Ratio Of Wave Height Research Articles

Breaking solitary wave evolution over a porous underwater step

Solitary wave evolution over a shelf including porous damping is investigated using Volume-Averaged Reynolds Averaged Navier–Stokes equations. Porous media induced damping is determined based on empirical formulations for relevant parameters, and numerical results are compared with experimental information available in the literature. The aim of this work is to investigate the effect of wave damping on soliton disintegration and evolution along the step for both breaking and non-breaking solitary waves. The influence of several parameters such as geometrical configuration (step height and still water level), porous media properties (porosity and nominal diameter) or solitary wave characteristics (wave height) is analyzed. Numerical simulations show the porous bed induced wave damping is able to modify wave evolution along the step. Step height is observed as a relevant parameter to influence wave evolution. Depth ratio upstream and downstream of the edge appears to be the more relevant parameter in the transmission and reflection coefficients than porosity or the ratio of wave height–water depth. Porous step also modifies the fission and the solitary wave disintegration process although the number of solitons is observed to be the same in both porous and impermeable steps. In the absence of breaking, porous bed triggers a faster fission of the incident wave into a second and a third soliton, and the leading and the second soliton reduces their amplitude while propagating. This decrement is observed to increase with porosity. Moreover, the second soliton is released before on an impermeable step. Breaking process is observed to dominate over the wave dissipation at the porous bottom. Fission is first produced on a porous bed revealing a clear influence of the bottom characteristics on the soliton generation. The amplitude of the second and third solitons is very similar in both impermeable and porous steps but they evolved differently due to the effect of bed damping.

Surface wave growth characteristics of the high speed liquid Li flow

The present paper reports on characteristics of surface waves on a liquid lithium jet for the International Fusion Materials Irradiation Facility (IFMIF). Surface waves at locations of 15 and 175 mm from the nozzle exit were examined experimentally, to see an influence of the initial growth of surface waves. Experiments were carried out using the lithium circulation loop at Osaka University. Surface fluctuations were measured using an electrical scanning probe across the Li surface. From the contact signal, wave height distributions of surface waves were obtained. Three statistical wave heights to represent characteristics of the wave height distribution were calculated, and the wave height ratios of three statistical meanings were examined. Characteristics of the wave height distributions at locations 15 and 175 mm were examined by comparing with the Rayleigh distribution.

Open-Ocean Barrier Islands: Global Influence of Climatic, Oceanographic, and Depositional Settings

A satellite-based inventory of barrier islands was used to study the influence of depositional setting, climate, and tide regime on island distribution and morphology. The survey reveals 20,783 km of shoreline occupied by 2149 barrier islands worldwide. Their distribution is strongly related to sea level history in addition to the influence of tectonic setting. Rising sea level in the late Holocene (5000 YBP–present) is associated with greatest island abundance, especially on North Atlantic and Arctic coastal plains. Stable or falling sea level in the same time frame, a pattern typical of the Southern Hemisphere, is associated with a lower abundance of islands and a higher percentage of islands along deltas rather than coastal plains. Both coastal plain and deltaic island morphology are sensitive to the wave–tide regime; however, island length is 40% greater along coastal plains whereas inlet width is 40% greater on deltas. Island morphology is also fundamentally affected by climate. Island lengths in the Arctic are on average (5 km) only half the global average (10 km) because of the effect of sea ice on fetch and thus wave energy. Storm frequency in the high and middle latitudes is suggested to result in shorter and narrower islands relative to those on swell-dominated low-latitude coasts. The ratio of storm wave height to annual mean wave height is a good indicator of the degree of storm influence on island evolution. The potential for significant climate and sea level change this century underscores the need to improve understanding of the fundamental roles that these two factors have played historically in island evolution in order to predict their future impacts on the islands.

