# 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.