Showing papers on "Wave height published in 1976"

A numerical model of the air flow above water waves

Abstract: A numerical model is proposed for the flow in a deep turbulent boundary layer over water waves. The momentum equations are closed by the use of an isotropic eddy viscosity and the turbulent energy equation. For small amplitudes the results are similar to those of Townsend's (1972) linear model, but nonlinear effects become important as the ratio of wave height to wavelength increases. With uniform surface roughness zo, the predicted fractional rate of energy input per radian advance in phase, ζ, decreases slightly with increasing amplitude and is of the same order of magnitude as in Miles’ (1957, 1959) and Townsend's linear theories. If zo is allowed to vary with position along the wave, however, the fractional rate of energy input can be significantly increased for small amplitude waves. If the variation in zo is half the mean value and the maximum wave slope zak is 0.01, we find ζ ≈ 60 (ρair/ρwater) (uo/c)2, where uo is the friction velocity and c the wave phase speed. Comparison is also made with recent laboratory and field data.

An Introduction to Water Waves

Abstract: The aim of this chapter is to present the theories for unsteady free surface flow subjected to gravitational forces. Such motions are called water waves, although pressure waves (such as acoustic waves) in water are also water waves. They are also called gravity waves, although atmospheric motions are also waves subjected to gravity.

Extreme wave parameters based on continental shelf storm wave records

Abstract: Measured storm wave records from several Continental Shelf areas were used to test the adequacy of estimating formulae for individual wave parameters. In all, 376 hours of storm wave records were analyzed, and their properties nondimensionalized by fundamental spectral parameters. Results are presented for surface deviation statistics, individual wave height statistics and individual wave period statistics. The results can be used by ocean engineers to eliminate unintended bias from wave parameters selected for the design of offshore facilities. The most significant result is that measured rare wave heights in the storm wave records are on the order of 10 percent less than predicted by the Rayleigh distribution at the 1 in 1000 probability level.

Deformation up to breaking of periodic waves on a beach

Abstract: An experimental description is presented for 'the transformation of periodic waves which approach breaking on a gently sloping beach. The data include the variation of wave height, phase velocity, wave surface profiles, and the maximum value of the wave height to water depth ratio (H/h)max around the breaking point. The results are compared with the theories of sinusoidal and cnoidal wave shoaling, and the latter is shown in most cases to agree remarkably well when the laminar energy loss along the walls and bottom of the wave tank is included. An empirical relation is established between wave length to water depth ratio L/h at the breaking point and the deep water wave steepness H0/L0. Also the maximum wave height to water depth ratio at breaking shows considerably less scattering than found previously, when plotted versus S = hx L/h, hx being bottom slope.

Closed-form expressions for determining the fatigue damage of structures due to ocean waves

Abstract: Closed-form mathematical expressions are derived for the fatigue damage of structures due to ocean waves. The expressions incorporate relationships between wave height and stress range, between stress range and number of cycles to failure (i.e. a fatigue curve), and the probability distribution for the occurrence of wave heights. The expressions can be utilized to predict the fatigue damage resulting from a single sea state, from a storm, or during the service life of a structure. In addition, the fatigue life of a structural element can be determined directly from the stress range resulting from the design wave, or conversely, an "allowable stress range" can be determined for the design wave which will insure a specified fatigue life. Example applications are given for areas having wave climates similar to the North Sea and similar to the Gulf of Mexico.

Probability Distributions of Breaking Wave Heights Emphasizing the Utilization of the JONSWAP Spectrum

Abstract: An approximate determination has been made of the probability distribution function for breaking wave heights in the deep ocean. It was necessary to make simplifying assumptions of the joint distribution of wave height and wave period so that a semi-closed mathematical solution could be obtained as an illustration of the total processes that actually occur. These assumptions lead one to a calculation which predicts more and larger breaking waves than those which actually occur. Thus, for the design of structures in the deep ocean which are sensitive to breaking waves, a conservative determination of the probability distribution function is obtained. The distributions can be obtained for any location in the deep ocean given a sufficient history of surface meteorological data on wind speed and fetch. The joint distribution of wind speed and fetch for station PAPA in the North Pacific Ocean proved to be independent of storm duration. Thus, 6 h unit storms were considered to be independent in the com...

Design Wave Information for the Great Lakes. Report 2. Lake Ontario.

