Spectral integration methods have been introduced for constant-coefficient two-point boundary value problems by Greengard, and pseudospectral integration methods for Volterra integral equations have been investigated by Kauthen. This thesis presents an approach to variable-coefficient two-point boundary value problems which employs pseudospectral integration methods to solve an equivalent integral equation. This thesis covers three topics in the application of spectral integration methods to two-point boundary value problems. The first topic is the development of the spectral integration concept and a derivation of the spectral integration matrices. The derivation utilizes the discrete Chebyshev transform and leads to a stable algorithm for generating the integration matrices. Convergence theory for spectral integration of C[subscript k] and analytic functions is presented. Matrix-free implementations are discussed with an emphasis on computational efficiency. The second topic is the transformation of boundary value problems to equivalent Fredholm integral equations and discretization of the resulting integral equations. The discussion of boundary condition treatments includes Dirichlet, Neumann, and Robin type boundary conditions. The final topic is a numerical comparison of the spectral integration and spectral differentiation approaches to two-point boundary value problems. Numerical results are presented on the accuracy and efficiency of these two methods applied to a set of model problems. The main theoretical result of this thesis is a proof that the error in spectral integration of analytic functions decays exponentially with the number of discretization points N. It is demonstrated that spectrally accurate solutions to variable-coefficient boundary value problems can be obtained in O(NlogN) operations by the spectral integration method. Numerical examples show that spectral integration methods are competitive with spectral differentiation methods in terms of accuracy and efficiency. / Graduation date: 2000

We consider the dynamics of an elastic sheet lubricated by the flow of a thin layer of fluid that separates it from a rigid wall. By considering long wavelength deformations of the sheet, we derive an evolution equation for its motion, accounting for the effects of elastic bending, viscous lubrication and body forces. We then analyze various steady and unsteady problems for the sheet such as peeling, healing, levitating and bursting using a combination of numerical simulation and dimensional analysis. On the macro-scale, we corroborate our theory with a simple experiment, and on the micro-scale, we analyze an oscillatory valve that can transform a continuous stream of fluid into a series of discrete pulses. / NSF

No description available.

The highly nonlinear nature of unsaturated flow results in different ways to approximate the delayed or instantaneous movement of the water table. In nearly all the approaches, the water table is conceptually treated as a “material surface”. This term defines the water table as having two simultaneous properties: 1) the pressure along the surface is atmospheric pressure, and 2) the water table is fixed to the material, i.e., a set of water particles. This article makes an attempt to explain that the water table, defined as the surface at atmospheric pressure, is not a material boundary, and the water table can move independent of the water particles. Velocity of the water table and velocity of drainage are compared with three analytical models: the Neuman model, which assumes instantaneous drainage from the unsaturated zone; the Moench model, which considered gradual drainage from the unsaturated zone using a series of exponential terms in the water table boundary condition; and the Mathias-Butler model, which obtained a new drainage function based on a linearized Richard’s equation but limited the variation of soil moisture and hydraulic conductivity in the unsaturated zone to exponential functions. Numerical analysis was conducted with VS2DT and both the numerical and the analytical results were compared with a 7-day, constant rate pumping test conducted by University of Waterloo researchers at Canadian Air Force Base Borden in Ontario, Canada.

On-going efforts to reduce aircraft drag through transition delay focus on understanding the process of boundary-layer transition from a physics-based perspective. For swept-wings subject to transition dominated by a stationary crossflow instability, one of the remaining challenges is understanding how freestream disturbances and surface features such as surface roughness create the initial amplitudes for unstable waves. These waves grow, modify the mean flow and create conditions for secondary instabilities to occur, which in turn ultimately lead to transition. Computational methods that model the primary and secondary instability growth can accurately model disturbance evolution as long as appropriate initial conditions are supplied. Additionally, transition delay using discrete roughness arrays that exploit known sensitivities to surface roughness has been demonstrated in flight and wind tunnel testing; however, inconsistencies in performance from the two test platforms indicate further testing is required. This study uses detailed hotwire boundary-layer velocity scans to quantify the relationship between roughness height and initial disturbance amplitude. Naphthalene flow visualization provides insight into how transition changes as a result of roughness height and spacing. Micron-sized, circular roughness elements were applied near the leading edge of the ASU(67)-0315 model installed at an angle of attack of -2.9 degrees in the Klebanoff-Saric Wind Tunnel. Extensive flow quality measurements show turbulence intensities less than 0.02% over the speed range of interest. A survey of multiple roughness heights for the most unstable and control wavelengths and Reynolds numbers of 2.4 x 10⁶ 2.8 x 10⁶ and 3.2 x 10⁶ was completed for chord locations of 10%, 15% and 20%. When care was taken to measure in the region of linear stability, it was found that the disturbance amplitude varies almost linearly with roughness height. Naphthalene flow visualization indicates that moderate changes in already-low freestream turbulence levels can have a significant impact on transition behavior.

