Highly Nonlinear Solitary Waves in Compressible Fluids

Principal Investigator

Brian Kennett

Seismology Group

Research School of Earth Sciences


Damien Bright

Seismology/GFD Groups

Research School of Earth Sciences


s52 - VPP

This project is concerned with the numerical

simulation of large amplitude trapped wave

motions in atmospheric waveguides. Observations of such waves in the atmosphere indicate that the formation, evolution and decay of these waves are strongly influenced by the structure of the waveguide and the degree to which the overlying tropospheric layer can support energy loss. A very high resolution model has been developed which includes boundary conditions which prevent reflections of both sound and gravity waves at all lateral boundaries and also at the upper boundary of the computational domain. This model is being used to study the evolution of solitary waves on a waveguide in a two layer system representing the lower atmosphere where the upper layer supports varying degrees of energy loss through internal gravity wave radiation.

What are the results to date and the future of the work?

Several mechanisms of solitary wave generation have been explored numerically. Simulations of solitary wave generation by the interaction of a modelled descending thunderstorm microburst with a stable layer, have been carried out and provided insight into the formation process. Such microburst generated wave motions are important atmospheric processes which can lead to hazardous windshear disturbances in the thunderstorm environment. Another mechanism for generating solitary waves numerically is to use as a starting solution a numerical solution of Longs equation (a nonlinear partial differential equation that describes the propagation of stationary two-dimensional finite-amplitude wave motions in an incompressible, inviscid and stably stratified fluid) . Such an approximate starting solution is expected to "relax"rapidly towards a true solution of the compressible model. These starting solutions which provide a range of different amplitudes and wavelengths are being used to study the radiative energy loss from solitary waves travelling in the modelled stable layer waveguide. A study of the mechanisms of decay of solitary wave motions provides valuable insight into how long-lived such a disturbance in the atmosphere may be.

- Appendix A

What computational techniques are used?

The properties of evolving large amplitude wave phenomena are determined from a series of numerical simulations which are based on the integration of the fully nonlinear nonhydrostatic primitive ensemble-averaged equations for compressible fluid flow. The radiative upper boundary condition implements a spectral filtering technique to eliminate fourier modes that correspond to downward propagating internal gravity waves. Also the generation of starting wave solutions requires the numerical solution of a nonlinear PDE using a modified SOR (successive over-relaxation) technique. Calculations of this type require large amounts of memory and are very computationally intensive.

Appendix A -