Rossby rogons in atmosphere and in the solar photosphere

TL;DR

This paper investigates Rossby rogue waves and envelope solitons in Earth's atmosphere and the solar photosphere using the nonlinear Schrödinger equation, revealing conditions for their stability and excitation.

Contribution

It demonstrates the generation of Rossby rogons and envelope solitons through modulational instability analysis in atmospheric and solar plasma contexts, applying the 1D NLSE.

Findings

Rossby wave packets can form stable or unstable structures depending on wave number.

Rossby rogons and bright envelope solitons can be excited in the solar photosphere.

Small or large scale perturbations may occur in magnetized plasma environments.

Abstract

The generation of Rossby rogue waves (Rossby rogons), as well as the excitation of bright and dark Rossby envelpe solitons are demonstrated on the basis of the modulational instability (MI) of a coherent Rossby wave packet. The evolution of an amplitude modulated Rossby wave packet is governed by one-dimensional (1D) nonlinear Schr\"odinger equation (NLSE). The latter is used to study the amplitude modulation of Rossby wave packets for fluids in Earth's atmosphere and in the solar photosphere. It is found that an ampitude modulated Rossby wave packet becomes stable (unstable) against quasi-stationary, long wavelength (in comparision with the Rossby wave length) perturbations, when the carrier Rossby wave number satisfies $k^2 < 1/2$ or $\sqrt{2}+1<k^2<3$ ($k^2 >3$ or $1/2<k^2<\sqrt{2}+1$). It is also shown that a Rossby rogon or a bright Rossby envelope soliton may be excited in the shallow water approximation for the Rossby waves in solar photosphere. However, the excitation of small or large scale perturbations may be possible for magnetized plasmas in the ionosphereic $E-$layer.