A general solution is presented for water waves generated by an arbitrary movement of the bed (in space and time) in a two-dimensional fluid domain with a uniform depth. The integral solution which is developed is based on a linearized approximation to the complete (nonlinear) set of governing equations. The general solution is evaluated for the {specific case of a uniform upthrust or downthrow of a block section of the bed; two time-displacement histories of the bed movement are considered. An integral solution (based on a linear theory) is also developed for a three-dimensional fluid domain of uniform depth for a class of bed movements which are axially symmetric. The integral solution is evaluated for the specific case of a block upthrust or downthrow of a section of the bed, circular in planform, with a time-displacement history identical to one of the motions used in the two-dimensional model. Since the linear solutions are developed from a linearized approximation of the complete nonlinear description of wave behavior, the applicability of these solutions is investigated. Two types of nonlinear effects are found which limit the applicability of the linear theory: (1) large nonlinear effects which occur in the region of generation during the bed movement, and (2) the gradual growth of nonlinear effects during wave propagation. A model of wave behavior, which includes, in an approximate manner, both linear and nonlinear effects is presented for computing wave profiles after the linear theory has become invalid due to the growth of nonlinearities during wave propagation. An experimental program has been conducted to confirm both the linear model for the two-dimensional fluid domain and the strategy suggested for determining wave profiles during propagation after the linear theory becomes invalid. The effect of a more general time-displacement history of the moving bed than those employed in the theoretical models is also investigated experimentally. The linear theory is found to accurately approximate the wave behavior in the region of generation whenever the total displacement of the bed is much less than the water depth. Curves are developed and confirmed by the experiments which predict gross features of the lead wave propagating from the region of generation once the values of certain nondimensional parameters (which characterize the generation process) are known. For example, the maximum amplitude of the lead wave propagating from the region of generation has been found to never exceed approximately one-half of the total bed displacement. The gross features of the tsunami resulting from the Alaskan earthquake of 27 March 1964 can be estimated from the results of this study.

© 1972 W. M. Keck Laboratory of Hydraulics and Water Resources. California Institute of Technology. The writer wishes to express his sincere gratitude to his thesis advisor, Professor Fredric Raichlen, for his kind guidance and generous assistance "above and beyond the call of duty" throughout every phase of this investigation. The writer also wishes to thank Professors Vito A. Vanoni, Theodore Y. T. Wu, and Jorg Imberger for many helpful discussions during the development of the theoretical analysis of this; study. Dr. Allen T. Y. Chwang also provided many stimulating comments and suggestions for which the writer is extremely grateful. A special debt of gratitude is owed to Mr. Elton IF. Daly, supervisor of the shop and laboratory, whose continuing assistance during the design, construction, and maintainance of the experimental equipment made the laboratory phase of this investigation both possible and pleasurable. Appreciation is also extended to Mr. Robert L. Greenway who assisted in the construction and maintainance of the experimental equipment; to Mr. Carl A. Green who assisted in the laboratory and performed the drafting of all figures appearing in this manuscript; and to Mrs. Arvilla F. Krugh who worked so diligently in typing this manuscript. Mr. Carl T. Eastvedt also assisted in some of the photographic work. The writer also wishes to thank the California Institute of Technology for financial assistance and for providing a most stimulating environment in which to work. This research was supported by NSF Grants GK-2370 and GK-24716; experiments were conducted at the W. M. Keck Laboratory of Hydraulics and Water Reasources.

Submitted - KH-R-28.pdf