Finite-amplitude interfacial waves in the presence of a current

Solutions for interfacial waves of permanent form in the presence of a current wcre obtained for small-to-moderate wave amplitudes. A weakly nonlinear approximation was used to give simple analytical solutions to second order in wave height. Numerical methods were usctl to obtain solutions for larger wave amplitudes, details are reported for a number of selected cases. A special class of finite-amplitude solutions, closely related to the well-known Stokes surface waves, were identified. Factors limiting the existence of steady solutions are examined

A new type of three-dimensional deep-water wave of permanent form

A new class of three-dimensional, deep-water gravity waves of permanent form has been found using an equation valid for weakly nonlinear waves due to Zakharov (1968). These solutions appear as bifurcations from the uniform two-dimensional wave train. The critical wave heights are given as functions of the modulation wave vector. The three-dimensional patterns may be skewed or symmetrical. An example of the skewed wave pattern is given and shown to be stable. The results become exact in the limit of very oblique modulations

A note on numerical computations of large amplitude standing waves

Numerical solutions of the inviscid equations that describe standing waves of finite amplitude on deep water are reported. The calculations suggest that standing waves exist of steepness, height and energy greater than the limiting wave of Penney & Price (1952). The computed profiles are found to be consistent with Taylor's (1953) experimental observations

Interview with Philip G. Saffman

An interview in three sessions, December 1997 and April 1999, with Philip Geoffrey Saffman, Theodore von Kármán Professor of Applied Mathematics and Aeronautics, in the Division of Engineering and Applied Science. Dr. Saffman received his undergraduate and graduate degrees at Cambridge University and moved to Caltech in 1964 as a professor of fluid mechanics, becoming a professor of applied mathematics in 1970 and Von Kármán Professor in 1995. He died on August 17, 2008. He discusses his Jewish family’s background in the United Kingdom; growing up in Leeds; the family’s experiences in World War II. At Cambridge: studies fluid mechanics with George Batchelor (PhD 1956); postdoctoral work with G. I. Taylor; joins faculty as assistant lecturer, 1958. Moves to King’s College, London, 1960, to work with Hermann Bondi. Recalls first visit to Caltech, at JPL with Janos Laufer, 1963; impressions after joining faculty in 1964; genesis of applied mathematics at Caltech; collaboration with neighbor Max Delbrück; sabbaticals at MIT (1970-71 and 1982); operations of Caltech’s applied math dept. Comments on two of his children as Caltech undergraduates. Recalls some of his 37 graduate students, particularly Henry Yuen; Yuen’s career and invention of VCR Plus. Discusses his reasons for rejecting Cambridge’s offer of the Taylor chair; his fears that Caltech is losing out on best graduate students and faculty, in part because of tight money. In a supplemental interview in 1999, he reminisces about his Cambridge supervisors Batchelor and Taylor; describes his research on water waves and vortices; and further remarks on offer of Taylor chair at Cambridg

Instability and confined chaos in a nonlinear dispersive wave system

Calculations of a discrete nonlinear dispersive wave system show that as the degree of nonlinearity increases, the system experiences in turn, periodic, recurring, chaotic, transitional, and periodic motions. A relationship between the instability of the initial configuration and the long-time behavior is identified. The calculations further suggest that the corresponding continuous system will exhibit chaotic motions and energy-sharing among a narrow band of unstable modes, a phenomenon which we call "confined chaos.

Bifurcation and symmetry breaking in nonlinear dispersive waves

The equation governing four-wave interactions in a nonlinear dispersive system is studied. It is shown that a nonlinear steady-state plane wave can bifurcate into nonplanar steady-state solutions. In the case of an isotropic medium, the bifurcation is degenerate and the bifurcated solutions may preserve or break the symmetry. An example is given of a symmetry-breaking solution for deep-water gravity waves and its stability is discussed

ACKNOWLEDGEMENTS

suggesting these problems and guiding the direction of this research. His valuable insight and encouragement were essential to the completion of this work. I wish to thank other members of the faculty and fellow graduate students for helpful discussions on these and other problems. During the course of this research I was supported b