Abstract: : This report contains hindcast wave information that is applicable to many planning and design purposes on Lake Ontario. Historical wind data from three stations along Lake Ontario served as input to the numerical hindcast model, and significant wave heights were calculated for 5-, 10-, 20-, 50-, and 100-yr return periods. These results are provided in tabular form for 17 points along the Lake Ontario shoreline. The mean significant period for each of these wave heights is also given. Information is provided for four seasons of the year (January-March, April-June, July-September, and October-December) and is separated into three approach directions relative to shroe. (Author)

Refraction of Finite-Height and Breaking Waves

Abstract: The primary objective of this study was to ascertain the influence of wave height and breaking on wave refraction over a three-dimensional shoal. The subject wave transformations were studied in an hydraulic model. Wave shoaling, decay in the breaker zone, and phase velocities were analyzed in a base test series over a bottom slope of 1:30. A second test series was conducted over a three-dimensional shoal. Wave patterns were photographed and wave heights and celerities were measured. The measurements were compared with wave refraction patterns and coefficients computed by analytical methods. Wave shoaling observed over the constant 1:30 slope was 25 percent greater than predicted by Airy theory at the breaking point for wave steepness H0/L0=.030 and 50 percent greater than predicted for H0/Lo = •002. Shoaling measurements were compared with other empirical data sets, confirming the inadequacy of commonly used practice using linear wave theory near the breaker zone. The celerity measurements indicated that the non-breaking celerity was given by C = (1+.25 H/d)Ca, where Ca is the Airy celerity. The discussion and results give a basic understanding of wave refraction near the breaker zone, supplementing analytical papers on refraction procedures using finite amplitude wave theories.

Preliminary dynamic assessment of deepwater platforms

Abstract: For purposes of preliminary analysis and design, a relatively simple form for estimating dynamic response of bottom-founded deepwater structures is developed. The structural system is assumed to be linear and the sea state is assumed to be two-dimensional. Structural motion is assumed to be small in computing wave loading. The simple response algorithm has the property of providing a mechanism for the efficient introduction of probabilistic design theory. Reliability estimates can be performed relative to each mode of structural failure. Statistical information on all design factors such as ocean wave heights and frequencies of occurrence of sea states, wave forces on structures, soil strengths, and material and joint strengths can easily be treated without resorting to Monte Carlo techniques.

Time dependent fluctuations in longshore currents

Abstract: During constant sea state conditions, longshore current velocities were monitored continuously for fifteen minute periods separated by fifteen minute periods separated by fifteen minute intervals. Three ducted impellor flowmeters were placed at equally spaced vertical positions through the water column. Sequential measurements were made with similar vertical current meter arrays at different locations across the surf zone. Simultaneous measurements of wave height, period and celerity were made at stations placed at equal intervals from the outer surf zone to the beach. The fifteen minute continuous records were subjected to spectral analysis. This analysis showed that the major power associated with fluctuations in the longshore current velocity field occurs in two major frequency bands. A significant spectral peak was coincident with the breaker period of the incident wave field, 4.2 seconds and, another dominant signature occurred at 78.8 seconds. Attenuation with depth of both the steady and fluctuating components of the longshore current flow field was relatively small. The maximum observed velocities for each station and each vertical current meter position varied from 90 to 150 percent above the observed mean longshore current velocity. However, at each station, variation of the means with depth was not appreciable and thus supports the results from time and space averaged theories of vertical uniformity in longshore currents, away from the boundary layer. Results from the field investigation of Wood and Meadows (1975) indicated that the steady state components are dominated by the fluctuating portions of the flow field. Therefore, time averaging of conservation equations in longshore current theory is a physically inappropriate procedure. In order to evaluate the magnitude of the unsteady components, a close examination of surf zone dynamics was made. The most obvious contribution to unsteadiness in longshore currents arises from the longshore component of the maximum horizontal particle velocity. However, the magnitude of observed current fluctuations is too large to be completely accounted for by this component. Spectral peaks at longer periods appear to be related to modes of edge wave phenomena. The long period spectral signature of 78.8 seconds is in direct agreement with the calculated period for a zero mode edge wave in shallow water.

Numerical Models for the Prediction of Wave Set-up and Nearshore Circulation.