SPECTRAL WAVE MODELLING IN TIDAL INLET SEAS: RESULTS FROM THE SBW WADDEN SEA PROJECT

Over the last five years a research program has been carried out to assess the performance of the spectral wave model SWAN in the Wadden Sea so that it may be used for the transformation of offshore wave conditions to wave boundary conditions near the sea defenses (dikes and dunes). The assessment was done on the basis of extensive wave measurements conducted in Ameland inlet and the Dutch Eastern Wadden Sea, as well as relevant data from lakes and estuaries. After a first round of assessment, we found that SWAN performed reasonably well for storm conditions but three aspects required further attention. Firstly, focusing on the main channel, SWAN formulations needed to be modified in order to eliminate overprediction of the significant wave height in opposing currents. Secondly, the primary spectral peak of North Sea waves penetrating into the inlet was underpredicted. Best results were obtained when the refraction of low-frequency waves was limited and the bottom friction coefficient was set at a lower value than the current default for wind seas. Thirdly, over the tidal flats the computed ratio of integral wave height over water depth showed an apparent upper limit using the conventional Battjes and Janssen (1978) depth-limited wave breaking formulation, because the wave growth over finite depth is hampered by the present formulation of depth-induced wave breaking. The problem has been solved using a new breaker formulation. All these improvements have lead to a wave transformation model with which reliable wave conditions in the Wadden Sea and related complex areas can be determined.

Freak waves of different types in the coastal zone of the Baltic Sea

Abstract. We present a statistical analysis of freak waves1 measured during the 203 h of observation on sea surface elevation at a location in the coastal zone of the Baltic Sea (2.7 m depth) during June–July 2008. The dataset contains 97 freak waves occurring in both calm and stormy weather conditions. All of the freak waves are solitary waves, 63% of them having positive shape, 17.5% negative shape and 19.5% sign-variable shape. It is suggested that the freak waves can be divided into two groups. Those of the first group, which includes 92% of the freak waves, have an amplification factor (ratio of freak wave height to significant wave height) which does not vary from significant wave height and has values largely within the range of 2.0 to 2.4; while for the second group, which contain the most extreme freak waves, amplification factors depend strongly on significant wave height and can reach 3.1. Analysis based on the Generalised Pareto distribution is used to describe the waves of the first group and lends weight to the identification of the two groups. It is suggested that the probable mechanism of the generation of freak waves in the second group is dispersive focussing. The time-frequency spectra of the freak waves are studied and dispersive tracks, which can be interpreted as dispersive focussing, are demonstrated. 1 taken to be waves whose height is 2 or more times greater than the significant wave height

Numerical investigation of the interactions between solitary waves and pile breakwaters using BGK-based methods

The interactions between a solitary wave, which can be used to model a leading tsunami wave, and a pile breakwater made of circular cylinders are numerically investigated. We use the depth-averaged shallow water equations, which are solved by the finite volume method based on the Bhatnagar–Gross–Krook (BGK) model. The numerical results are compared with the experimental data, which yields very good agreement between them when the ratio of wave height to water depth is small (<0.25). As this ratio exceeds the value of 0.25, the larger the ratio is, the bigger deviation of numerical results from experimental data is observed, the possible reasons for this observation are discussed. Both numerical and experimental results indicate that the transmission of the solitary wave decreases and the reflection of the wave increases with reducing gaps between the adjacent cylinders, and that both transmission and reflection coefficients are not very sensitive to the variation in wave height.

Surf zone physical and morphological regime as determinants of temporal and spatial variation in larval recruitment

Larvae of intertidal species develop in the coastal ocean, and the last body of water they must cross while migrating back to shore is the surf zone. We hypothesized that the surf zone is a semipermeable barrier to this shoreward migration and that differences in water exchange across the surf zone result in temporal and spatial variation in larval delivery to the shore. We tested the hypotheses that larval delivery 1) should increase with larger waves and 2) should be higher on more dissipative beaches than on more reflective beaches. We found a significant positive correlation between the daily averaged ratio of wave height to wave period ( H/ T) and daily cyprid settlement at Dike Rock, California and Bastendorff Beach, Oregon, USA. We tested the second hypothesis by comparing populations of barnacles, limpets, and benthic algae on rocks on four more dissipative and six more reflective sandy beaches in northern California and southern Oregon. Newly recruited barnacles and limpets were significantly more abundant at more dissipative than reflective beaches, and the higher abundance was most likely due to differences in settlement rather than post-settlement mortality. The density and percent cover of barnacles and the density of limpets were significantly higher at more dissipative beaches. In contrast, the density and percent cover of algae were significantly higher at more reflective beaches. The results are consistent with the hypothesis that the surf zone is a semipermeable barrier to the shoreward migration of larvae and that differences in water exchange across the surf zone as function of the beach hydrodynamics result in temporal and spatial variation in larval delivery to the shore.

