Thesis (M.S. in Meteorology and Physical Oceanography)--Naval Postgraduate School, September 2003. / Thesis advisor(s): Peter C. Chu, Steve Haeger. Includes bibliographical references (p. 73-77). Also available online.

Thesis (Ph. D.)--University of Texas at Austin, 2002. / Vita. Includes bibliographical references. Available also from UMI Company.

Thesis (Ph. D. in Meteorology)--Naval Postgraduate School, March 2003. / Dissertation supervisor: Wendell Nuss. Includes bibliographical references (p. 167-169). Also available online.

In this dissertation, we study a free boundary problem obtained as a limit as [epsilon omplies 0] to the following regularizing family of semilinear equations [Delta]u = [Beta subscript epsilon](u)F([gradient]u), where [Beta subscript epsilon] approximates the Dirac delta in the origin and F is a Lipschitz function bounded away from 0 and infinity. The least supersolution approach is used to construct solutions satisfying geometric properties of the level surfaces that are uniform. This allows to prove that the free boundary of the limit has the "right" weak geometry, in the measure theoretical sense. By the construction of some barriers with curvature, the classification of global profiles for the blow-up analysis is carried out and the limit function is proven to be a viscosity and pointwise solution (a.e) to a free boundary problem. Finally, the free boundary is proven to be a C[superscript 1, alpha] surface around H[superscript n-1] a.e. point.

The broad aim of the work presented in this thesis is to investigate the wake of an airfoil under the combined effects of streamwise curvature and pressure gradient. This was accomplished by an experimental investigation using hot-wire anemometry and large eddy simulation (LES). The wake was generated by placing a NACA 0012 airfoil in a uniform stream of air, which is then subjected to an abrupt 90o curvature created by a duct bend. The experimental work was conducted in a subsonic open-return type wind tunnel. The test section measured 457 mm × 457 mm in cross-section and consisted of a 90o bend with radius-to-height ratio of 1.17. The symmetrical airfoil was of chord length (c) 150 mm, and its trailing edge was located one chord length upstream of the bend entry. The effects of airfoil angle of attack and mainstream velocity on the mean velocity and turbulence quantities of the near-wake were examined. In addition, the mean velocity and turbulence intensity profiles of the boundary layer on the upper surface of the airfoil were measured. In the numerical investigation, the three-dimensional, incompressible turbulent flow in the duct was computed using the finite volume method. The effect of modelling parameters, namely, grid resolution and sub-grid scale (SGS) model were studied. Three different sub-grid scale models were employed, namely, the classical Smagorinsky, its dynamic variant (DSMG) and the dynamic kinetic energy transport. The effect of grid resolution was assessed by conducting simulations with the DSMG model on three different grids. The first two grids incorporated the full spanwise extent of the duct (3c), and the third grid comprised a reduced spanwise segment (0.5c) with periodic conditions set in the spanwise direction. A bounded central differencing scheme was employed for the discretization of the convection terms. The temporal discretization was by a second-order implicit method that incorporated a forward difference approximation. The performance of LES in depicting the experimental flow was assessed and compared with the results predicted by the Reynolds Stress Model. The experimental profiles at zero angle of attack revealed the differing effects of curvature on the mean and turbulence quantities in the inner-side and outer-side of the wake. The spanwise distributions of mean velocity and turbulence intensity, in the near-wake, indicated variations with identifiable peaks and troughs which corresponded to the presence of streamwise vortices in the wake. The spanwise variations were larger on the inner side of the wake and significantly reduced on the outer side. The results showed that close to the trailing edge, the dominant effect on the wake was from the airfoil boundary layer, whereas one chord length downstream of the trailing edge, it was the effect of curvature and pressure gradient from the duct which was dominant. The results from the numerical study showed the advantages of LES over Reynolds-averaged Navier-Stokes methods in predicting separation on the convex wall of the bend on relatively coarse grids, but also shortcomings in the prediction of the wake parameters. The dynamic variants of the SGS models were more accurate in predicting the flow in the wake. On a considerably finer grid with near-wall airfoil grid spacings of Δx+ < 80, Δy+ < 0.5, and 20 < Δz+ < 50, LES resulted in much improved comparisons with the experimental data. The improved prediction of the wake parameters was attributed to the improved simulation of the boundary layers on the upper surface of the airfoil. However, the effect of the reduced spanwise extent resulted in a lack of prediction of separation on the convex wall of the duct.