Abstract: : A finite difference model for predicting time-dependent, wave-induced nearshore circulation is discussed. The formulation includes wave refraction, wave-current interaction, an anistropic bottom friction, wave set-up, wind effects and coastal flooding. Results are shown for three cases including: set-up in a wave channel due to steady waves and wave groups, circulation in a rectangular wave tank under oblique wave attack, and for wave and wind induced circulation on a longshore periodic beach. Important results are that tuned wave groups can incite seiching in an enclosed basin and harbors and that rip currents will be induced or maintained by the presence of surf zone channels. (Author)

Analysis of a stratified sample of ocean wave records at station "india"

Abstract: Results are presented of an extensive stratified random sampling of spectra obtained by analysis of wave records at Station "India" in the North Atlantic Ocean (59 degrees N, 19 degrees W). Spectra were obtained for five different wind speed groups, and except in the highest wind group represented a roughly equal sampling of all four seasons. The final sample of 323 spectra are presented in graphical and tabular form in an appendix, along with tabulations of the principal spectrum parameters. The report presents the results of analysis of the spectra to show a variety of trends, such as significant height vs. wind speed and average period, seasonal variations in significant height, etc. Typical groups of spectra having significant heights of 25-35 feet and 35-45 feet are presented graphically and compared to several ideal spectrum formulations, showing considerable differences. It is concluded that this collection of spectra can be grouped into families, on the basis of significant wave height, which can be useful for ship designers.

Environmental wave data for determining hull structural loadings

Abstract: A survey evaluation is given of observed and measured wave data covering major U.S. routes, with appendices, tabulations and maps. The introduction of theoretical formulations leads to the discussion and evaluation of wave spectral hindcasting techniques. The methods used to predict ship motions and loads are explained followed by a section discussing the wave data format required for predicting short and long-term loads and motions as well as numerical examples showing the effect on and sensitivity of predictions to variation in wave data format. Based on the preceding discussion, presently available data suggested for use in determining ship loads are given. The use of a combination of statistics based on observations on the frequency of occurrence of various wave heights and a spectral family of measured spectra grouped by wave height is recommended. Finally, a survey of current and planned data collection projects is given.

Review of the technology for wave power conversion

Abstract: Presented is a review of the technology of wave power conversion. Hundreds of patents have been issued on wave power conversion; these include propulsion schemes, buoy power supply devices, offshore power plants and shore-based power stations. Energy densification is a requirement before conversion, and schemes used for it have been resonance, accumulation with time and wave height amplification by converging channels or refraction. Variability of the mean power with time, presence of tide and the possibility of occasional onslaught by very high waves pose challenging problems.

The viscous damping of cnoidal waves

Abstract: The viscous damping of cnoidal waves progressing over a smooth horizontal bed is investigated. First approximations are derived for the attenuation of wave height with distance and for the friction coefficient at the bed. Attenuation coefficients are larger than those predicted on the basis of shallow-water sinusoidal wave theory and, unlike the case of sinusoidal waves, they are not independent of wave height. The limiting case of the solitary wave, considered previously by Keulegan (1948), is also discussed.

Characteristic wave period

Abstract: The wave period estimates obtained from different procedures are not consistent unlike statistical distribution analysis of wave heights. Thus not one definition of wave period is satisfactory for engineering analysis of coastal processes. There are at least 10 different measures of wave periods including the zero up-crossing period, the average wave period, significant height period and peak of the energy density spectrum period. For Lhe analysis of periods, 20 min. records were obtained from offshore pressure recorders. Summer and winter records were analysed separately. In the analysis, zero up-crossing period and average period were taken as reference periods. There were significant differences between the wave periods and they were found to depend also on the spectral width parameter. Finally comparison was made between the energy flux obtained under the spectral diagrams and energy flux obtained using various wave periods and heights. Study shows that if the total energy flux is desired, then the most appropriate values to be used are the root mean square wave height and period corresponding to that wave height. Use of significant wave height, along with zero up-crossing period gives higher values.

