A numerical model which determines the geometry of a threshold channel was recently developed. Such a model is an important tool for designing unlined irrigation canals and channelization schemes, and is useful when considering flow regulation. However, its applicability is limited in that its continuously curving boundary does not allow for sediment transport, which is an essential feature of natural rivers and streams. That model has thus been modified to predict the shape and stress distribution of an optimal stable channel; a channel with a flat-bed region over which bedload transport occurs, and curving bank regions composed of particles that are all in a state of incipient motion. It is the combination of this channel geometry and the phenomenon of momentum-diffusion, that allows the present model to simulate the "stable bank, mobile bed" condition observed in rivers. The coupled equations of momentum-diffusion and force-balance are solved over the bank region to determine the shape of the channel banks (the bank solution). The width of the channel1s flat-bed region is determined by solving the momentum-diffusion equation over the flat-bed region (the bed solution), using conditions at the junction of the flat-bed and bank regions that ensure matching of the bed and bank solutions. The model was tested against available experimental and field data, and was found to adequately predict the bank shape and significant dimensions of stable channels. To make the model results more amenable to the practic ing engineer, design equations and plots were developed. These can be used as an alternative solution for stable channel design; relieving the practitioner of the need to run the numerical program. The case of a stable channel that transports both bedload and suspended sediment is briefly discussed. Governing equations and a possible solution scheme for this type of channel are suggested; laying the groundwork for the development of an appropriate numerical model. / Ph. D.

The de Broglie-Bohm (BB) approach to quantum mechanics gives trajectories similar to classical trajectories except that they are also determined by a quantum potential. The quantum potential is a "fictitious potential" in the sense that it is part of the quantum kinetic energy. We use quantum trajectories to treat quantum chaos in a manner similar to classical chaos. For the kicked rotor, which is a bounded system, we use the Benettin et al. method to calculate both classical and quantum Lyapunov exponents as a function of control parameter K and find chaos in both cases. Within the chaotic sea we find in both cases nonchaotic stability regions for K equal to multiples of π. For even multiples of π the stability regions are associated with classical accelerator mode islands and for odd multiples of π they are associated with new oscillator modes. We examine the structure of these regions. Momentum diffusion of the quantum kicked rotor is studied with both BB and standard quantum mechanics (SQM). A general analytical expression is given for the momentum diffusion at quantum resonance of both BB and SQM. We obtain agreement between the two approaches in numerical experiments. For the case of nonresonance the quantum potential is not zero and must be included as part of the quantum kinetic energy for agreement. The numerical data for momentum diffusion of classical kicked rotor is well fit by a power law DNβ in the number of kicks N. In the anomalous momentum diffusion regions due to accelerator modes the exponent β(K) is slightly less than quadratic, except for a slight dip, in agreement with an upper bound (K2/2)N2. The corresponding coefficient D(K) in these regions has three distinct sections, most likely due to accelerator modes with period greater than one. We also show that the local Lyapunov exponent of the classical kicked rotor has a plateau for a duration that depends on the initial separation and then decreases asymptotically as O(t-1lnt), where t is the time. This behavior is consistent with an upper bound that is determined analytically.