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A numerical method has been developed for solving the complete compressible Navier-Stokes equations. The method is applicable for Direct Numerical Simulations (DNS) and Large-Eddy Simulations (LES) and was used here to study the evolution of three-dimensional disturbances in the laminar and turbulent near wake of axisymmetric bluff bodies with a blunt base in supersonic flows. The main objective of this research is to investigate the time dependent behavior of these disturbances and their influence on and interaction with the global flow field. The equations are solved in a cylindrical coordinate system using finite difference approximations of fourth-order accuracy in axial and radial directions and and a fourth-order accurate explicit Runge-Kutta scheme for the time integration. A pseudo-spectral method is employed in the azimuthal direction. Direct Numerical Simulations (DNS) were performed for a subsonic free stream Mach number of M ͚ = 0.2 and for supersonic free stream Mach numbers of M ͚ = 1.2 and M ͚ = 2.46. Large-Eddy Simulations (LES) were carried out for a subsonic free stream Mach number of M ͚ = 0.2 and a global Reynolds number of ReD = 2,000 and for a supersonic free stream Mach number of M ͚ = 2.46 and global Reynolds numbers of ReD = 30,000 and ReD = 100,000. Comparison of the instantaneous flow field for subsonic calculations with water channel experiments and incompressible simulations show good qualitative agreement. An absolute instability with regard to helical disturbances was found for the subsonic flow at ReD = 1,000 and for the supersonic flows for M ͚ = 1.2 and ReD ≥ 4,000 and for M ͚ = 2.46 and ReD ≥ 30,000. Small disturbances appear in the flow field near the corner of the base. As the disturbances are propagating downstream they grow and form intense vortical structures. These structures have a strong influence on the flow field, which results in a drastic change of the base pressure distribution and thus of the base drag.

Some aspects of the barotropic instability of continental boundary currents are investigated herein. In the first problem, a piecewise linear wall-jet is perturbed by the most unstable linear mode and the nonlinear evolution of the disturbance is computed. It is shown that the eddies in the wall-jet case evolve much differently than those resulting from the instability of a free jet. This simple model illustrates that even without dissipative processes, a rapid diffusion of mean momentum and vorticity occurs. This contrasts with the main result of this study presented in the second problem where it is argued that the use of a classical eddy parametrization in the analysis of continental boundary currents leading to the diffusion of momentum and relative vorticity fails to recognize that the relevant eddies are dominated by the conservation of potential vorticity, which in turn may produce an increase in the mean relative vorticity. To illustrate this effect, we examine a non-inflected barotropic shear flow destabilized by the cross stream variation in the bottom topography of a continental slope. The finite amplitude evolution of the waves is analyzed in a simple model with a steplike bottom topography and with piecewise uniform potential vorticity distribution. The increase in maximum mean vorticity is computed for various values of the Rossby number and the topographic elevation, and it is suggested that a similar effect, taking into account the isopycnal topography as well as the isobaths, could maintain the large inshore shear of the Gulf Stream. Cross shelf transport of different water types (i.e.: potential vorticity and passive tracers) are also computed and suggested to be pertinent to the more realistic oceanic problem involving baroclinic effects. The numerical calculation employs the well known method of contour dynamics, and the Green's function appropriate for the step-like topography is derived. / Source: Dissertation Abstracts International, Volume: 54-07, Section: B, page: 3531. / Major Professor: Melvin E. Stern. / Thesis (Ph.D.)--The Florida State University, 1993.