Surface Wave Field Research Articles

On the Energy Input from Wind to Surface Waves

Abstract A basic model relating the energy dissipation in the ocean mixed layer to the energy input into the surface wave field is combined with recent measurements of turbulent kinetic energy dissipation to determine the average phase speed of the waves acquiring energy from the wind. This phase speed and the square root of the corresponding wavelength are proportional to the vertically integrated dissipation. The calculations show that the maximum energy input occurs at the high-frequency end of the wave spectrum. Dissipation data from other investigators are used to estimate the effective phase speed between 0.55 and 0.72 m s−1 and corresponding wavelengths varying between 0.2 and 0.33 m for the waves receiving most of the energy.

Propagation of Surface Waves Across an Anisotropic Layer

Propagation of elastic surface waves across a thin anisotropic interface layer between two vertically inhomogeneous isotropic quarter-spaces is considered. The relationship between the surface wave fields at the opposite sides of the layer is obtained in the form of matrix differential operators. Based on the Green’s function technique, an analytical method is developed to calculate reflection and transmission coefficients of Rayleigh waves at the layer. The reflection and transmission coefficients of Rayleigh waves at the interface layer are calculated as a function of the angle of incidence for various models of layers with hexagonal symmetry and results are discussed in some detail. Several isotropic layers of low or high velocity materials are also considered to examine the trade-off between anisotropy and inhomogeneity of the interface layer.

Plane-wave diffraction by a two-part impedance strip

A uniform asymptotic high-frequency solution is developed for the diffraction of (E-polarised) electromagnetic plane waves by a two-part impedance strip. Uniform expressions for the interactions up to third order between the edges of the strip, including the conversion of surface-wave fields into space-wave fields, and vice-versa, via edge or junction diffraction, are obtained. The solution is based on a spectral iteration technique consisting of taking the spectral representation of the n-tuply diffracted field by one edge as the incident held for a half-plane (or a two-part plane) associated with the other edge (or junction) where the (n+1)th diffraction will take place. The analysis is then performed through the Wiener-Hopf technique for the (n+1)th diffraction. Bistatic diffraction patterns are obtained for different values of the surface impedances of the strip.

Energy transfer between surface and internal waves in the North Pacific Ocean

The energy transfer between internal and surface waves is formulated as a scattering process of surface waves by packets of internal waves. For weak internal wave fields, the Born approximation may be used, and this is shown to give the same transfer rate as the “modulation model” of the resonant triad theory for weak nonlinear interactions. For stronger internal wave fields, the eikonal theory of ray paths is used to calculate surface wave scattering. The theory is applied to historical Väisälä frequency profiles and wind data for the North Pacific ocean. Energy transfer rates from the internal wave to the surface wave field in the range of 10−4 W/m2 and higher are found, except during winter months at higher latitudes, where the rates are somewhat lower. For the weaker internal wave fields, the resonant triad theory (or, equivalently, the Born theory) must be used. For the strongest fields observed, the weak interaction theory is not valid and the interaction is described as ray path scattering. There is a region of overlap for which the two theoretical models give comparable results.

Attenuation of the surface wave fields into a degenerate plasma: another Kohn anomaly

It is demonstrated that due to the Kohn singularity the attenuation of surface waves into the bulk of a semi-infinite degenerate plasma can follow a power-law (no exponential decrease, as in a "classical" plasma). This effect is analogous to the power-law decrease of the field of a test charge in a degenerate plasma.

