On the propagation of waves in the atmosphere

Exact Solutions Modelling Nonlinear Atmospheric Gravity Waves

Exact solutions to the governing equations for atmospheric motion are derived which model nonlinear gravity wave propagation superimposed on atmospheric currents. Solutions are explicitly prescribed in terms of a Lagrangian formulation, which enables a detailed exposition of intricate flow characteristics. It is shown that our solutions are well-suited to modelling two distinct forms of mountain waves, namely: trapped lee waves in the Equatorial f-plane, and vertically propagating mountain waves at general latitudes.

The Existence of Weak Solutions for the Vorticity Equation Related to the Stratosphere in a Rotating Spherical Coordinate System

In this paper, based on the Euler equation and mass conservation equation in spherical coordinates, the ratio of the stratospheric average width to the planetary radius and the ratio of the vertical velocity to the horizontal velocity are selected as parameters under appropriate boundary conditions. We establish the approximate system using these two small parameters. In addition, we consider the time dependence of the system and establish the governing equations describing the atmospheric flow. By introducing a flow function to code the system, a nonlinear vorticity equation describing the planetary flow in the stratosphere is obtained. The governing equations describing the atmospheric flow are transformed into a second-order homogeneous linear ordinary differential equation and a Legendre’s differential equation by applying the method of separating variables based on the concepts of spherical harmonic functions and weak solutions. The Gronwall inequality and the Cauchy–Schwartz inequality are applied to priori estimates for the vorticity equation describing the stratospheric planetary flow under the appropriate initial and boundary conditions. The existence and non-uniqueness of weak solutions to the vorticity equation are obtained by using the functional analysis technique.

On azimuthally propagating equatorial atmospheric waves

We investigate the existence of solutions to a recent model for large-scale equatorial waves, derived recently by an asymptotic method driven by the thin-shell approximation of the Earth's atmosphere in rotating spherical coordinates.

On the propagation of nonlinear waves in the atmosphere

Starting from the general equations of fluid dynamics that describe the atmosphere, and using asymptotic methods, we present the derivation of the leading-order equations for nonlinear wave propagation in the troposphere. The only simplifying assumption is that the flow in the atmosphere exists in a thin shell over a sphere. The systematic approach adopted here enables us to find a consistent balance of terms describing the propagation, and to identify the temperature and pressure gradients that drive the motion, as well as the heat sources required. This produces a new nonlinear propagation equation that is then examined in some detail. With the morning glory in mind, we construct a few exact solutions, which, separately, describe breezes, bores and oscillatory motion.