Note on Bragg scattering of water waves by parallel bars on the seabed

1988 ◽  
Vol 186 ◽  
pp. 147-162 ◽  
Author(s):  
Chiang C. Mei ◽  
Tetsu Hara ◽  
Mamoun Naciri
Keyword(s):  
Surface Waves ◽  
Water Waves ◽  
Oblique Incidence ◽  
Recent Theory ◽  
Bragg Scattering

A recent theory of Bragg scattering of surface waves by sinusoidal sandbars on a seabed is applied to three cases not examined heretofore: (1) oblique incidence on a strip of infinitely long bars, (2) oblique incidence on the corner of a bar field and (3) seabed with a mean slope. While the Bragg mechanism has been studied previously for sandbars present on many shorelines, it can be a basis for breakwaters where the soil is not strong enough to support a single massive breakwater.

DISPERSION IN SEISMIC SURFACE WAVES

Geophysics ◽  
1951 ◽  
Vol 16 (1) ◽  
pp. 63-80 ◽  
Author(s):  
Milton B. Dobrin
Keyword(s):  
Surface Waves ◽  
Water Waves ◽  
Seismic Refraction ◽  
Wave Theory ◽  
Wave Dispersion ◽  
Surface Zone ◽  
Surface Wave Dispersion ◽  
Near Surface ◽  
Arrival Times ◽  
Ground Roll

A non‐mathematical summary is presented of the published theories and observations on dispersion, i.e., variation of velocity with frequency, in surface waves from earthquakes and in waterborne waves from shallow‐water explosions. Two further instances are cited in which dispersion theory has been used in analyzing seismic data. In the seismic refraction survey of Bikini Atoll, information on the first 400 feet of sediments below the lagoon bottom could not be obtained from ground wave first arrival times because shot‐detector distances were too great. Dispersion in the water waves, however, gave data on speed variations in the bottom sediments which made possible inferences on the recent geological history of the atoll. Recent systematic observations on ground roll from explosions in shot holes have shown dispersion in the surface waves which is similar in many ways to that observed in Rayleigh waves from distant earthquakes. Classical wave theory attributes Rayleigh wave dispersion to the modification of the waves by a surface layer. In the case of earthquakes, this layer is the earth’s crust. In the case of waves from shot‐holes, it is the low‐speed weathered zone. A comparison of observed ground roll dispersion with theory shows qualitative agreement, but it brings out discrepancies attributable to the fact that neither the theory for liquids nor for conventional solids applies exactly to unconsolidated near‐surface rocks. Additional experimental and theoretical study of this type of surface wave dispersion may provide useful information on the properties of the surface zone and add to our knowledge of the mechanism by which ground roll is generated in seismic shooting.

An application of Miles' theory to Bragg scattering of water waves by doubly composite artificial bars

2006 ◽  
Vol 33 (3-4) ◽  
pp. 331-349 ◽  
Author(s):  
Swun-Kwang Wang ◽  
Tai-Wen Hsu ◽  
Li-Hung Tsai ◽  
Sheng-Hung Chen
Keyword(s):  
Water Waves ◽  
Bragg Scattering

Asynchronous whirl in a rotating cylinder partially filled with liquid

1985 ◽  
Vol 150 ◽  
pp. 311-327 ◽  
Author(s):  
A. S. Berman ◽  
T. S. Lundgren ◽  
A. Cheng
Keyword(s):  
Surface Waves ◽  
Shallow Water ◽  
Solitary Waves ◽  
Water Waves ◽  
Rotating Cylinder ◽  
The Self ◽  
Hydraulic Jumps ◽  
Centrifugal Forces ◽  
Shallow Water Waves ◽  
Analytical Results

Experimental and analytical results are presented for the self-excited oscillations that occur in a partially filled centrifuge when centrifugal forces interact with shallow-water waves. Periodic and aperiodic modulations of the basic whirl phenomena are both observed and calculated. The surface waves are found to be hydraulic jumps, undular bores or solitary waves.