Laboratory-generated, shallow-water surface waves: Analysis using the periodic, inverse scattering transform

The space-time evolution of laboratory-generated, shallow-water wave trains is considered in one-space and one-time dimensions. An electronic control-and-feedback system is used to generate periodic/quasiperiodic wave trains in a laboratory flume (0.76×0.8×46 m3) in which five spatially distributed, resistance wave gauges simultaneously record time series of the surface wave field. A concrete ramp with a slope of 0.02 minimizes reflections, and thus ensures near-unidirectional wave motion. The data are analyzed using both (1) linear Fourier analysis and (2) a relatively new kind of nonlinear Fourier analysis based upon the inverse scattering transform (IST) for the periodic Korteweg–de Vries (KdV) equation. The periodic IST formalism consists of a linear superposition of the ‘‘hyperelliptic-function oscillation modes,’’ which are intrinsically nonlinear, while simultaneously undergoing nonlinear interactions with each other. The KdV oscillation modes may be viewed as the ‘‘sine waves’’ of the periodic scattering transform, although they are generally nonsinusoidal in shape. The amplitudes of the oscillation modes are constants of the motion for wave motion governed purely by KdV. For a series of experiments in the Ursell number range 0.30<U<0.99, it is found that the linear Fourier modes have amplitudes that vary substantially in space and time, while the inverse scattering modes are found to be nearly constant. It is therefore suggested that the inverse scattering formulation may be more appropriate than linear Fourier analysis for describing the nonlinear dynamical motions studied experimentally herein. Introducing the concept of ‘‘phase locking’’ among the IST modes, features in the data that are referred to as ‘‘coherent structures’’ are identified. Such structures are found not to be strictly solitons (they constitute multiple cnoidal wave interactions), although they have many of the properties normally identified with solitons, including preservation of their amplitudes after collisions with other waves.

Modified form of diffraction tomography to image boundary structures : Rekdal, T; Doornbos, D J GeophysicsV58, N8, Aug 1993, P1136–1147

Wavefield extrapolation downward from the surface, as applied in migration and associated inversion methods, is a common procedure to image subsurface reflectors. These methods require adequate (i.e., extensive and unaliased) sampling of the surface wavefield. Seismic tomography on the other hand, relates parameters of the upward propagated wavefield to the diffracting image, and sampling requirements are less severe; it is usually the only option to image deep structures from sparse data. The ordinary form of ray tomography, however, imposes a severe smoothness constraint on the boundary; in particular the tops and valleys of a relatively rough structure are not well-resolved. We have implemented a generalized form of tomography, which uses both the ray term and the diffraction term linearized in the boundary perturbation. We introduce a generalized reflection coeffi-

Nonlinear surface waves in a plasma with a diffuse boundary

The propagation of surface waves in a plasma with a diffuse boundary is considered. Three equations governing the evolution of the system are derived. If the excursion length of the electrons in the surface wave field is smaller than the width of the plasma–vacuum transition layer, it is found that typically the nonlinear density modifications in the boundary layer are more important than the previously investigated bulk nonlinearities.

Heating Mechanism of Self‐Interaction of Potential Surface Waves in a Warm Nonisothermal Plasma Bounded by Metal

AbstractThe influence of electrons heating in the high‐frequency potential surface wave (SW) field on dispersion properties of the considered SW is studied in this paper. High‐frequency SW propagate at the interface between a warm nonisothermal plasma and a metal. The nonlinear dispersion relation for the SW is derived and investigated. The obtained results are valid in both semiconductor and gaseous plasmas in a weak heating approximation.

Dielectric cover effect on rectangular microstrip antenna array

A theoretical model to analyze a covered rectangular antenna with an arbitrary dielectric constant superstrate is developed. The antenna is simulated by the radiation of two magnetic dipoles located at the radiating edges of the patch. The Green's function of an elementary magnetic dipole in a superstrate-substrate structure, utilizing spectral-domain analysis, is formulated, and the surface-wave and radiation field are computed. An improved transmission line model, which considers the stored energy near the radiating edges and the external mutual coupling, is used to compute the input impedances and radiation efficiency. Design considerations on the superstrate thickness and its dielectric constant are discussed. Experimental data for a single element and a 4/spl times/4 microstrip array is presented to validate the theory. >

The diffraction of an E-polarized plane wave by a resistive strip located on a dielectric interface

Uniform asymptotic expressions for the doubly diffracted fields excited on the edges of a resistive strip located on a dielectric interface are obtained using a spectral iteration technique. The incident electric field is assumed to be parallel to the edges of the strip. The results also include the contribution of the surface wave fields to the secondary diffraction.