This dissertation analyzes the effect of periodic roughness elements on the stability of a flat plate boundary layer. Receptivity data is extracted from direct numerical simulations and experimental data and the results are compared to theoretical predictions. This analysis shows that flow in the immediate vicinity of roughness elements is non-linear; however, the evolution of roughness-induced perturbations is a linear phenomena. New techniques are developed to calculate receptivity information for cases where direct numerical simulations are not yet possible. Additionally, the stability behavior of the roughness wake is analyzed. New instability modes are found, and the effect of boundary layer complexity, perturbation amplitude and other factors are examined. It is shown that the wake is much less stable than optimal perturbation theory predicts, and highlights the importance of receptivity studies. The implication of these results on transition-to-turbulence is discussed, and future work is proposed. T

Automated detection of geological boundaries and determination of cyclic events controlling deposition can facilitate stratigraphic analysis and reservoir characterization. This study applies the wavelet transformation, a recent advance in signal analysis techniques, to interpret cyclicity, determine its controlling factors, and detect zone boundaries. We tested the cyclostratigraphic assessments using well log and core data from a well in a fluvio-eolian sequence in the Ormskirk Sandstone, Irish Sea. The boundary detection technique was tested using log data from 10 wells in the Apiay field, Colombia. We processed the wavelet coefficients for each zone of the Ormskirk Formation and determined the wavelengths of the strongest cyclicities. Comparing these periodicities with Milankovitch cycles, we found a strong correspondence of the two. This suggests that climate exercised an important control on depositional cyclicity, as had been concluded in previous studies of the Ormskirk Sandstone. The wavelet coefficients from the log data in the Apiay field were combined to form features. These vectors were used in conjunction with pattern recognition techniques to perform detection in 7 boundaries. For the upper two units, the boundary was detected within 10 feet of their actual depth, in 90% of the wells. The mean detection performance in the Apiay field is 50%. We compared our method with other traditional techniques which do not focus on selecting optimal features for boundary identification. Those methods resulted in detection performances of 40% for the uppermost boundary, which lag behind the 90% performance of our method. Automated determination of geologic boundaries will expedite studies, and knowledge of the controlling deposition factors will enhance stratigraphic and reservoir characterization models. We expect that automated boundary detection and cyclicity analysis will prove to be valuable and time-saving methods for establishing correlations and their uncertainties in many types of oil and gas reservoirs, thus facilitating reservoir exploration and management.

Particle Image Velocimetry (PIV) and pressure measurement techniques were performed to investigate the drag reduction due to microbubble injection in the boundary layer of a fully developed turbulent channel flow. Two-dimensional full-field velocity components in streamwise-near-wall normal plane of a turbulent channel flow at Reynolds number of 5128 based on the half height of the channel were measured. The influence of the presence of microbubbles in the boundary layer was assessed and compared with single phase channel flow characteristics. A drag reduction of 38.4% was achieved with void fraction of 4.9%. The measurements were analyzed by studying the turbulence characteristics utilizing wavelet techniques. The wavelet cross-correlation and auto-correlation maps with and without microbubbles were studied and compared. The two-dimensional and threedimensional wavelet maps were used to interpret the results. The following observations were deduced from this study: 1. The microbubble injection within the boundary layer increases the turbulent energy of the streamwise velocity components of the large scale (large eddy size, low frequency) range and decreases the energy of the small scale (small eddy size, high frequency) range. 2. The wavelet cross-correlation maps of the normal velocities indicate that the microbubble presence decrease the turbulent energy of normal velocity components for both the large scale (large eddy size, low frequency) and the small scale (small eddy size, high frequency) ranges. 3. The wavelet auto-correlation maps of streamwise velocity shows that the intensities at low frequency range were increased with microbubble presence and the intensities at high frequency range were decreased. 4. The turbulent intensities for the normal fluctuating velocities at both low frequency and high frequency range were decreased with microbubble injection. This study presents the modifications in the characteristics of the boundary layer of channel flow which are attributed to the presence of microbubbles. Drag reduction studies with microbubble injections utilizing wavelet techniques are promising and are needed to understand the drag reduction phenomena.

Thesis (Ph. D.)--Lehigh University, 2000. / Includes vita. Includes bibliographical references (leaves 179-183).

Thesis (Ph. D.)--Lehigh University, 2000. / Includes vita. Includes bibliographical references (leaves 186-192).