Wave resistance and wave patterns of thin ships

Abstract: The wave resistance R and wave height h(x,z) are evaluated asymptotically for small Froude number F = U(gl)-1/2 for a slender hull of any shape. Michell's theory for a thin ship of length L moving with constant speed U along a straight line is the starting point. It is found that asymptotically R and h depend only upon four properties of the ship -- the slope of the hull and the slope of the profile curve of the hull at the waterline at bow and stern. Simple formulas are obtained for R and h in terms of these slopes. The wave pattern consists of four waves -- a longitudinal and a transverse wave from the bow and a similar pair from the stern. Their phases are the same as those of Kelvin waves due to pressure points at the bow and stern, and they also decay with distance like cylindrical waves. However, their amplitudes have different angular variations from those of Kelvin waves.

Wave action on large off-shore structures

Abstract: The paper describes investigations carried out in order to design for the wave action, both wave force and scour, on large off-shore berthing structures sited approximately 1.3 miles (2.1 km) off-shore near Hay Point, North Queensland, in 56 feet (17 m) of water at low tide, the tidal range being 20 feet (6 m). The region is a cyclone area and the structures must be capable of withstanding attack from maximum predicted waves with period of 8.25 seconds and amplitude of 24 feet (7.3 m). The main units in the berthing structures are concrete caissons sunk on to the ocean bed and the largest of these have plan dimensions of approximately 150 feet (46.7 m) by 135 feet (41.4 m) with four columns approximately 40 feet (12.2 m) square projecting through the water surface. No theoretical method available at the time of the investigation was capable of accurate calculation of wave forces on these structures. A scale model was tested to obtain wave forces and the paper compares results from the model with those of numerical methods and discusses the application of the results to the design functions. Scour effects were also modelled and the results used as the basis for design of scour protection.

Wave climate analysis for engineering purpose

Abstract: The North Sea (Fig. 1) is known as a random sea with depths in the southern part between 40 m and 100 m so that in contrary to the Atlantic and Pacific coastlines deep sea wave conditions do not exist. After four years of comprehensive wave measurements in the offshore area of the Island of Sylt near the Danish border a general analysis of the wave climate in that region was possible. In this paper results and suggestions will be presented under the aspect of replacing qualitative judgements by quantitative statements which are derived from the knowledge of the adjacent wave climate. Because the wave action varies from year to year a general time unit is not advisable for the evaluation of shore processes; therefore the time scale should be substituted by the integral of incoming wave energy occurring after a certain time. The investigated method of expressing the total energy of one season or one year in the electrical unit Kilowatthour (kWh) per meter (m) width of shoreline could prove in future as a feasible way of classifying the irregular seasonal and yearly wave intensities. It is further shown that wave measurements over a period of several years can be sufficient for the investigation of correlations between the wind velocities occurring from all directions and the resulting wave heights. In case of satisfying correlation factors it will then be possible to carry out feedback operations for periods from which only records of wind velocities and directions are available and even to hindcast the wave heights for certain not yet measured wind velocities.

Wave height meter of acceleration detection type

Abstract: PURPOSE: To eliminate the finfluence of up and down movement to tide and to carry out the measurement of complex wave pattern, by integrating with double integral after intercepting the DC component in the acceleration signal, in case of measuring a wave hight from the above signal by the vertical movement of wave. COPYRIGHT: (C)1977,JPO&Japio

The effect of probe location on a model wave resistance survey along a longitudinal cut

Abstract: Longitudinal-cut wave survey experiments using lateral wave slope data and wave height data were carried out on a Series 60, 0.60-block model in the Webb Model Tank. The results in each case show a dependence on the lateral distance of the wave cut away from the model at the higher Froude numbers (speeds) tested. Consistently lower results were obtained when using lateral wave slope data compared with those obtained when using wave height data. A discussion of possible causes of these findings is given.

Seakeeping Characteristics of the XR-5, A High Length-Beam Ratio Manned Surface Effect Testcraft: III. Results of Random Wave Experiments Investigation of Linear Superposition for Ship Motions and Trim and Draft in Random Waves,

Abstract: : Motion responses derived from model experimental results in regular and irregular head waves for the XR-5 high length-beam ratio surface effect ship are presented. Frequency response functions for pitch, heave, relative bow motion, heave acceleration and bow acceleration were computed from the random wave experiments and are presented herein. Comparisons are made with responses derived from regular wave experiments. The results indicate that the rigid body motions are reasonably linear for the Froude numbers and sea conditions investigated. Nonlinear effects that increase with the severity of the sea state are evident in the accelerations. In addition, the motion of the stern seal with respect to the relative motion at the stern is presented. These responses are generally linear although some nonlinear effects appear with increasing Froude number. Probability distributions for the double amplitude of wave height, heave and pitch are presented. Comparisons are made with Rayleigh probability distributions based on the variances of the sample data and on the minimum Chi Square estimators computed from the distributions. (Author)