Insights on the SASW nondestructive testing method

Spectral analysis of surface waves (SASW) is a nondestructive and in-situ method used for determining the thickness and elastic properties of pavement and soil sites using the dispersion characteristics of surface waves. In this paper, computer simulations of actual surface wave field tests are used to clarify errors that may arise in experimental dispersion curves of pavement sites when the usual test and data analysis procedures of the SASW method are followed. Two aspects of these procedures are considered: (i) relative phase angle unwrapping and (ii) source-to-near-receiver distance. The results of these simulations reveal that the currently used procedures may lead to erroneous results for some sites; the simulations offer valuable insights on the underlying causes. An overview of the theoretical aspects and field procedures of the surface wave method is briefly presented. Key words: surface waves, nondestructive testing, pavements, soils, elastic modulus.

A 2-D complex wavelet analysis of an unsteady wind-generated surface wave field

Nonlinear wave-wave interactions can be quite localised in space and an appropriate spectral analysis of such a wave field must retain this local phase information. To this end, the 2-D, complex wavelet functions ‘Arc’ and ‘Morlet2D’ can be used to decompose a wave field in space b and scale a. As both wavelets are Hardy functions, the transform result is complex, and the phase, φ, is defined over all b . Arc can be used to measure the energy of the wave field over b as a function of z.sfnc; k| , and the direction-specific wavelet, Morlet2D, can be used for the spatial energy distribution of k . Surface waves generated by unsteady wind have dislocations in phase that are widespread and persist until the initial wave field becomes disordered in appearance. While the energy at fundamental wavelengths (the wavelength of the initial instability) appears to saturate, the energy of the subharmonic component continues to increase with time. There appears to be significant energy in both modes, from early on in the life history of these organised wave fields. The energy of wavevectors aligned at a small angle off the mean wind direction vector (the including angle, α ≈ 20°) increases to become a substantial fraction of the total energy. The possible role of the pattern defects in local nonlinear mechanisms of energy transfer is discussed, and analogies are drawn with recent results in plane mixing layers. Techniques for the measurement of the complex dispersion relation, ω( k) , and group velocity, U g( k) , utilising the local space-scale decomposition of the 2D wavelet transform, are proposed.

Acoustic radiation from breaking waves

Observations of the sound from breaking surface waves using a small hydrophone array illustrate the temporal and spatial characteristics of this sound source and its dependence on the surface wave field. Such observations provide a source description that might have application in ambient noise model development. By tracking the propagation speed of the breaking event its wave scale is inferred; other measured properties include breaking length, duration, and spatial separation. Analysis indicates that the dependence of breaking probability on the fourth moment of the wave spectrum is consistent with a linear model. The measured speeds of breaking events imply that their scale is less than the dominant wind‐wave scale. Group structure of wave breaking, in which there is a tendency for waves to break repetitively at twice the wave period and spaced one wavelength apart, also occurs but is more readily identifiable at lower wind speeds.

Observations of planview flux patterns within convective structures of the marine atmospheric surface layer

Air/sea flux variability on horizontal scales from 50 m to several km results, in part, from the presence of coherent convective structures within the atmospheric boundary layer. The horizontal distribution of fluxes within these convective updrafts and downdrafts is, therefore, central to studies of air/sea interaction and remote sensing of sea surface wind and wave fields. This study derives these flux patterns from observations of the Marine Atmospheric Surface Layer (MASL).