Wind-generated gravity-capillary waves: laboratory measurements of temporal growth rates using microwave backscatter

1975 ◽  
Vol 70 (3) ◽  
pp. 417-436 ◽  
Author(s):  
T. R. Larson ◽  
J. W. Wright
Keyword(s):  
Growth Rates ◽  
Water Waves ◽  
Friction Velocity ◽  
Capillary Waves ◽  
Spectral Amplitude ◽  
Bragg Scattering ◽  
Laboratory Measurements ◽  
Wind Speeds ◽  
Tightly Coupled ◽  
Microwave Backscatter

The growth rates of wind-induced water waves at fixed fetch were measured in a laboratory wave tank using microwave backscatter. The technique strongly filters out all wavenumber component pairs except for a narrow window at the resonant Bragg scattering conditions. For these waves the spectral amplitude was measured as a function of the time after a fixed wind was abruptly started. The radars were aligned to respond to waves travelling in the downwind direction at wavelengths of 0·7-7 cm. Wind speeds ranged from 0·5 to 15 m/s. Fetches of 1·0, 3·0 and 8·4 m were used. In every case, the spectral amplitude initially grew at a single exponential rate β over several orders of magnitude, and then abruptly ceased growing. No dependence of the growth rate on fetch was observed. For all wavelengths and wind speeds the data can be fitted by \[ \beta (k,u_{*},{\rm fetch})=f(k)\,u^n_{*}, \] with n = 1·484 ± 0·027. Here u* is the friction velocity obtained from vertical profiles of mean horizontal velocity. For each wind speed, f(k) had a relative maximum near k = kn ≃ 3·6 cm−1. Rough estimates of β/2ω, where ω is the water wave frequency, and of the wind stress supported by short waves indicate that the observed growth rates are qualitatively very large. These waves are tightly coupled to the wind, and play a significant role in the transfer of momentum from wind to water.

scholarly journals A Mild-Slope System for Bragg Scattering of Water Waves by Sinusoidal Bathymetry in the Presence of Vertically Sheared Currents

2019 ◽  
Vol 7 (1) ◽  
pp. 9 ◽  
Author(s):  
Kostas Belibassakis ◽  
Julien Touboul ◽  
Elodie Laffitte ◽  
Vincent Rey
Keyword(s):  
Resonant Frequency ◽  
Water Waves ◽  
Bottom Topography ◽  
Wave System ◽  
Bragg Scattering ◽  
Wave Flume ◽  
Seabed Topography ◽  
Incident Waves ◽  
Slope System ◽  
A Current

Extended mild-slope models (MMSs) are examined for predicting the characteristics of normally incident waves propagating over sinusoidal bottom topography in the presence of opposing shearing currents. It is shown that MMSs are able to provide quite good predictions in the case of Bragg scattering of waves over rippled bathymetry without a current, but fail to provide good predictions concerning the resonant frequency in the additional presence of a current. In order to resolve the above mismatch, a two-equation mild-slope system (CMS2) is derived from a variational principle based on the representation of the wave potential expressed as a superposition of the forward and backward components. The latter system is compared against experimentally measured data collected in a wave flume and is shown to provide more accurate predictions concerning both the resonant frequency and the amplitude of the reflection coefficient. Future work will be devoted to the examination of the derived model for a more general wave system over realistic seabed topography.

Reflection of water waves in a channel with corrugated bed

1987 ◽  
Vol 185 ◽  
pp. 249-274 ◽  
Author(s):  
T. Brooke Benjamin ◽  
B. Boczar-Karakiewicz ◽  
W. G. Pritchard
Keyword(s):  
Experimental Study ◽  
Surface Waves ◽  
Water Waves ◽  
Bragg Reflection ◽  
Water Channel ◽  
Sand Bars ◽  
Multiple Processes ◽  
Linearized Theory ◽  
Coastal Sand ◽  
Frictional Effects

Intended as a contribution towards understanding the multiple processes entailed in the development of coastal sand bars due to wave action, this theoretical and experimental study deals with the Bragg reflection of long-crested surface waves in a water channel whose bed is corrugated sinusoidally. The present findings complement and in a few respects improve upon those in previous investigations, particularly Davies & Heathershaw (1984).In §2 a linearized theory is presented, being directed to the elucidation of experimental situations where monochromatic waves propagate into a channel with a limited stretch of corrugations on its bed and an imperfectly absorbing beach at its far end. Allowance is made fully for dispersive effects (§2.2) and approximately for small frictional effects (§2.3). Points of interpretation (§2.4) include accounts of degenerate but non-trivial solutions that apply at frequencies terminating the stopping band, wherein the spatial wavefield has an exponential envelope. The experimental results presented in §4 derive from measurements of the wavefield over a stretch of 24 corrugations, at various frequencies both inside and outside the stopping band. Quantitative comparisons (§4.2 and 4.3) demonstrate close agreements with the theory.

scholarly journals Nonlinear long waves over a muddy beach

2013 ◽  
Vol 718 ◽  
pp. 371-397 ◽  
Author(s):  
Erell-Isis Garnier ◽  
Zhenhua Huang ◽  
Chiang C. Mei
Keyword(s):  
Boundary Layer ◽  
Thin Layer ◽  
Surface Waves ◽  
Nonlinear Waves ◽  
Water Waves ◽  
Long Waves ◽  
Fluid Mud ◽  
Weakly Nonlinear ◽  
Sea Bottom ◽  
Oscillatory Boundary Layer

