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The analysis is a second-order analysis of the resonant interactions among triads of waves with wavelengths in the capillary-gravity and pure capillary ranges. The analysis is not a power series perturbation analysis, and one of the objects is the removal of the secularity which arises through power series perturbations. It is further found that the interactions are energy-conserving to the order considered here. Suitable modifications are made to accommodate the inevitable viscous attenuation associated with these small wavelengths. A start is made toward describing more completely the various spectra of random seas in wave-number and frequency regions where these interactions are dynamically significant. (Author).
The method of multiple scales is used to derive equations governing the temporal and spatial variation for the amplitudes and phases of inviscid capillary-gravity traveling waves in the case of second harmonic resonance (Wilton's ripples), but including the effects of near resonance, liquid depth, and pressure perturbations exerted by an external subsonic gas on the liquid/gas interface. The spatial form of the equations shows that, below a critical gas velocity, energy is transferred between the fundamental and its first harmonic in keeping with the energy conservation law. However, the amplitude of the first harmonic decreases with gas velocity. Above the critical gas velocity, the gas/liquid interface grows monotonically with distance. It is found that pure amplitude-modulated waves are possible only at perfect resonance. Pure phase-modulated, near-resonant waves are periodic, as the resonance forces a readjustment of the phases to produce perfect resonance. The effectiveness of the resonance in rippling the interface increases as the liquid depth decreases. (Author).
This up-to-date and comprehensive account of theory and experiment on wave-interaction phenomena covers fluids both at rest and in their shear flows. It includes, on the one hand, water waves, internal waves, and their evolution, interaction, and associated wave-driven means flow and, on the other hand, phenomena on nonlinear hydrodynamic stability, especially those leading to the onset of turbulence. This study provide a particularly valuable bridge between these two similar, yet different, classes of phenomena. It will be of value to oceanographers, meteorologists, and those working in fluid mechanics, atmospheric and planetary physics, plasma physics, aeronautics, and geophysical and astrophysical fluid dynamics.
In December 1994 Professor Enok Palm celebrated his 70th birthday and retired after more than forty years of service at the University of Oslo. In view of his outstanding achievements as teacher and scientist a symposium entitled "Waves and Nonlinear Processes in Hydrodynamics" was held in his honour from the 17th to the 19th November 1994 in the locations of The Norwegian Academy of Science and Letters in Oslo. The topics of the symposium were chosen to cover Enok's broad range of scientific work, interests and accomplishments: Marine hydrodynamics, nonlinear wave theory, nonlinear stability, thermal convection and geophys ical fluid dynamics, starting with Enok's present activity, ending with the field where he began his career. This order was followed in the symposium program. The symposium had two opening lectures. The first looked back on the history of hydrodynamic research at the University of Oslo. The second focused on applications of hydrodynamics in the offshore industry today.
Further studies have been made on the effect of viscosity and on the spectral-shape dependence on the energy flux of a gravity-capillary spectrum. Viscous effects have been included as a perturbation of the inviscid results and also in a more exact manner, producing an effective decoupling of gravity and capillary waves, suggesting that the growth of gravity-capillary waves in the front face of the spectrum must be mostly dependent on the energy flux from the wind. However, at an early stage of development, the nonlinear resonant interactions may still play a significant contribution to the growth of the gravity-capillary wave spectrum. The investigation is concluded with a brief description on the effect of nonlinear resonant interactions and surface tension to the second-order contributions to the doppler spectrum of radio waves backscattered from a water-wave system.
The outcome of a conference held in East Carolina University in June 1982, this book provides an account of developments in the theory and application of nonlinear waves in both fluids and plasmas. Twenty-two contributors from eight countries here cover all the main fields of research, including nonlinear water waves, K-dV equations, solitions and inverse scattering transforms, stability of solitary waves, resonant wave interactions, nonlinear evolution equations, nonlinear wave phenomena in plasmas, recurrence phenomena in nonlinear wave systems, and the structure and dynamics of envelope solitions in plasmas.
A rigorously comprehensive and interdisciplinary text on wave turbulence, for graduate students and researchers in physics-related fields.
The integration of modern paleomagnetic, radiometric, and biostratigraphic studies has provided an accurate geochronological framework for the past 10 million years--the Late Neogene. Marine zones based on calcareous and siliceous planktonic organisms are recognized from the sub-Arctic region to the sub-Antarctic and their correlation to the paleomagnetic time scale is now feasible in some detail for the past 5 my. Likewise, the relationship of geochemically calibrated mammalian biochronology to the marine succession has been greatly improved. Within this framework of time it is possible to delineate the history of major features in Late Neogene paleontology, climatology, and oceanography. (Author).