical shape of the Earth, widely known as Rossby waves, was one of the major breakthroughs in the development of a theoretical understanding of the large scale circulation of the atmosphere and ocean [1]
Extensive research has focused on the ray paths, wavenumber profiles, wave periods, amplitudes and wave energy of barotropic Rossby waves in horizontally uniform basic flows
This paper investigated the variations in wave energy and amplitude along rays that were generated at different locations in both the analytical and observed horizontally nonuniform jet streams

Summary

Introduction

Carl Gustaf Rossby’s discovery in the 1930s of a special class of waves that owe their existence to the spherical shape of the Earth, widely known as Rossby waves, was one of the major breakthroughs in the development of a theoretical understanding of the large scale circulation of the atmosphere and ocean [1]. Hoskins and Karoly [5] firstly applied the wave ray theory to discuss the meridional propagation of stationary Rossby waves and the observed teleconnection patterns in large scale atmospheric circulation. More and more observations suggest that Rossby waves could propagate across the equator through the strong cross-equatorial flows in the tropical easterly wind regions (e.g., [13,14,15,16]). This involves the propagation of Rossby waves in horizontally non-uniform basic flows. This paper tries to discuss the variations in wave energy and amplitude along the wave rays by deriving the wave energy equation in the horizontally non-uniform basic flow

Wave Energy Equation in the Non-Uniform Basic Flow

Analytical Horizontally Non-Uniform Basic Flow

Observed Horizontally Non-Uniform Basic Flow

Conclusions

Discussion

E Dgω ω 2 DT