The goal of this research project is to determine the fractal nature, if any, which surface water waves exhibit when viewed on a microscopic scale. Due to the relatively recent development of this area of mathematics, a brief introduction to the study of fractal geometry, as well as several examples of fractals, are included in this paper. From that point, this paper addresses the specific situation of a surface wave as it nears the breaking point and attempts to detect the fractal structure of a wave at this given point when viewed on a microscopic scale. This is done from both a physical standpoint based on observations at the Hinsdale Wave Facility at Oregon State University and at Cape Perpetua, Oregon on the Pacific Coast, and from a theoretical standpoint based on a spring model. / Graduation date: 1992

This research focuses on estimating the shear wave velocity (Vs) profile based on the dispersion curve obtained from SASW field test data (i.e., inversion of SASW data). It is common for the person performing the inversion to assume the prior information required to constrain the problem based on his/her own judgment. Additionally, the Vs profile is usually shown as unique without giving a range of possible solutions. For these reasons, this work focuses on: (i) studying the non-uniqueness of the solution to the inverse problem; (ii) implementing an inversion procedure that presents the estimated model parameters in a way that reflects their uncertainties; and (iii) evaluating tools that help choose the appropriate prior information. One global and one local search procedures were chosen to accomplish these purposes: a pure Monte Carlo method and the maximum likelihood method, respectively. The pure Monte Carlo method was chosen to study the non-uniqueness by looking at the range of acceptable solutions (i.e., Vs profiles) obtained with as few constraints as possible. The maximum likelihood method was chosen because it is a statistical approach, which enables us to estimate the uncertainties of the resulting model parameters and to apply tools such as the Bayesian criterion to help select the prior information objectively. The above inversion methods were implemented for synthetic data, which was produced with the same forward algorithm used during inversion. This implies that all uncertainties were caused by the nature of the SASW inversion problem (i.e., there were no uncertainties added by experimental errors in data collection, analysis of the data to create the dispersion curve, layered model to represent a real 3-D soil stratification, or wave propagation theory). At the end of the research, the maximum likelihood method of inversion and the tools for the selection of prior information were successfully used with real experimental data obtained in Memphis, Tennessee.

This research studies higher harmonics of Rayleigh surface waves propagating in nickel base superalloys. Rayleigh waves are used because they carry most of the energy and travel along the surface of a specimen where fatigue damage is typically initiated. The energy concentration near the free surface leads to stronger nonlinear effects compared to bulk waves. An ultrasonic piezoelectric transducer together with a plastic wedge is used for the experimental generation of the Rayleigh wave. The detection system consists of a laser heterodyne interferometer. Measurements are performed to detect the fundamental wave as well as the second harmonic. The amplitude ratio is related to the nonlinearity parameter beta which is typically used to describe changes in microstructure and investigate fatigue damage.

The paper extends the analytical results obtained by Hwung et al. (1981) and further considers the non-linearity of waves to investigate variation horizontal velocity, temperature distribution induced by interaction of 2-D plane jet and waves. On the steady state, the nonlinear wave is considered as external force in motion equations, the property of momentum conservation of jet flow, and radiation stress are applied to analyze the interaction of waves- jet flow in arbitrary profile. The scale function 1 £` £\1(x) , 2 2£` £\ (x) between the variation function f (x,y) and velocity distribution can also be obtained. The non-dimensional theoretical solution is also useful to estimate the relative characteristics in the physical field. The momentum equation and velocity distribution of interaction without property of temperature diffusion are employed to find the temperature distribution for arbitrary sections. Based on the experiments and theory solution obtained by Hwung et al. (1981) it is found that time-averaged horizontal velocity and temperature are Gaussian distribution, the coefficient of horizontal velocity 1 c , and temperature distribution 2 c are 0.105, 0.148, respectively. In the present, two coefficients considered as non-linearity of waves 1 c = 0.124 and 2 c = 0.152 are determined. In other words, it is shown that exact solution and boundary effect included non-linearity of waves is related to velocity of jet flow, wave periods, relative depth and steepness of waves respectively. Comparing with experiments indicated that the analytical solution of the present for MSE is well confirm the experimental results and better than linear results obtained by Hwung et al. (1981) The influence due to interaction of 2-D turbulent jet flow and Stokes waves can be obtained by using dimension analysis. Moreover, the related properties inside the flow also can be estimated.

