Atmospheric undular bores

Abstract

We show that a recently-derived model for the propagation of nonlinear waves in the atmosphere admits undular bores as travelling-wave solutions. These solutions represent waves consisting of a damped oscillation behind a front that is preceded by a uniform breeze-type flow. The generation of such wave profiles requires a jump in the heat source across the leading front of the wave, a feature that is consistent with observations.

Weak and Classical Solutions to an Asymptotic Model for Atmospheric Flows

“…We refer to [11] for precise information on the physical background and the derivation of the model. It is important to point out that, apart from the special oscillatory solution found in [11,Section 6 (d)] and the travelling wave solutions investigated in [10], no mathematical results related to (1.1) are available yet. This paper is thus a first attempt at laying the groundwork of the mathematical analysis of this model, which, in the future, may hopefully help to add additional insight into this fascinating meteorological phenomenon to that which is already available.…”

Analysis of a Sturm–Liouville Problem Arising in Atmosphere

“…Note that the results we discuss in this paper are also relevant for the study of atmospheric undular bores (see the discussions in [8,14,16]).…”