Modulational instability and collapse of internal gravity waves in the atmosphere

TL;DR

This paper investigates the nonlinear behavior of internal gravity waves in Earth's and Sun's atmospheres, predicting their modulation instability and potential collapse due to nonlocal nonlinear effects.

Contribution

It introduces a generalized nonlinear Schrödinger equation with nonlocal nonlinearity to model IGWs and analytically derives instability thresholds and growth rates.

Findings

Prediction of modulation instability in IGWs

Analytical instability thresholds and growth rates

Demonstration of possible wave collapse due to nonlocal nonlinearity

Abstract

Nonlinear two-dimensional internal gravity waves (IGWs) in the atmospheres of the Earth and the Sun are studied. The resulting two-dimensional nonlinear equation has the form of a generalized nonlinear Schr\"{o}dinger equation with nonlocal nonlinearity, that is when the nonlinear response depends on the wave intensity at some spatial domain. The modulation instability of IGWs is predicted, and specific cases for the Earth's atmosphere are considered. In a number of particular cases, the instability thresholds and instability growth rates are analytically found. Despite the nonlocal nonlinearity, we demonstrate the possibility of critical collapse of IGWs due to the scale homogeneity of the nonlinear term in spatial variables.