Surface waves on water of non-uniform depth

1958 ◽  
Vol 4 (6) ◽  
pp. 607-614 ◽  
Author(s):  
Joseph B. Keller
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Surface Waves ◽  
Linear Theory ◽  
Gravity Waves ◽  
Geometrical Optics ◽  
Surface Wave Propagation ◽  
Special Cases

Gravity waves occur on the surface of a liquid such as water, and the manner in which they propagate depends upon its depth. Although this dependence is described in principle by the equations of the ‘exact linear theory’ of surface waves, these equations have not been solved except in some special cases. Therefore, oceanographers have been unable to use the theory to describe surface wave propagation in water whose depth varies in a general way. Instead they have employed a simplified geometrical optics theory for this purpose (see, for example, Sverdrup & Munk (1944)). It has been used very successfully, and consequently various attempts, only partially successful, have been made to deduce it from the exact linear theory. It is the purpose of this article to present a derivation which appears to be satisfactory and which also yields corrections to the geometrical optics theory.

Surface Wave Propagation in Thin Silver and Aluminium Films

2005 ◽  
Vol 60 (11-12) ◽  
pp. 789-796
Author(s):  
Anouar Njeh ◽  
Nabil Abdelmoula ◽  
Hartmut Fuess ◽  
Mohamed Hédi Ben Ghozlen
Keyword(s):  
Thin Films ◽  
Wave Propagation ◽  
Surface Wave ◽  
Surface Waves ◽  
Acoustic Waves ◽  
Frequency Interval ◽  
Constant Frequency ◽  
Surface Wave Propagation ◽  
Coated Materials ◽  
Bulk Waves

Three kinds of acoustic waves are known: bulk waves, pseudo-surface waves and surface waves. A plane wave section of a constant-frequency surface of a film serves as a hint for the expected nature. Calculations based on slowness curves of films reveal frequency ranges where each type of acoustic waves is predominant. Dispersion curves and displacement acoustic waves are calculated and commented in each frequency interval for different coated materials. Both dispersion and sagittal elliptical displacement are sensitive and depend on diagrams mentioned above. Silver and aluminium thin films having different anisotropy ratios, namely 2.91 and 1.21, are retained for illustration.

scholarly journals ON SURFACE WAVES IN A FINITELY DEFORMED MAGNETOELASTIC HALF-SPACE

2011 ◽  
Vol 03 (04) ◽  
pp. 633-665 ◽  
Author(s):  
P. SAXENA ◽  
R. W. OGDEN
Keyword(s):  
Magnetic Field ◽  
Wave Propagation ◽  
Surface Wave ◽  
Surface Waves ◽  
Half Space ◽  
Wave Speed ◽  
Sagittal Plane ◽  
Isotropic Energy ◽  
Surface Wave Propagation ◽  
Homogeneous Strain

Rayleigh-type surface waves propagating in an incompressible isotropic half-space of nonconducting magnetoelastic material are studied for a half-space subjected to a finite pure homogeneous strain and a uniform magnetic field. First, the equations and boundary conditions governing linearized incremental motions superimposed on an initial motion and underlying electromagnetic field are derived and then specialized to the quasimagnetostatic approximation. The magnetoelastic material properties are characterized in terms of a "total" isotropic energy density function that depends on both the deformation and a Lagrangian measure of the magnetic induction. The problem of surface wave propagation is then analyzed for different directions of the initial magnetic field and for a simple constitutive model of a magnetoelastic material in order to evaluate the combined effect of the finite deformation and magnetic field on the surface wave speed. It is found that a magnetic field in the considered (sagittal) plane in general destabilizes the material compared with the situation in the absence of a magnetic field, and a magnetic field applied in the direction of wave propagation is more destabilizing than that applied perpendicular to it.

Effect of boundaries on wave propagation in media with microstructure: II. Surface waves in a half-space

1974 ◽  
Vol 64 (2) ◽  
pp. 387-392
Author(s):  
M. Farshad ◽  
G. Ahmadi
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Surface Waves ◽  
Half Space ◽  
Couple Stress ◽  
Couple Stress Theory ◽  
Classical Elasticity ◽  
Stress Theory ◽  
Material Parameters ◽  
Surface Wave Propagation

abstract The surface-wave propagation in a half-space according to couple-stress theory is studied herein. Dispersion curves as well as displacement variations with the depth coordinate are obtained for a range of material parameters. Comparison is made with the classical elasticity predictions upon which certain conclusions are reached.

Tracking of Cracks in Airplane Components Using Nonlinear Surface Wave Propagation Techniques

2005 ◽  
Vol 293-294 ◽  
pp. 549-556 ◽  
Author(s):  
Steve Vanlanduit ◽  
Patrick Guillaume ◽  
Jimmy Vermeulen ◽  
Kristof Harri
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Surface Waves ◽  
High Voltage Pulse ◽  
Operation Conditions ◽  
Safety Regulations ◽  
Surface Wave Propagation ◽  
Force Signal ◽  
On Line ◽  
Ultrasonic Surface Waves

Ultrasonic surface waves provide a sensitive means to detect cracks in airplane structures. Until now several obstacles remained to use ultrasonic surface waves for on-line damage detection (i.e. in-flight). In this article a method will be proposed to detect a growing fatigue crack while the aircraft is operating. In contrast to classical ultrasonic measurement methods, that use a high voltage pulse, we applied an optimized multi-sine excitation signal with an amplitude of a few volts only (this agrees better with the applicable safety regulations for aircraft). Furthermore, an indicator quantifying the nonlinearity of the ultrasonic surface wave propagation is used. By using a nonlinearity index the influence of changing operation conditions that can be observed with most linear methods is eliminated. The proposed method is validated on a steel beam that is fatigue loaded with a force signal obtained from in-flight data.