Wave Attenuation across an Intertidal Sand Flat: Implications for Mudflat Development

Abstract On many tidal flats, there is a transition from sand flat at the more energetic seaward margin to mudflat further inland. However, the ability of sand flats to attenuate incident wave energy is an important but poorly understood constraint on mudflat development and morphology. This paper presents the results of an instrumented field study of incident wave attenuation across Roberts Bank, the sandy intertidal portion of the Fraser River Delta. The attenuation of wave height was monitored at four stations along a shore-normal transect for a period of 2 months (December 23, 2003, to February 10, 2004). The attenuation varied with the relative wave height ratio (Hs h−1) along the seaward margin, with dissipation increasing as water depths decrease and/or incident wave heights increase. Under the most dissipative conditions observed (Hs h−1 ≈ 0.25), the exponential decay coefficient reached 0.00045. This decay coefficient is an order of magnitude smaller than predicted by a simple wave transformation...

Reanalysis of Regular and Random Breaking Wave Statistics

Statistics of breaking waves across the surf zone are reanalyzed on the basis of various sets of field and laboratory data so as to provide coastal engineers with reliable information on breaking waves. The breaker index or the ratio of wave height to water depth is to be expressed as a function of the two parameters of beach slope and relative depth, and Goda's breaker index formula is slightly to reduce the slope effect. The breaker index for regular waves has inherent variability as expressed with the coefficient of variability, which increases from 6% to 14% as the beach slope becomes steep up to 1/10. The incipient breaking height of the significant wave is about 30% lower than that of regular waves, but the ratio of significant wave height to water depth gradually increases within the surf zone toward the shoreline. The wave height distribution is the narrowest in the middle of the surf zone, but it returns to the Rayleigh distribution near the shoreline owing to wave regeneration after breaking. The nonlinearity of random waves is strongest at the outer edge of the surf zone, but it is destroyed by the wave breaking process inside the surf zone. The ratios of statistical wave heights H 1/10, H 1/3 and H rms to the spectral significant wave height H m0 are shown to increase as the wave nonlinearity parameter increases up to the outer edge of the surf zone.

Boundary element modelling of wave diffraction by interaction with wave-offshore structure and dredged region

Boundary element modelling of wave diffraction by interaction with wave-offshore structure and dredged region The purpose of this study is to estimate the wave height at the front face of breakwater (Refracted breakwater and Straight breakwater), when dredging like the submarine pit is performed in the distant offshore from outer breakwater. The wave field of the problem is considered to be two dimensional planes and the configuration of the pit region is designated by a single horizontal long-rectangular system. The numerical approach uses the Green function based on the boundary integral approach. The results of the present numerical works are illustrated by applying the normal and inclined incidence. It is shown that in the case of normal incidence, the ratio of wave height reduction at the front face of both types of breakwaters is approximately more than 20% due to the effect of the submarine pit on the sea bed. Furthermore, regardless of the type of breakwater and the difference in incident wave angles, the ratio of wave height was shown to be reduced.

Numerical investigation of fluid resonance in two narrow gaps of three identical rectangular structures

