Highly Nonlinear Solitary Waves in Compressible Fluids
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 extent to which the overlying tropospheric layer absorb energy. The numerical simulation is based on a high resolution model of compressible fluid behaviour under different styles of forcing. A two layer system with a sharp change in the gradients of physical properties has been used to explore the development of strong disturbances from down drafts, e.g., due to thunderstorms.
Significant Achievements, Anticipated Outcomes and Future Work
The project was successful in generating stable numerical solutions for the fully compressible fluid models of the lower atmosphere subjected to large deformations. The way in which the nonlinear disturbances propagate depends strongly on the physical conditions and a wide variety of behaviour was explored in the PhD thesis written by Damien Bright in 2000. Nonlinear disturbances were generated by using down draft models of descending cold fluid, which tend to entrain their surroundings, and by careful transfer of results from incompressible flow followed by an adjustment period to allow the effects of compressibility to come into play. This study indicates that it is possible to achieve long-lived disturbances of high amplitudes whose effects can extend through much of the atmosphere.
Computational Techniques Used
The properties of the evolution on large amplitude wave phenomena need to be determination from integration of the fully nonlinear equations for compressible fluid flow. The conditions are nonhydrostatic and local dissipation below the scale of the numerical mesh is included through a second order operator. The boundary conditions are implemented using a combination of symmetry conditions and Fourier representations to allow for outward wave propagation at the top and sides of the model. The internal solution is carried out with a fine mesh second order finite-difference scheme including the full set of physical equations, e.g. diffusion of heat for the fluid.