Leakage of MHD surface waves in structured media

1989 ◽  
Vol 41 (1) ◽  
pp. 23-30 ◽  
Author(s):  
V. M. Čadež ◽  
V. K. Okretič
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Surface Waves ◽  
Double Step ◽  
Numerical Example ◽  
Structured Media ◽  
Surface Wave Propagation

Surface-wave propagation along a double step is investigated within ideal compressible MHD. The occurrence of surface-wave leakage is emphasized and the relevant conditions are discussed. A numerical example is presented to illustrate the process.

Surface Wave Propagation of an Ultra Thin Liquid Film on a Rotating Disk

2004 ◽  
Author(s):  
Lin Wu
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Shock Waves ◽  
Liquid Film ◽  
Surface Waves ◽  
Thin Liquid Film ◽  
Rotating Disk ◽  
Disjoining Pressure ◽  
Shearing Force ◽  
Surface Wave Propagation

We theoretically and numerically study the propagation of axisymmetrical long surface waves of an ultra thin liquid film on a rotating disk. When breaking condition is satisfied, shock waves form and propagate driven by the centrifugal and external shearing forces. The disjoining pressure due to van der Waals force provides diffusion to the system. The surface waves are planarized by the centrifugal force, external shearing force and the disjoining pressure.

Experimental observation of surface wave propagation for a transversely isotropic medium

Geophysics ◽  
1995 ◽  
Vol 60 (1) ◽  
pp. 185-190 ◽  
Author(s):  
Chih‐Hsiung Chang ◽  
Gerald H. F. Gardner ◽  
John A. McDonald
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Surface Waves ◽  
Transversely Isotropic ◽  
Insulation Material ◽  
Velocity Anisotropy ◽  
Vertical Seismic Profiling ◽  
Surface Wave Propagation ◽  
Transversely Isotropic Media ◽  
Isotropic Media

Velocity anisotropy of surface‐wave propagation in a transversely isotropic solid has been observed in a laboratory study. In this study, Phenolite™, an electrical insulation material, was used as the transversely isotropic media (TIM), and a vertical seismic profiling (VSP) geometry was used to record seismic arrivals and to separate surface waves from shear waves. Results show that surface waves that propagate with different velocities exist at certain directions.

Wave propagation in transversely isotropic elastic media - II. Surface waves

1989 ◽  
Vol 422 (1862) ◽  
pp. 67-101 ◽  
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Surface Waves ◽  
Plane Waves ◽  
Transversely Isotropic ◽  
Theoretical Background ◽  
Clear Understanding ◽  
Elastic Media ◽  
Surface Wave Propagation ◽  
Anisotropic Elastic

The treatment of homogeneous plane waves given in part I provides the basis for the detailed study of the nature of surface-wave propagation in transversely isotropic elastic media presented in this paper. The investigation is made within the framework of the existence theorem of Barnett and Lothe and the developments underlying its proof. The paper begins with a survey of this essential theoretical background, outlining in particular the formulation of the secular equation for surface waves in the real form F(v) = 0, F(v) being a nonlinear combination of definite integrals involving the acoustical tensor Q (⋅) and the associated tensor R (⋅,⋅) introduced in part I. The calculation of F(v) for a transversely isotropic elastic material is next undertaken, first, in principle, for an arbitrary orientation of the axis of symmetry, then for the α and β configurations, shown in part I to contain all the exceptional transonic states. In the rest of the paper the determination of F(v) is completed, in closed form, for the α and β configurations and followed in each case by a discussion of the properties of F(v) and illustrative numerical results. This combination of analysis and computation affords a clear understanding of surface-wave behaviour in the exceptional configurations comprising, in the classification of part I, cases 1, 2 and 3. The findings for case 1 exhibit continuous transitions, within the α configurations, between subsonic and supersonic surface-wave propagation. Those for case 3 prove that there are discrete orientations of the axis for which no genuine surface wave can propagate and that this degeneracy typically has a marked influence on surface-wave properties in a sizeable sector of neighbouring β configurations. Neither effect appears in previous accounts of surface-wave propagation in anisotropic elastic media.

Guided Surface Waves on an Elastic Half Space

1971 ◽  
Vol 38 (4) ◽  
pp. 899-905 ◽  
Author(s):  
L. B. Freund
Keyword(s):  
Wave Propagation ◽  
Surface Wave ◽  
Surface Waves ◽  
Half Space ◽  
Body Wave ◽  
Three Dimensional ◽  
Elastic Half Space ◽  
Normal Displacement ◽  
Rigid Barrier ◽  
Wave Disturbances

Three-dimensional wave propagation in an elastic half space is considered. The half space is traction free on half its boundary, while the remaining part of the boundary is free of shear traction and is constrained against normal displacement by a smooth, rigid barrier. A time-harmonic surface wave, traveling on the traction free part of the surface, is obliquely incident on the edge of the barrier. The amplitude and the phase of the resulting reflected surface wave are determined by means of Laplace transform methods and the Wiener-Hopf technique. Wave propagation in an elastic half space in contact with two rigid, smooth barriers is then considered. The barriers are arranged so that a strip on the surface of uniform width is traction free, which forms a wave guide for surface waves. Results of the surface wave reflection problem are then used to geometrically construct dispersion relations for the propagation of unattenuated guided surface waves in the guiding structure. The rate of decay of body wave disturbances, localized near the edges of the guide, is discussed.

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