A modified form of diffraction tomography to image boundary structures

Wavefield extrapolation downward from the surface, as applied in migration and associated inversion methods, is a common procedure to image subsurface reflectors. These methods require adequate (i.e., extensive and unaliased) sampling of the surface wavefield. Seismic tomography on the other hand, relates parameters of the upward propagated wavefield to the diffracting image, and sampling requirements are less severe; it is usually the only option to image deep structures from sparse data. The ordinary form of ray tomography, however, imposes a severe smoothness constraint on the boundary; in particular the “tops” and “valleys” of a relatively rough structure are not well‐resolved. We have implemented a generalized form of tomography, which uses both the ray term and the diffraction term linearized in the boundary perturbation. We introduce a generalized reflection coefficient that can be linearized in terms of the (unknown) boundary gradient, and we demonstrate the adequacy of this approximation with the help of synthetic seismograms. We compare the performance of the new inversion method with migration and ray tomography in a number of model experiments where a source and receiver array are used to image (1) a rough sea bottom and (2) a rough sedimentary layer boundary. In these experiments the new method is superior, especially in the outer part of the inversion region where migration and seismic tomography suffer seriously because of the lack of adequate surface information. Even for well‐controlled surveys there is the potential to successfully image a much larger area of the reflector than is possible with migration. Our experiments involved a single reflector in a known velocity‐density structure. The method’s applicability or modifications required when relaxing these assumptions, remains to be investigated.

Boundary Integral Solution to the Diffraction and Surface Wave Mechanisms in the Coated Edge

A method for numerically extracting the diffraction and surface wave scattering mechanisms present in the coated edge is described. An exact boundary integral formulation is used without resorting to the impedance boundary condition approximation. To handle the semi-infinite problem numerically, the non-decaying physical optics (PO) and surface wave fields are removed from the boundary integral equation such that the final discretization domain involves only a finite region near the edge. Numerical diffraction coefficients and surface wave launch coefficients are extracted from the scattered field. Solutions to several finite sized coated strips are constructed using the numerical diffraction coefficients and are shown to be valid for a variety of strip configurations.

Propagation characteristics of a slow surface wave in a 70 ghz solid-plasma waveguide containing an n-Insb slab carrying an applied current

The propagation characteristics of a 70 GHz slow surface wave in a transversely magnetised, partially filled, parallel-plate, solid-plasma waveguide have been investigated experimentally using n-InSb as the plasma material to which a pulsed current was applied. The surface-wave resonant magnetic field increased substantially with an increase in the applied current. Subsequently, a variation of the electron density of the plasma material with the current was determined by measuring the reflection from the plasma slab. The results indicate that the variation of the propagation characteristics is primarily explained by the variation of the electron density in the plasma material, and that the propagation characteristics of the slow surface wave in the above mentioned plasma waveguide can be controlled electronically by applying a current to the solid-plasma material.

A new model for surface wave propagation over undulating topography

A new model is presented for the propagation of monochromatic surface waves over a region of arbitrary, one-dimensional bottom topography. The smoothly varying bed profile is divided into a series of shelves separated by abrupt steps. The wave fields on either side of each step are related by a “transfer matrix”, and the propagation of waves along the shelf between adjacent steps is described by a “rotation matrix”. Starting from a point where the surface wavefield is known, the step by step application of the appropriate combination of these matrices allows computation of the wavefield over the region of interest. If the individual steps are small then the transfer matrix reduces to a simpler plane-wave form, with considerable savings in computational effort. Comparisons are made with an exact potential solution for single and double steps in order to investigate the accuracy and validity of the matrix method. Finally, the model is applied to the case of wave reflection by fixed sinusoidal bottom undulations, and good agreement is found between its predictions and existing laboratory data.

Dispersion characteristics and radial field distribution of surface waves in the collisional regime

The influence of collisional damping and the radial electron density profile on the characteristics of the wave propagation as well as on the radial distribution of the electric field of electromagnetic surface waves is studied. The discussion is mostly addressed to the situation of surface wave plasmas in the RF frequency range in a strongly collisional case. Some aspects of the influence of the collisional damping on the wave propagation, particularly in view of diagnostic applications, are discussed. The range of validity of the 'thin cylinder approximation' in the collisional case is compared with predictions of the collisionless theory. Furthermore the possibility of the occurrence of a resonant field enhancement as the position of a local plasma resonance under microwave conditions is pointed out.