Damping Of Water Waves Research Articles

Oblique water wave damping by two submerged thin vertical porous plates of different heights

Oblique water wave damping by two fully submerged vertical parallel porous plates of different heights is investigated within the framework of linear water wave theory. A channel of infinite horizontal extent but of finite depth is divided into three regions in each of which three different velocity potentials are considered and subsequently the corresponding boundary value problems are formulated. By means of eigenfunction expansion and least square method, complete analytical solution in each of the regions is obtained. With the help of the matching conditions along the vertical boundaries between any two successive regions, the reflection and transmission coefficients, and hence the energy loss (in %), are obtained numerically by applying a matrix method. Numerical study is carried out for various relevant parameters and it is found that with an appropriate choice of the parameters and positioning of the porous plates, both of the reflection and transmission coefficients become significantly low and consequently the porous plates can be utilized as an effecting wave absorber. Comparison of this work with earlier available work is made, and the good agreement in the results suggests the applicability of this method in further engineering purposes. A particular case of two free surface piercing plates is also investigated on similar line and the results are presented in order to observe the difference with the earlier case.

Wave damping by a vertical porous structure placed near and away from a rigid vertical wall

Damping of water waves by a vertical porous structure placed at some distance from a vertical wall is investigated within the framework of linear water wave theory. The rectangular porous structure is placed on a small rectangular elevation. An incident wave of small amplitude propagates through the structure – some portion gets reflected back while some portion gets transmitted to a third region bounded vertically by a rigid wall which is considered to be at a distance near the porous structure, and also away from the wall at a large distance as a separate case. Boundary value problems are set up in all three regions and, by using the matching conditions along the vertical boundaries, a system of linear equations is deduced. The roots of the relevant dispersion relation are used in setting up the system of equations. The overall scattering phenomenon is studied with respect to different relevant parameters. The dependence of the coefficients on the thickness (width) of the porous structure is investigated for different numbers of modes and porosity. It is observed that, except for the case when the porous structure is thin, the reflection and transmission coefficients give rise to values as expected. In the case, when the rigid wall is nearer to the structure, the reflection coefficient decreases rapidly for a thin structure and converges for all numbers of evanescent modes afterwards. The transmission coefficient also decreases as the width increases, ultimately converging and vanishing for a wide structure. When the wall is at a large distance away from the structure, the behavior of both the reflection and transmission coefficients remain the same. For both cases of the wall being nearer and away from the structure, higher porosity gives rise to lower reflection coefficients and higher transmission coefficients. However, the transmission coefficients converge and vanish when the porous structure is very wide. We also discuss the energy loss against the width of the porous structure for different values of number of modes and porosity. Irrespective of the positioning of the rigid wall, we observe that for higher values of porosity, energy loss is more pronounced when the structure is not thin, whereas energy loss is same for all numbers of modes. All our observations are supported by graphs. Good agreement of our result with earlier results justifies our model.

A note on the effect of surface contamination in water wave damping

Asymptotic formulas are derived for the effect of contamination on surface wave damping in a brimful circular cylinder; viscosity is assumed to be small and contamination is modelled through Marangoni elasticity with insoluble surfactant. It is seen that an appropriately chosen finite Marangoni elasticity provides an explanation for a significant amount of the unexplained additional damping rate in a well-known experiment by Henderson & Miles (1994); discrepancies are within 15%, significantly lower than those encountered by Henderson & Miles (1994) under the assumption of inextensible film.

Classification of sea slicks by multifrequency radar techniques: New chemical insights and their geophysical implications

Sea slick experiments with an airborne five‐frequency radar scatterometer were performed in the presence of surface active substances that represent different fractions of biogenic slicks (fats, amines, sugar derivatives, and fatty acids). Measurements at water temperatures of 282.2 K (9.0°C) and 290.6 K (17.4°C) showed that temperature effects appear to play a secondary role for slick‐induced water wave damping, at least in the temperature range encountered during the present experiments. Different procedures of slick generation, with and without application of a spreading solvent, indicated that the wave‐damping effect in the short‐gravity/capillary wave range, and thus the modification of backscattered radar signals, is not only dependent on the chemical structure but also on the arrangement and distribution (morphology; formation of domains) of the surface‐active compounds. Thus far this aspect, which appears to be of particular importance for biogenic sea slicks, has been completely ignored. External infrared reflection‐absorption spectroscopy laboratory measurements with infrared radiation in the wavelength range between 3.3 μm and 7 μm enabled us allowed to form a link between some important elements of the morphological structure of the monolayers and their viscoelastic characteristics, which are closely related to the wave‐damping effect of surface active compounds and to the compounds influence on remote sensing signals. Furthermore, the IRAS measurements supplied detailed insight into the relaxation process that occurs during the generation of a sea slick and on a slick‐covered undulating water surface. In particular, strong hydration/dehydration effects appear to play an important role.