In this study, the fluid resonance in two narrow gaps between three identical fixed rectangular structures subjected to incident waves normal to the narrow gaps are investigated employing a two-dimensional numerical wave flume. The numerical wave flume is based on the finite element solution of Navier–Stokes equations to account for the viscous dissipation. The free surface is captured using the CLEAR-Volume of Fluid (CLEAR-VOF) method. The water waves are generated using an internal wave maker which is located at a certain distance upstream from the structures. Wave absorption is achieved by two numerical sponge layers located at the upstream and downstream ends of the numerical wave flume. Numerical results of wave height variation in the narrow gaps with incident wave frequency are found to agree well with the available experimental data. It is found that the maximum resonant wave height in the narrow gaps is about as high as four times of the incident wave height. Moreover, the fluid resonance is observed to occur at two distinct frequencies in both of the narrow gaps. The ratio of incident wave height to the wave height in the narrow gaps is found to be proportional to the ratio of the maximum vertical particle velocity of incident waves at the still water level to the average amplitude of vertical velocity in the narrow gaps. It is also observed that the maximum wave height in front of the upstream structure decreases greatly in the band of resonant frequencies. The numerical investigation in this work shows that the horizontal forces on the three structures are closely correlated to water level difference between the opposite sides of the structure in the region far from the resonant frequencies, while the wave/structure interactions play an important role in the band of resonant frequencies. It is also found that the total vertical force, with rather limited oscillation amplitudes, is dominated by the static buoyancy.

Steep wave, turbulence, and sediment concentration statistics beneath a breaking wave field and their implications for sediment transport

A new methodology based on wavelet analysis is used to estimate steep wave statistics under depth-limited conditions and the corresponding high concentration sediment statistics. Steep waves here are defined as wave crests within the wavelet transform exceeding a root mean square derived acceleration threshold. The method is applied to laboratory data obtained in a large-scale wave-flume experiment conducted in 2005 at Oregon State University's O. H. Hinsdale Wave Research Laboratory from an acoustic Doppler velocimeter and a fiber optic backscatter sensor array above a mobile sand bed. The steep wave and high concentration statistical results for the erosive condition suggest that sand suspensions are intermittent when a wave-breaking timescale (the ratio of breaking wave height and rms wave velocity) is used to detect the concurrence among steep wave, high velocity turbulent fluctuations, and sand concentration events near the bed. More importantly, at 1 cm above the bed, though the accretive case has more steep wave events, the erosive case has more steep waves and concurrent high concentration events, suggesting a more intense breaking wave process near the sensors. The use of a longer time window, based on the dominant wave period in the detection process of steep wave and high concentration events at 1 cm above the bed, does not change the resulting statistics for the erosive condition. However, increased percentages of high concentration events correlated with steep wave and high velocity turbulence events for the accretive condition are obtained. These increased percentages are conjectured to be due to advection of non-local turbulent events and sediment concentration peaks from upstream. A one-dimensional vertical two-phase model for sand transport is modified here to take measured breaking wave turbulence quantities as top boundary conditions to simulate the effect of breaking wave-turbulence on bottom sediment transport. Model results suggest that high intensity turbulence accompany breaking waves can enhance net transport by 50–150%. However, the direction of the enhanced transport is determined by the relative timing between the high intensity turbulent fluctuations and wave velocity phase. Statistical analysis of measured data suggest that about 2/3 of the wave turbulence maxima that exceed the root mean square derived velocity threshold are negatively correlated with the wave velocity. If these maxima can be taken as due to breaking wave events, these results suggest that breaking wave-turbulence tends to enhance offshore sand transport. Model results of net transport rate show consistency with these results for the measured erosive condition in that net transport is offshore directed.

Hurricane Response of Nearshore Borrow Pits from Airborne Bathymetric Lidar

Airborne bathymetric lidar surveys taken in Florida before and after the severe 2004 and 2005 hurricane seasons show infilling of seventeen dredged nearshore borrow pits. During these seasons, groups of pits captured volumes that were the equivalent of up to four years of net longshore transport, even though only one of the seventeen pits studied was inside the presumed depth of closure. Unsurprisingly, dimensionless infilling increased strongly with the ratio of wave height to pit depth. For open coast pits with large alongshore lengths, cross-shore infilling appeared to dominate over longshore infilling but both processes may be of comparable importance in shorter pits. Infilling of three borrow pits adjacent to ebb shoals was found to be considerably larger than on open coasts. Bathymetric changes in borrow pits occurred at greater depths than on nearby undisturbed profiles. Crude estimates of the long term infilling rates from tropical cyclones indicate that annual infilling volumes may be equivalent to more than one quarter of the expected net longshore transport at some locations. However, the episodic nature of hurricanes means that infilling events will be highly irregular.