Seasat-A - An ocean observation satellite

Abstract: Mission details, onboard equipment, and measurements to be taken are described for the Seasat-A global ocean monitoring satellite. The satellite is designed for mapping the global ocean geoid, charting ice fields and leads, precision measurement of sea surface topography, global monitoring of wave height and wave directional spectra, surface winds and wind direction, current patterns, and ocean temperature. Data handling subsystems, a compressed pulse radar altimeter, coherent synthetic aperture imaging radar, microwave wind scatterometer, scanning visible/IR radiometer, scanning multispectral (5 freq) microwave radiometer mounted on the satellite are described briefly.

Estimating coastal design extremes for given risks: A new approach

Abstract: For many reasons, e.g., port operations, coastal construction planning, undersea structure survival, and underwater transport, man wishes to know the extreme values that are likely to occur in coastal oceanographic variables. This paper presents a hybrid statistics/ computer simulation method that uses archived oceanographic observations to estimate confidence levels on the most extreme values likely to occur over a given period in the future. The difference from previously developed methods is the ability to estimate the most extreme value over a time period for a given probability (as opposed to estimating the probability of exceeding a given value) and the ability to obtain results from empirical data without a great deal of theoretical oceanography. The method is applied to the California coast for a period of 100 years on the following variables: bottom surge particle velocity by water depth, wave height by water depth, wavelength by water depth, wave period, current velocity, regions of high density, regions of low density, and earthquake magnitude. Values are given for the 99- and 99.9-percent probability levels.

Nearshore processes on a fringing reef.

Abstract: : A field experiment was conducted on Grand Cayman Island during 1972 and on Barbados during 1973 to determine the characteristics of wave-dominated nearshore processes in a fringing reef. Results from these field experiments indicate that nearshore processes on reefs occur in a distinctly different pattern from that on sandy coasts. Deepwater wave characteristics are significantly modified by reef morphology before the waves reach the shoreline. Shelf morphologic features produce a significant reduction in wave height (approx. 20%), owing to the combined effects of friction, scattering, and reflection, at a rate significantly greater than that occurring on sandy coasts. At the fringing reef crest energy loss resulting from breaking produces a substantial reduction in wave height which is accompanied by an extreme modification to the wave spectrum, including the introduction of multiple low-frequency peaks. Wave-induced currents cross the fringing reef crest and interact with lagoon geometry to produce a circulation pattern in the back-reef lagoon characterized by velocities which increase toward the main lagoon outlet. Sediment thickness within the lagoon decreases toward the lagoon opening and increases toward the shoreline. This pattern is in qualitative agreement with the generally predicted lagoon current movement. (Author)

Three-dimensional conditions of surf

Abstract: Wave height variability along the crest of breaking waves is shown to be a significant factor in the assessment of surf zone dynamics. Variations in excess of 50 percent of the maximum wave height can occur along a single crest without significant variations in bathymetry. The horizontal scale of this longshore variability in crest height corresponds to the wave length of incident breaking waves. Four possible mechanisms for this variability are postulated and then evaluated individually on the basis of field observations. A major result of these evaluations is that two-dimensional shallow-water wave equations appear to be inappropriate for expressing natural surf zone wave transformations and water motions even under the condition of waves encroaching on a plane sloping bottom. Consequently, three-dimensional equations of surf should be used for describing most natural surf zone dynamics.

On the reliability of the spectral method for the design of offshore structures

Abstract: Two sources of uncertainties to be considered when computing spectral densities of wind-generated wave forces are discussed. The size of resolution and degree of confidence of spectral estimates as well as the filtering process are found to be important for the spectral shape particularly in the subrange significant for structural design of dynamically excited linear systems. The second type of uncertainty is introduced by the fact that the coefficients of drag and inertia are random variables. The effect of their dispersion on the variation of the force spectral estimate in terms of exceedance probabilities of the dynamic wave loads - using similarity wave height spectra - is discussed. The analysis is illustrated utilizing a template steel platform in 550 ft of water as a sample structure.