Nonlinear internal gravity waves in the atmosphere: Rogue waves, breathers and dark solitons

TL;DR

This paper investigates nonlinear internal gravity waves in the atmosphere, deriving equations for wave envelopes, and explores phenomena like rogue waves, breathers, and dark solitons through analytical solutions.

Contribution

It introduces a nonlinear model for atmospheric IGWs using the NLS equation, identifying conditions for rogue wave and dark soliton formations.

Findings

Identification of focusing and defocusing regimes for IGWs

Analytical solutions for rogue wave candidates like Peregrine soliton

Existence of dark solitons in the defocusing case

Abstract

We study nonlinear internal gravity waves (IGWs) in the atmosphere. The reductive perturbation method is used to derive a system of two-dimensional nonlinear equations for the envelope of velocity stream function and the mean flow. In the one-dimensional case, we obtain a nonlinear Schr\"{o}dinger (NLS) equation corresponding to both horizontal and vertical propagation of IGWs. Depending on the characteristic wavelengths, the NLS equation is focusing or defocusing. In the focusing case, non-stationary solutions in the form of the Peregrine soliton, the Akhmediev breather and the Kuznetsov-Ma breather are considered as potential candidates for the modeling of rogue waves in the atmosphere. In the defocusing case, stationary nonlinear IGWs are considered in the form of nonlinear periodic waves and dark solitons.