Matthew Mills

Thesis Approved May 1994

An Analysis of Trajectories in Fluids

Ultimately, atmospheric motions originate through the input of solar energy and end through viscous dissipation of kinetic energy resulting in internal energy. While a variety of methods exist for examining these motions, ranging from large numerical models to scaling arguments, an approach that has yet to be considered is to examine individual trajectories within a circulation. This thesis examines the theory and some practical applications for a trajectory approach to energetics.

In the first part of the thesis the theory for closed steady-state trajectories is developed and compared to the theory for closed steady-state volumes. Next the trajectory theory is applied to the highly simplified atmospheric trajectories. Reasonable circulation times for several atmospheric circulations are predicted by finding the circulation time which gives zero heating from radiation, and latent and sensible heating for a trajectory in the circulation. Finally a finite difference model of Rayleigh-Benard convection is then used to examine in detail trajectories of closed steady-state flow. It is found that interaction between trajectories is important, that a trajectory exists for which kinetic energy production is balanced by dissipation and that the dissipation involved in the entire volume can be determined by examining a single trajectory.