Approximate solution of nonlinear triad interactions of acoustic-gravity waves in cylindrical coordinates

The three-dimensional radial propagation of wave disturbances over a slightly compressible fluid of constant depth is discussed. We focus on resonant triads comprising two gravity modes and one acoustic mode. The derivation of the evolution equations in a non-integral form is made possible by approximating the radial solution by cosine functions in two regions, inner and outer, that are matched at a location where all relevant derivatives are in agreement with the exact Bessel solution. When the interaction takes place in the inner region of all modes, the amplitude evolution equations are found to be similar to the two-dimensional case. However, focusing of one gravity mode and de-focusing of the other is observed when the interaction involves an inner region of the acoustic mode, and outer regions of the gravity modes. (C) 2020 Elsevier B.V. All rights reserved.

Automated summary

This study discusses the three-dimensional radial propagation of wave disturbances over a slightly compressible fluid of constant depth, focusing on resonant triads with two gravity modes and one acoustic mode. Derivation of evolution equations is achieved by approximating radial solutions with cosine functions in inner and outer regions. When interaction occurs in the inner region of all modes, amplitude evolution equations are similar to the two-dimensional case, but focusing of one gravity mode and de-focusing of the other is observed when involving an inner region of the acoustic mode and outer regions of gravity modes.