Particle motion in unsteady two-dimensional peristaltic flow with application to the ureter

Particle motion in an unsteady peristaltic fluid flow is analyzed. The fluid is incompressible and Newtonian in a two-dimensional planar geometry. A perturbation method based on a small ratio of wave height to wavelength is used to obtain a closed-form solution for the fluid velocity field. This analytical solution is used in conjunction with an equation of motion for a small rigid sphere in nonuniform flow taking Stokes drag, virtual mass, Faxén, Basset, and gravity forces into account. Fluid streamlines and velocity profiles are calculated. Theoretical values for pumping rates are compared with available experimental data. An application to ureteral peristaltic flow is considered since fluid flow in the ureter is sometimes accompanied by particles such as stones or bacteriuria. Particle trajectories for parameters that correspond to calcium oxalates for calculosis and Escherichia coli type for bacteria are analyzed. The findings show that retrograde or reflux motion of the particles is possible and bacterial transport can occur in the upper urinary tract when there is a partial occlusion of the wave. Dilute particle mixing is also investigated, and it is found that some of the particles participate in the formation of a recirculating bolus, and some of them are delayed in transit and eventually reach the walls. This can explain the failure of clearing residuals from the upper urinary tract calculi after successful extracorporeal shock wave lithotripsy. The results may also be relevant to the transport of other physiological fluids and industrial applications in which peristaltic pumping is used.

Optical measurement of the instantaneous wavy surface structure on a water plane jet

Laser beam refraction technique for measurement of free surface waves on a high-speed water jet has been developed in the present work. The new method employs two pulse laser diodes and the single light-spot detector. Through detecting the two dimensional trajectory of laser beams refracted at free surface, the local slope-angle fluctuation at two measuring locations 1.2 mm apart on a jet free surface is evaluated. The experiments are conducted for several locations along the jet center axis within the range of average velocity up to 5 m/s. The wave speed is evaluated from dominant time lag of cross-correlation coefficient for individual waves, which are discriminated by applying the zero-up-crossing method to the slope-angle time series data. The shape of waves is also calculated by integrating the free-surface slope angle data numerically. The ensemble averaged wavelength increases with the distance from nozzle exit almost monotonically. On the other hand, the mean wave height first increase with distance, reaches a maximum and then decreases. The maximum value of wave height is less than 0.23 mm for the tested velocity range. The steepness of free surface wave, that is the ratio of wave height and wavelength, takes a maximum at 20 ∼ 30 mm downstream nozzle exit. This suggests that the wave breaking occurs on the jet free surface for higher velocity case.

STABILITY OF WATERFRONT RETAINING WALL SUBJECTED TO PSEUDO-DYNAMIC EARTHQUAKE FORCES AND TSUNAMI

The paper pertains to a study in which the waterfront retaining wall has been analyzed for its stability when it is exposed to the forces jointly coming from an earthquake and tsunami. Closed form solutions following the simple limit equilibrium principles have been proposed. For the calculation of the seismic passive earth pressure and the wall inertia force, pseudo-dynamic approach has been considered, while the hydrodynamic and the tsunami wave pressures have been calculated using different approximating solutions available in literature. The results presented in the sliding and overturning modes of failure of the wall show that the stability of the wall gets seriously challenged when it gets jointly exposed to the effects of the tsunami and earthquake. About 92% decrease is observed in the value of the factor of safety in sliding mode of failure of the wall as the ratio of tsunami wave height to the upstream still water height increases from 0 to 1.5. Also, the critical mode of failure of the wall has been found to be that of the overturning. Effect of different parameters involved in the analysis has also been studied and it has been observed that quite a few of them like kh, kv, ϕ, δ, ru have a significant effect on the stability of the wall. Comparison with a previously existing methodology using pseudo-static approach suggests that the present pseudo-dynamic approach is more realistic and comparatively less conservative and hence can be used as a handy simple economic method for the design of the waterfront retaining walls exposed to the combined effects of earthquake and tsunami.

