Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution September, 1973 ; This thesis presents an investigation of the dynamics of bottom boundary currents in the ocean. The major emphasis is to develop simple mathematical models in which various dynamical features of these complex geophysical flows may be isolated and explored. Two separate models are formulated and the theoretical results are compared to observational data and/or laboratory experiments. A steady flow over a constant sloping bottom is treated in each model. A streamtube model which describes the variatlon in average cross-sectional properties of the flow is derived to examine the interaction between turbulent entrainment and bottom friction in a rotating stratified fluid. Empirical laws are used to parameterize these processes and the associated entrainment and friction coefficients (Eo,K) are evaluated from data for two bottom currents: the Norwegian Overflow and the Mediterranean Outflow. The ability to fit adequately all observations with the solutions for a single parameter pair demonstrates the dynamical consistency of the streamtube model. The solutions indicate that bottom stresses dominate the frictional drag on the dense fluid layer in the vicinity of the source whereas relatively weak entrainment slowly modulates the flow properties in the downstream region. The combined influence of entrainment and ambient stratification help limit the descent of the Mediterranean Outflow to a depth of approximately 1200 m. while strong friction acting over a long downstream scale allows the flow of Norwegian Sea water to reach the ocean floor. A turbulent Ekman layer model with a constant eddy viscosity is also formulated. The properties of the flow are defined in terms of the layer thickness variable d(x,y), whose governing equation is judged intractable for the general case. However, limiting forms of this equation may be ...