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

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.

On the Energy Dispersion of Magnetic Rossby Waves

“…The ray demonstrates the propagation of the perturbation energy and differs from the phase propagation. Along the ray, the potential, kinetic, and magnetic energies can be solved, and their interaction with the basic flow and the basic magnetic field can be discussed (e.g., similar studies for Rossby waves can be seen in Li et al 2021b, 2022and Li & Kang 2022. Therefore, we can also apply the energy dispersion of magnetic Rossby waves to interpret the observed events involving the magnetic field.…”

The energy dispersion of magnetic Rossby waves in zonally nonuniform basic states

“…where t denotes time and t d denotes a short time interval; S d denotes the unit area that is perpendicular to the local group velocity vector. Based on the method, the variations in wave energy and amplitude along a moving ray are extensively discussed for Rossby waves on the Earth's atmosphere (Li et al 2021b, 2022.…”

“…Wave ray theory can be applied in interpreting teleconnection phenomena on the Earth's atmosphere and thereby has been extensively investigated (Karoly and Hoskins 1982, Karoly 1983, Hoskins and Ambrizzi 1993, Li and Nathan 1994, Yang and Hoskins 1996, Li and Nathan 1997, Li et al 2015. Recently, Li et al (2021a) derived a formula to solve the divergence of group velocity and discussed the variations in wave energy and amplitude (Li et al 2021a, Li et al 2021b, 2022.…”