Influence of Spectral Width on Wave Height Parameter Estimates in Coastal Environments

In this study, we present comparisons of wave height estimates using data from acoustic Doppler wave gauges in ten coastal and estuarine environments. The results confirm that the agreement between significant wave height estimates based on spectral moments (Hm0) versus zero-crossing analysis (H1∕3) is linked to the underlying narrow band assumption, and that a divergence from theory occurs as spectral width increases with changes in the wave field. Long-term measurements of the maximum to significant wave height ratio, Hmax∕H1∕3, show a predictable dependence on the site-specific wave climate and sampling scheme. As an engineering tool for other investigators, we present empirically derived equations relating Hm0∕H1∕3 and H1∕3∕m0 to the spectral bandwidth parameter, ν, and evaluate two procedures to predict Hmax from the spectrum when the surface elevation time series is unavailable. Comparisons with observations at each site demonstrate the utility of the methods to predict Hmax within 10% on average.

Rogue Waves: Results of the MaxWave Project

Safety of shipping is an ever growing concern. In a summary, Faulkner investigated the causes of shipping casualties (2002, “Shipping Safety: A Matter of Concern,” Ingenia, The Royal Academy of Engineering, Marine Matters, pp. 13–20) and concluded that the numbers of unexplained accidents are far too high in comparison to other means of transport. From various sources, including insurers data over 30% of the casualties are due to bad weather (a fact that ships should be able to cope with) and a further 25% remain completely unexplained. The European project MaxWave aimed at investigating ship and platform accidents due to severe weather conditions using different radars and in situ sensors and at suggesting improved design and new safety measures. Heavy sea states and severe weather conditions have caused the loss of more than 200 large cargo vessels within the 20years between 1981 and 2000 (Table 1 in Faulkner). In many cases, single “rogue waves” of abnormal height as well as groups of extreme waves have been reported by crew members of such ships. The European Project MaxWave deals with both theoretical aspects of extreme waves and new techniques to observe these waves using different remote sensing techniques. The final goal is to improve the understanding of the physical processes responsible for the generation of extreme waves and to identify geophysical conditions in which such waves are most likely to occur. Two-dimensional sea surface elevation fields are derived from marine radar and space borne synthetic aperture radar data. Individual wave parameters such as maximum to significant wave height ratios and wave steepness, are derived from the sea surface topography. Several ship and offshore platform accidents are analyzed and the impact on ship and offshore design is discussed. Tank experiments are performed to test the impact of designed extreme waves on ships and offshore structures. This article gives an overview of the different work packages on observation of rogue waves, explanations, and consequences for design.

Alternative forms of the higher-order Boussinesq equations: Derivations and validations

An alternative form of the Boussinesq equations is developed, creating a model which is fully nonlinear up to O( μ 4) ( μ is the ratio of water depth to wavelength) and has dispersion accurate to the Padé [4,4] approximation. No limitation is imposed on the bottom slope; the variable distance between free surface and sea bottom is accounted for by a σ-transformation. Two reduced forms of the model are also presented, which simplify O( μ 4) terms using the assumption ε = O( μ 2/3) ( ε is the ratio of wave height to water depth). These can be seen as extensions of Serre's equations, with dispersions given by the Padé [2,2] and Padé [4,4] approximations. The third-order nonlinear characteristics of these three models are discussed using Fourier analysis, and compared to other high-order formulations of the Boussinesq equations. The models are validated against experimental measurements of wave propagation over a submerged breakwater. Finally, the nonlinear evolution of wave groups along a horizontal flume is simulated and compared to experimental data in order to investigate the effects of the amplitude dispersion and the four-wave resonant interaction.

Conceptual Model for Cross-shore Sediment Transport due to Tides and Waves over Intertidal Flat

Conceptual model for geomorphology and sediment transport due to tides and waves over intertidal mudflat has been proposed based on the field measurements of water depth, flow velocity and suspended sediment concentration from July 2004 to January 2008. Suspended-load flux and bed-load ability are expressed relative to the ratio of significant wave height to water depth. The maintenance mechanism for typical convex-upward profile over intertidal mudflat can be explained by the bed-load superiority for suspended-load using the conceptual model.