The Effect of Rain in Calming the Sea

Abstract The effect of rain in damping surface waves appears to be significant in the estimation of wind speed from the backscatter of radar signal from the sea surface. The radar backscatter depends on the small-scale roughness of the sea surface. This is modified by the generation of capillary and gravity-capillary ripples by raindrops and by the increased damping of the wavelengths of 10-cm scale. The phenomenon is also important in wave generation and wave breaking, since in both cases the short wavelengths play a key role. A laboratory experiment has been performed to investigate the damping of water waves by rain in the absence of wind. Rain of intensity of 300 mm h−1 falls on mechanically generated progressive waves. The wave amplitude is measured before the wave enters and after it exits the rain section of a tank 2.35 m long. On the assumption of exponential damping, it is found that the effect of rain can be described by an eddy viscosity νE ≈ 0.3 cm2 s−1. The major part of the damping is attrib...

Damping of Water Waves Propagating over a Mud Bottom

Soft muddy bottoms have significant effects on damping coefficient of water waveswhich propagate over them. Model tests of wave damping are done for two different mudmaterials (kaolinite mud, bentonite mud) and these results are compared with thetheoretically predicted results. The theoretical damping rates determined by assuminga viscoelastic mud layer agree well with the rates obtained by experiments that kaoriniteis the bottom mud materials. In the case of bentonite mud, the predicted results byviscous fluid model agree well with experimental results.

Sideband damping of water waves over a soft bed

The Benjamin & Feir sideband instability of gravity waves over a rigid bed is extended here to the case of wave propagation over a compliant bed. The bed is assumed elastic with inhomogeneous properties, following some vertical stratification profile. The elastic stiffness at the mudline is assumed very small, as is typically the case for upper-stratum gel-like marine mud, so that its effect is assumed comparable in magnitude with that of wave nonlinearity. It is then shown that through the sideband instability, the carrier gravity wave would lose energy to sideband oscillations. These sidebands will be shown to be contaminated with small-amplitude, but very short elastic shear waves. These shear waves will interact with the viscous boundary layer at the bed-water interface, and thus significantly enhance the viscous damping of wave energy in the boundary layer.

Experiments on wave-soil interaction and wave-driven soil transport in clay beds

Wavelength and wave damping of water waves propagating over soft clay beds are measured in a soil-wave tank. Mudline motion and wave-induced mass transport in the clay beds are also measured. It is confirmed experimentally that the wave dispersion is uniquely governed by the mudline motion. Mass transport develops in a clay bed when shear strain amplitude exceeds the limit shear strain of about 5%. The rate of wave-induced mass transport in a clay bed is found to be proportional to the rate of wave energy dissipation in the clay bed. This paper presents a complete report of the measurements and data.

Relaxation effects in monolayers and their contribution to water wave damping: I. Wave-induced phase shifts

The newly developed experimental approach of measuring surface potential variations over propagating water waves cover with monolayers allows direct determination of phase angles θ between the hydrodynamic surface area variation and the surface film concentration (surface tension, surface potential) variation depending on the chemical structure and the relaxation behavior of the film molecules. These phase shift data and independently measured laboratory surface viscosity values determined by means of the canal method are used for calculating dilational modulus E values which turn out to be lower than E values obtained by classical Langmuir-trough measurements. As shown in Part II of this work (H. Hühnerfuss, P. A. Lange, and W. Walter, J. Colloid Interface Sci. 108, 442, 1985) these E values obtained under dynamic conditions are much more suitable for describing quantitatively the wave damping effects of monolayers.

Relaxation effects in monolayers and their contribution to water wave damping: II. The Marangoni phenomenon and gravity wave attenuation

The Marangoni wave theory is reviewed and extended to the short gravity water wave regime. This theoretical approach is verified by wave damping measurements in the Hamburg wind-wave tunnel performed in the presence of monomolecular hexadecanoic acid methyl ester, (Z)-9-octadecen-1-ol, and hexadecyltrimethylammonium bromide surface films. A good agreement of the theoretical with the experimental results is obtained, when performing the calculations with the help of dilational modulus and phase angle values, which were obtained from dynamic surface potential measurements over a wavy water surface (H. Hühnerfuss, P. A. Lange, and W. Walter, J. Colloid Interface Sci. 108, 430, 1985). Dilational modulus values determined by classical Langmuir-trough measurements are not suitable for determining wave damping ratios and give rise to too large values.

A Laboratory Experimentation on the Interactions Between Water Waves and Soft Clay Beds

Wave tank experiments are conducted to measure the wave damping of water waves propagating in a constant water overlaying an underconsolidated clay bed. It is found that water waves attenuate at a ...

