Uniform Asymptotics of Internal Gravitational Wave Fields from an Initial Radially Symmetric Perturbation
В. В. Булатов, I. Yu. Vladimirov
Abstract
In this paper, we solve the problem of constructing uniform asymptotics of the far fields of internal gravitational waves from the initial perturbation of lines of equal density with radial symmetry. A constant model distribution of the buoyancy frequency is considered, and an analytical solution to the problem is obtained as the sum of wave modes using the Fourier–Hankel transform. Uniform asymptotics of solutions describing the spatiotemporal characteristics of the elevation of isopycnals (equal density lines) and vertical and horizontal (radial) velocity components are obtained. The asymptotics of an individual wave mode of the main wave field components are expressed as the squared Airy function and its derivatives. The exact and asymptotic results are compared. At times on the order of ten or more buoyancy periods, we show that the uniform asymptotics make it possible to efficiently calculate the far fields of waves.