Highly Nonlinear Solitary Waves in Compressible Fluids


Principal Investigator

Brian Kennett

Research School of Earth Sciences

We are modelling a two layer atmosphere where the most rapid change in density occurs in the lower layer. This acts as a waveguide in the simulation of highly nonlinear solitary waves propagating in the lower atmosphere. This project aims to study the loss of wave energy from the "parent" solitary wave as it generates vertically propagating internal gravity waves in the upper layer. These radiated waves carry away wave energy and alter the morphology of the "parent" waveform.  



Damien Bright

Douglas Christie

Research School of Earth Sciences




s52 - VPP



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

A limited domain numerical model is used and thus requires a wave permeable upper boundary condition to avoid reflections. Also a set of starting wave solutions that correspond to a range of different amplitudes and values of the buoyancy frequency in the upper layer are required so that an appropriate parameter space can be mapped. The last grant period has seen the development of appropriate boundary conditions and the numerical generation of starting wave solutions from highly nonlinear wave theory. This preliminary work has mostly been carried out using a low resolution grid on a high end Sun workstation. However, now that this is completed and we need to perform a set of numerical experiments over the parameter range using high grid resolution, computation will be done on the VPP300. These simulations will answer important questions about the effect of radiated energy loss on highly nonlinear internal solitary waves in a parameter range that includes internal circulation within the wave which forms as the amplitude increases beyond the point of effective "wave breaking".

What computational techniques are used?

The algorithm used solves a set of finite difference prognostic equations which represent a fully compressible, non-hydrostatic mesoscale atmosphere. These equations are solved on a standard Cartesian mesh that represents the flow domain with imposed boundary conditions. Chosen boundary conditions for the experiments outlined above consist of a rigid type bottom boundary condition and wave permeable radiation conditions imposed on the lateral and upper boundaries. The upper boundary condition requires a spectral filtering technique to effectively remove all upward propagating Fourier components of the vertical velocity field. Leapfrog

Appendix A -

time differencing is used to update the model and a time filter has been imposed to remove any tendency for mesh drifting instability. A simple first order approximation for eddy diffusion is used to dissipate the energy of the smallest scales and the model relies on high resolution to represent the turbulent features of interest.
- Appendix A