Principal Investigator Douglas R Christie Project q51, s52

Research School of Earth Sciences Machine VP, CM

Co-Investigator David J Brown

Research School of Earth Sciences

Highly Nonlinear Solitary Waves in Compressible Shear Flows

It is becoming increasingly clear that the dynamical behaviour of large amplitude internal solitary waves in compressible viscous fluids is much more complex than the behaviour of similar waves in incompressible fluids. This investigation has been primarily concerned with a detailed numerical study of the influence that recirculating fluid in the interior of large amplitude waves has on the morphology of solitary waves which propagate in a realistically stratified and sheared atmosphere. It has been found that the presence of recirculating flow in the relative streamline pattern has a dominating influence on the morphology and propagation properties of these highly nonlinear waves. Simulations of isolated solitary waves in the atmospheric boundary layer reveal an interesting overturning instability in the interior of large amplitude waves which modulates the propagation speed and profile of the wave. This instability appears to be associated with the mixing of warmer air from aloft into the circulation of the colder fluid trapped in the interior of the wave. The numerical experiments have also shown that colliding solitary waves of large amplitude exhibit unexpected behaviour. In particular, it has been found that highly nonlinear solitary waves, like their weakly nonlinear counterparts, are surprisingly stable entities which emerge from head-on collision with almost the same shape and speed as the shape and speed of the waves before collision. In addition, however, it has been found that when waves of different amplitude collide, fluid which is trapped within the smaller amplitude wave prior to collision is totally reflected at the collision boundary and appears in the closed circulation cell of the emerging larger amplitude wave. The transport of fluid which is trapped in the larger amplitude wave prior to collision is also blocked by the collision process. Some of this fluid is deposited at the surface in the wake of both emerging waves near the collision boundary. The rest is reflected back after collision and is carried away from the collision boundary as recirculating trapped fluid in the interior of the larger amplitude wave. These results are directly relevant to studies of the dispersal of pollutants in the atmospheric boundary layer, and to the interpretation of recent field observations of colliding Morning Glory solitary waves over the Gulf of Carpentaria in northern Australia.

What are the basic questions addressed?

Are large amplitude atmospheric solitary waves with closed circulation solitons? Do diffusive processes play an important role in determining the properties of solitary waves in compressible fluids? Can results derived from incompressible fluid theory be used to describe solitary waves in compressible fluids?

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

The results of this investigation clearly show that the properties of solitary waves in compressible fluids are substantially different from those found for waves in incompressible fluids. Solitary waves of large amplitude have been found to be surprisingly stable under nonlinear interaction. The results of this investigation provide a firm foundation for the comparison of theoretical predictions with field observations of atmospheric solitary wave phenomena.

What computational techniques are used and why is a supercomputer required?

Numerical simulations of nonlinear wave phenomena in the atmosphere are carried out by solving the full nonhydrostatic primitive ensemble-averaged equations for a compressible fluid in finite difference form, using an accurate and efficient time-splitting prognostic technique. The use of a supercomputer is essential for calculations of this type because a very fine mesh is required to resolve important features in the evolving flow patterns and this means that simulations of this type are very computationally intensive.

Publications

Numerical simulations of interacting solitary waves of large amplitude, D J Brown and D R Christie, Proceedings Tenth Conference on Numerical Weather Prediction, American Meteorological Society, 17-22 July, Portland, Oregon, 235-237 (1994).

Fully nonlinear solitary waves in the lower atmosphere, D J Brown and D R Christie, Proceedings Sixth Conference on Mesoscale Processes, American Meteorological Society, 17-22 July, 1994, Portland, Oregon, 194-196 (1994).

Interacting Morning Glories over Northern Australia, M J Reeder, D R Christie, R K Smith and R Grimshaw, Bull. Amer. Meteor. Soc., submitted.