Independent sets of reflection seismic and seismoelectric data were collected, processed, and interpreted with the aim of generating and studying guided waves within a fault zone. While seismic surveys have recently been utilized to investigate fault zones, past and current seismoelectric experiments have been more focused on identifying lithological interfaces and the presence of fluids within the shallow subsurface. The utilization of a fault structure to study seismoelectric conversions associated with guided waves has not hitherto been reported in the literature. The purpose of this research is to investigate the capabilities of the seismoelectric geophysical method to image fault structures, and to compare these to the capabilities of the conventional reflection seismic technique. I hypothesize that the presence of subsurface fluids will enhance seismoelectric imaging of a fault system. My results show that seismoelectric data contribute significant new for fault zone characterization and subsurface. I collected seismic and seismoelectric data sets across a fault system in the Llano Uplift of central Texas. The seismic reflection data were collected with a Geometrics Strataview seismograph equipped with 36 geophones. The seismoelectric data utilized three Geometrics Geode seismographs, with electric fields recorded by stainless steel dipole pairs instead of geophones. A sledgehammer and an accelerated weight drop provided the seismic energy sources throughout the experiment. Elementary processing techniques were applied to both data sets to enhance the signal to noise ratio. Seismic reflection studies previously have been shown capable of identifying fault zones through the characterization of guided waves. The seismoelectric phenomenon has not yet been utilized for this purpose. Identification of fault-zone trapped waves within each data set was attempted separately before the two data types were qualitatively compared as to their relative capabilities for illuminating the fault zone. The seismic data revealed dispersive energy packets, indicative of guided waves, within the fault zone and absent in the surrounding lithologies. The seismoelectric data was able to produce comparable signals in the fault zone showing guided waves.

This thesis is study about the capability of guided waves in the inspection of cracks in pipelines, and studying about the guided waves of mode conversion phenomenon caused by cracks. The generally used inspection methods in industry are all localized area inspection. It will cost expensively and spend lots of human resource and time consuming, if we want to inspect the whole area in pipelines in factory. Thus, guided waves are used to improve these shortcomings of traditional inspection methods. Guided Waves can propagate fast and long range along the pipelines without decay. With the ability that guided waves can incident at a single location then inspect the whole region of pipelines under efficiently propagating distance. In this thesis, with using laboratory equipment, 3 Toneburst Cycles, 400¡B500¡B600 kHz, and L(0,1)¡BL(0,2) incident mode set up for crack detective sensitivity experiment. By calculating the group velocity of the signals of crack, it is known that there are three separated modes L(0,1)¡BL(0,2) and F(1,2) from reflected waves by cracks. These modes are exactly mode converted by cracks. The results show that in the same crack circumferential length or crack depth, the longer length or the deeper depth cause the higher reflection coefficient. It means they are more sensitive on the inspection of cracks. Also the reflection coefficient increases with the raising cross section area loss of cracks. In two dimensional fast Fourier transform experiment (2-D FFT), with 3 Toneburst Cycles, 400¡B500¡B600 kHz, L(0,1)¡BL(0,2) incident mode, and 0.5 cm interval set up to gather 40-point signals for proceeding the experiment. It can separate signals with different group velocity which are mixing together in time domain. From results, there are three different modes L(0,1)¡BL(0,2) and F(1,2) mode separated at three-dimensional picture. Finally, using the guided waves inspection system with 3 toneburst, 90 kHz and T(0,1) incident mode set up to proceed the experiment as before. In inspecting crack sensitive experiment, the use of this system has the similar result with the use of laboratory equipment. It proves that the excellent capability of guided waves in inspection of cracks in pipelines. While in mode identification, this system can identify there is only T(0,1) and F(1,2) mode with the same group velocity exist. Then the same result is verified by 2-D FFT experiment. It shows that this system generate or receive the specific mode in detection cracks by phase construction or phase destruction of phase interference.

ABSTRACT This paper treats the standing waves formed by two progressive waves possessing same properties but opposite direction in stationary atmosphere and uniform depth. The third-order approximation to two-wave trains interactions obtained by Chen¡]1990¡^is cited. From the solution that can be reduced to the cases such as standing waves, the properties resulted in standing wave due to the nonlinear interactions between two wave trains intersection, particularly, the two peaks of wave pressure, are described clearly. Furthermore, the profile, pressure and angular frequency is also verified in good agreement with the experimental results.

Thesis (M.S.)--West Virginia University, 2001. / Title from document title page. Document formatted into pages; contains iv, 76 p. : ill. (some col.). Includes abstract. Includes bibliographical references (p. 47-51).

Thesis (Ph.D)--University of Texas at Arlington, 2008.

Thesis (M. Phil.)--University of Hong Kong, 2010. / Includes bibliographical references (leaves 72-80). Also available in print.