Topic

# Dispersion (water waves)

About: Dispersion (water waves) is a research topic. Over the lifetime, 10134 publications have been published within this topic receiving 248462 citations.

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01 Jan 1974

TL;DR: In this paper, a general overview of the nonlinear theory of water wave dynamics is presented, including the Wave Equation, the Wave Hierarchies, and the Variational Method of Wave Dispersion.

Abstract: Introduction and General Outline. HYPERBOLIC WAVES. Waves and First Order Equations. Specific Problems. Burger's Equation. Hyperbolic Systems. Gas Dynamics. The Wave Equation. Shock Dynamics. The Propagation of Weak Shocks. Wave Hierarchies. DISPERSIVE WAVES. Linear Dispersive Waves. Wave Patterns. Water Waves. Nonlinear Dispersion and the Variational Method. Group Velocities, Instability, and Higher Order Dispersion. Applications of the Nonlinear Theory. Exact Solutions: Interacting Solitary Waves. References. Index.

8,808 citations

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TL;DR: In this article, a method for measuring the surface energy of solids and for resolving surface energy into contributions from dispersion and dipole-hydrogen bonding forces has been developed based on the measurement of contact angles with water and methylene iodide.

Abstract: A method for measuring the surface energy of solids and for resolving the surface energy into contributions from dispersion and dipole-hydrogen bonding forces has been developed. It is based on the measurement of contact angles with water and methylene iodide. Good agreement has been obtained with the more laborious γc method. Evidence for a finite value of liquid-solid interfacial tension at zero contact angle is presented. The method is especially applicable to the surface characterization of polymers.

7,695 citations

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TL;DR: In this paper, the theory of propagation of stress waves in a porous elastic solid developed in Part I for the low-frequency range is extended to higher frequencies, and the breakdown of Poiseuille flow beyond the critical frequency is discussed for pores of flat and circular shapes.

Abstract: The theory of propagation of stress waves in a porous elastic solid developed in Part I for the low‐frequency range is extended to higher frequencies. The breakdown of Poiseuille flow beyond the critical frequency is discussed for pores of flat and circular shapes. As in Part I the emphasis of the treatment is on cases where fluid and solids are of comparable densities. Dispersion curves for phase and group velocities along with attenuation factors are plotted versus frequency for the rotational and the two dilational waves and for six numerical combinations of the characteristic parameters of the porous systems. Asymptotic behavior at high frequency is also discussed.

3,600 citations

01 Jan 1973

TL;DR: In this article, wave spectra were measured along a profile extending 160 kilometers into the North Sea westward from Sylt for a period of two weeks in 1968 and 1969, with particular emphasis on wave growth under stationary offshore wind conditions and the attenuation of swell in water of finite depth.

Abstract: "Wave spectra were measured along a profile extending 160 kilometers into the North Sea westward from Sylt for a period often weeks in 1968 and 1969. During the main experiment in July 1969, thirteen wave stations were in operation, of which six stations continued measurements into the first two weeks of August. A smaller pilot experiment was carried out in September 1968. Currents, tides, air-sea temperature differences and turbulence in the atmospheric boundary layer were also measured. The goal of the experiment (described in Part 1) was to determine the structure of the source function governing the energy balance of the wave spectrum, with particular emphasis on wave growth under stationary offshore wind conditions (Part 2) and the attenuation of swell in water of finite depth (Part 3). The source functions of wave spectra generated by offshore winds exhibit a characteristic plus-minus signature associated with the shift of the sharp spectral peak towards lower frequencies. The two-lobed distribution of the source function can be explained quantitatively by the nonlinear transfer due to resonant wave-wave interactions (second order Bragg scattering). The evolution of a pronounced peak and its shift towards lower frequencies can also be understood as a selfstabilizing feature of this process. For small fetches, the principal energy balance is between the input by wind in the central region of the spectrum and the nonlinear transfer of energy away from this region to short waves, where it is dissipated, and to longer waves. Most of the wave growth on the forward face of the spectrum can be attributed to the nonlinear transfer to longer waves. For short fetches, approximately (80 ± 20) % of the momentum transferred across the air/sea interface enters the wave field, in agreement with Dobson's direct measurements of the work done on the waves by surface pressures. About 80-90 % of the wave-induced momentum flux passes into currents via the nonlinear transfer to short waves and subsequent dissipation; the rest remains in the wave field and is advected away. At larger fetches the interpretation of the energy balance becomes more ambiguous on account of the unknown dissipation in the low-frequency part of the spectrum. Zero dissipation in this frequency range yields a minimal atmospheric momentum flux into the wave field of the order of (10 to 40) % of the total momentum transfer across the air-sea interface -- but ratios up to 100 % are conceivable if dissipation is important. In general, the ratios (as inferred from the nonlinear energy transfer) lie within these limits over a wide (five-decade) range of fetches encompassing both wave-tank and the present field data, suggesting that the scales of the spectrum continually adjust such that the wave-wave interactions just balance the energy input from the wind. This may explain, among other features, the observed decrease of Phillips' "constant" with fetch. The decay rates determined for incoming swell varied considerably, but energy attenuation factors of two along the length of the profile were typical. This is in order of magnitude agreement with expected damping rates due to bottom friction. However, the strong tidal modulation predicted by theory for the case of a quadratic bottom friction law was not observed. Adverse winds did not affect the decay rate. Computations also rule out wave-wave interactions or dissipation due to turbulence outside the bottom boundary layer as effective mechanisms of swell attenuation. We conclude that either the generally accepted friction law needs to be significantly modified or that some other mechanism, such as scattering by bottom irregularities, is the cause of the attenuation. The dispersion characteristics of the swells indicated rather nearby origins, for which the classical (i event model was generally inapplicable. A strong Doppler modulation by tidal currents was also observed.

3,264 citations

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TL;DR: It is established that electromagnetic waves in both materials are governed by an effective permittivity of the same plasma form, which allows the creation of designer surface plasmons with almost arbitrary dispersion in frequency and in space.

Abstract: Metals such as silver support surface plasmons: electromagnetic surface excitations localized near the surface that originate from the free electrons of the metal. Surface modes are also observed on highly conducting surfaces perforated by holes. We establish a close connection between the two, showing that electromagnetic waves in both materials are governed by an effective permittivity of the same plasma form. The size and spacing of holes can readily be controlled on all relevant length scales, which allows the creation of designer surface plasmons with almost arbitrary dispersion in frequency and in space, opening new vistas in surface plasmon optics.

2,740 citations