On the response of a Coulomb‐damped poroelastic bed to water waves

Abstract The problem of forced vibration of a slightly inelastic porous bed by water waves is treated analytically on the basis of a linearized expression of the nonlinear damping term for the grain‐to‐grain friction in bed soils and the linear theory by Biot (1962a [Jour. Appl. Physics, 33:1482–1498]) on the elastic wave propagation in porous media. A dispersion relation of water waves is obtained as a function of wave frequency, water depth, permeability, Poisson's ratio, rigidity, and specific loss of bed soil. Three types of elastic waves are induced in a bed by water waves: a shear wave and a compressional wave in the skeletal frame of soil, and a compressional wave in the pore fluid. The compressional wave, due to the motion of the pore fluid relative to the skeletal frame of soil, is highly damped by the viscosity of pore fluid and only a short range effect near the boundaries of discontinuity, such as a sea‐seabed interface. The seabed response to water waves is characterized by the two Mach numbers, i.e., the ratio of water‐wave speed to shear‐wave speed in soil and the ratio of water‐wave speed to compressional‐wave speed in soil. Most of the water‐wave propagation problems fall into the subsonic flow condition, where elastic waves in the bed travel faster than water waves. For sandy beds, generally the speeds of compressional and shear waves are much higher than the phase velocity of the water wave. For this case, the solution of the Coulomb‐damped poroelastic bed response presented in this paper approaches the solution of the massless poroelastic bed response in Yamamoto et al. (1978 [Jour. Fluid Mech., 87(1): 193–206]). The damping of water waves due to internal grain‐to‐grain friction is equally or more significant than the damping due to percolation in sand beds. For clay beds, the speed of the shear wave in soil becomes low and comparable to the phase speed of the water wave. The bed motion for this case is considerably amplified due to the near‐resonance vibration of shear mode of bed vibration. The water wavelength on a clay bed is significantly shortened compared to the water wavelength over a rigid bed. The water wave damping due to internal grain‐to‐grain friction in soil becomes much larger compared to the water wave damping due to percolation in clay beds. Long water waves over a soft clayey bed attenuate within several wavelengths of travel distance.

Non-linear mechanics of ocean wave interactions with sediment beds

The dispersion and attenuation of ocean wave spectra propagating over sloped poro-elastic beds with non-linear Coulomb internal damping are calculated using Biot's poro-elastic theory. Elastic properties and Coulomb dampings of sediments are functions of horizontal and vertical coordinates as well as the energy levels of wave spectra. The response of a seabed to water waves is characterized by a Mach number which is the ratio of the propagation velocity of the water wave to the local shear wave velocity. When the shear Mach number is small, as in sandy beds, the bed response is quasistatic and wave damping due to Coulomb internal damping in the soil is relatively small. When the shear Mach number approaches one, such as in normally consolidated clay, the bed motion is amplified dynamically, and the water wave damping due to the Coulomb internal friction becomes large compared to the damping owing to a turbulent boundary layer. The damping of water waves is very sensitive to wave height or wave energy level in this bed condition. Large waves damp out rapidly while small waves damp slowly. The shear Mach number becomes much larger than one in a very soft mud, which behaves as something like a ‘fluid’ with a Coulomb friction owing to the dynamic softening effect of clay under a large shear deformation. The wave damping becomes nearly independent of wave height or wave energy level in this bed condition. Soil-wave tank experiments substantiate the theoretical findings.

The effect of large grooves on the damping of water waves

Damping of water waves in a wave tank with a grooved base has been studied both theoretically and experimentally. It is shown that, for grooves of triangular or approximately sinusoidal cross-section, the damping is increased by an amount proportional to the total surface area of the grooved surface, and is independent of the direction of flow with respect to the grooves. The theoretical model applies when the groove spacing is small compared to the fluid depth and wavelength of the waves, but is large compared to the viscous boundary layer thickness. By carrying out observations in two surface modes, it is shown that the observed increased damping is caused by the grooved surface alone and cannot be attributed to spurious surfactant effects.

Damping of water waves in containers with roughened surfaces

Both roughened container walls and surfactant layers on air-water interfaces can increase the damping of surface waves on shallow water. An experimental technique is described to enable the relative importance of these two effects to be determined unambiguously. It is found that the roughness of the container walls makes only a minor contribution to variations in the damping of shallow water waves.

Closure to “Damping of Water Waves Over Porous Bed”

Closure to “Damping of Water Waves Over Porous Bed”

Closure to “Damping of Water Waves Over Porous Bed”

Closure to “Damping of Water Waves Over Porous Bed”

Discussion of “Damping of Water Waves over Porous Bed”

Discussion of “Damping of Water Waves over Porous Bed”

Erratum for “Damping of Water Waves over Porous Bed”

Erratum for “Damping of Water Waves over Porous Bed”

On the damping of water waves by monomolecular films : Goodrich, F. C. 1962. J. phys. chem. 66(10): 1858–1863

On the damping of water waves by monomolecular films : Goodrich, F. C. 1962. J. phys. chem. 66(10): 1858–1863