No description available.

Oscillatory boundary layer flow is found under waves in the near shore region. This region is responsible for large volumes of sediment transport and whilst a large number of studies have investigated the broader problem only a handful of studies have investigated the boundary layer flow in detail. Most of these studies have also only considered boundary layer flow over rough impermeable beds and therefore do not take into account the potential effect of the flow interaction with a permeable bed. Similar studies in other felds of environmental fluid mechanics have concluded that the presence of a permeable bed can lead to significant diff erence in the boundary layer hydrodynamics when compared to the equivalent flow over an impermeable bed. This thesis presents a series of laboratory experiments that have been conducted over an impermeable gravel bed and a permeable gravel bed to identify the differences in the boundary layer hydrodynamics with a particular reference to the differences in the horizontal velocity profile, the shear stress, turbulence and the bed friction factor. The results indicate that a difference exists in the near-bed flow between the two bed cases. The results also demonstrate that the magnitude of the differences vary with flow Reynolds number, so the more energetic the wave the larger the impact of the permeable bed. The bed shear stress and resulting friction factor was found to be 40% greater for the flows over the permeable bed for the most energetic test case whilst the friction factor for the two bed cases for the least energetic test case are similar. The results also indicate that the permeable bed introduces an unexpected asymmetry in the flow cycle. This is attributed to the high vertical velocities that have been observed. A second series of experiments have been conducted to shed light on the interaction between the flow above the bed and within the bed to help explain the results from the initial gravel-bed experiments. The second series of experiments have been conducted over a regular permeable bed that allows for velocity measurements within the pores. The results indicate that the horizontal velocity, shear stress and turbulence all display signs of being effected by the exchange of flow, or ventilation, that naturally occurs.

Receptivity processes by which free-stream acoustic waves generate instability waves in boundary layers are investigated. Concentration is placed on mechanisms associated with local regions of short scale variation in wall suction or admittance distribution. These mechanisms are relevant to laminar flow control technology, in which suction is utilized to control the growth of boundary layer instabilities. The receptivity process requires a transfer of energy from the long wavelength of the free-stream disturbance to the short wavelength of the instability wave. In the case of wall suction, this occurs through the unsteady modulation, by the acoustic wave, of the short scale mean flow variation due to the steady wall suction. In the wall admittance mechanism, the boundary condition for the unsteady motion contains a short scale variation which directly scatters energy from the acoustic wave into the instability wave. The latter mechanism does not require a short scale adjustment in the mean boundary layer. Time harmonic, two and three-dimensional interactions are analyzed using the asymptotic, high Reynolds number, triple deck structure. The influence of subsonic compressibility is examined for the case of two-dimensional interactions, and a similarity transform is found which reduces the problem to an equivalent incompressible flow. For three-dimensional interactions, a similarity transform is possible only in the Fourier transform wavenumber space, and in the equivalent two-dimensional problem the frequency is complex. However, in many cases of practical interest, the imaginary component of this frequency is quite small and can be neglected. The acoustic wave orientation and the geometry of the wall suction or admittance distribution are found to significantly influence the amplitude of the generated instability wave. For an isolated, three-dimensional region of wall suction or admittance, instability wave growth is confined to a downstream, wedge shaped region. The saddle point method is utilized to calculate the characteristics of this instability wave pattern. In some ranges of parameter space, two saddle points are found to make comparable contributions. The instability wave pattern in these directions exhibits a beat phenomenon, due to constructive and destructive interference of the contributions from the two saddle points.

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published_or_final_version / Civil Engineering / Doctoral / Doctor of Philosophy