AbstractWe analyse theoretically the interaction between water waves and a thin layer of fluid mud on a sloping seabed. Under the assumption of long waves in shallow water, weakly nonlinear and dispersive effects in water are considered. The fluid mud is modelled as a thin layer of viscoelastic continuum. Using the constitutive coefficients of mud samples from two field sites, we examine the interaction of nonlinear waves and the mud motion. The effects of attenuation on harmonic evolution of surface waves are compared for two types of mud with distinct rheological properties. In general mud dissipation is found to damp out surface waves before they reach the shore, as is known in past observations. Similar to the Eulerian current in an oscillatory boundary layer in a Newtonian fluid, a mean displacement in mud is predicted which may lead to local rise of the sea bottom.

A depth-resolved framework for the coupling of sub-surface flows and surface gravity water waves

2020 ◽  
Author(s):  
Simen Ådnøy Ellingsen ◽  
Stefan Weichert ◽  
Yan Li
Keyword(s):  
Surface Waves ◽  
Water Waves ◽  
Multiple Scales ◽  
Subsurface Flow ◽  
Vertical Gradient ◽  
Finite Depth ◽  
Surface Gravity ◽  
Linear Wave ◽  
Flow Equations ◽  
Direct Integration Method

<p>This work aims to develop a new framework for the interaction of a subsurface flow and surface gravity water waves, based on a perturbation and multiple-scales expansion.  Surface waves are assumed of a narrow band δ (δ ), indicating they can be expressed as a carrier wave whose amplitude varies slowly in space and time relative to its phase. Using the Direct Integration Method proposed in Li & Ellingsen (2019), the effects of the vertical gradient of a subsurface flow are taken into account on the linear wave properties in an implicit fashion. At the second order in wave steepness ϵ, the forcing of the sub-harmonic bound waves is considered that plays a role in the primary equations for a subsurface flow.</p><p>The novel framework derives the continuity and momentum equations for a subsurface flow in two different formats, including both the depth integrated as well as the depth resolved version. The former compares with Smith (2006) to examine the roles of the rotationality of wave motions in the subsurface flow equations. The latter employs the sigma coordinate system proposed in Mellor (2003, 2008, 2015) and extends the framework therein to allow for quasi-monochromatic surface waves and the effects of the shear of a current on linear surface waves. Compared to Mellor (2003, 2008, 2015), the vertical flux/vertical radiation stress term in the proposed framework is approximated to one order of magnitude higher, i.e. O(ϵ<sup>2</sup>δ<sup>2</sup>).</p><p><strong>References</strong></p><p>Li, Y., Ellingsen, S. Å. A framework for modeling linear surface waves on shear currents in slowly varying waters. J. Geophys. Res. C: Oceans, (2019) <strong>124</strong>(4), 2527-2545.</p><p>Mellor, G. L. The three-dimensional current and surface wave equations. J. Phys. Oceanogr., (2003) <strong>33</strong>, 1978–1989.</p><p>Mellor, G. L. The depth-dependent current and wave interaction equations: a revision. J. Phys. Oceanogr., (2008) <strong>38</strong>(11), 2587-2596.</p><p>Smith, J. A. Wave–current interactions in finite depth. Journal of Physical Oceanography, (2006) <strong>36</strong>(7), 1403-1419.</p>

An explicit Hamiltonian formulation of surface waves in water of finite depth

1992 ◽  
Vol 237 ◽  
pp. 435-455 ◽  
Author(s):  
A. C. Radder
Keyword(s):  
Surface Waves ◽  
Water Waves ◽  
Hamiltonian Formulation ◽  
Vertical Plane ◽  
Finite Depth ◽  
Short Wave ◽  
Linear Dispersion ◽  
Energy Functionals ◽  
Canonical Variables ◽  
Wave Nonlinearity

A variational formulation of water waves is developed, based on the Hamiltonian theory of surface waves. An exact and unified description of the two-dimensional problem in the vertical plane is obtained in the form of a Hamiltonian functional, expressed in terms of surface quantities as canonical variables. The stability of the corresponding canonical equations can be ensured by using positive definite approximate energy functionals. While preserving full linear dispersion, the method distinguishes between short-wave nonlinearity, allowing the description of Stokes waves in deep water, and long-wave nonlinearity, applying to long waves in shallow water. Both types of nonlinearity are found necessary to describe accurately large-amplitude solitary waves.

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