Showing papers on "Swell published in 1991"

Shelf sandstones and hummocky cross-stratification: New insights on a stormy debate

Abstract: A new depositional model for hummocky cross-stratified sandstones is based on the following observations. (1) Storms transport coastal sand to the inner shelf under oscillatory-dominant combined flows exerting peak instantaneous bed shear stresses roughly normal to shore. (2) Isotropic hummocky cross-stratification is formed experimentally by large, three-dimensional, symmetrical bed forms generated by long-period, purely oscillatory flow and very strongly oscillatory-dominant combined flow. Anisotropic hummocky cross-stratification is formed by strongly oscillatory-dominant flow. (3) Grain fabric in hummocky sandstones indicates rapid reversals of bed shear stress consistent with deposition under a shore-normal oscillatory flow, initially superimposed on a relatively weak bottom current with a seaward-directed component of motion. Thus, shore-normal transport of coarse bedload on the inner shelf during storms (inferred from studies of ancient units) is caused by the interaction of high-speed oscillatory bottom motions under long-period shoaling waves and a relatively slow shore-oblique bottom current driven by geostrophically balanced coastal downwelling. Turbidity currents are not required to form shore-normal paleoflow indicators from hummocky beds. Large three-dimensional wave ripples generated by waning-storm or swell waves are responsible for much of the hummocky cross-stratification in the stratigraphic record.

Macro-Meso Tidal Beach Morphodynamics: An Overview

Abstract: Macro- and meso-tidal beaches are ubiquitous global coastal features about which comparatively little is known compared to their micro-tidal counterparts. A review of the literature reveals a considerable range in macro-tidal beach morphology and dynamics but with little perceived order in the range. This review together with recent morphological data from macrotidal beaches on the central Queensland coast are combined to provide an overview, and to identify three types of macro-tidal beaches. Two are true beaches. Higher waves, and particularly swell produces moderate gradient (1-3°), concave, planar beaches dominated by incident, though infragravity wave energy. Moderate waves and sea conditions tend to produce lower gradient (0.5°), multi-bar (ridge and runnel) topography also attributable to infragavity standing waves. As wave energy drops still further a third type results with a high tide beach fronting tide-dominated tidal flats. This latter is not a true beach but rather a transition from beach to tidal flat.

Infragravity waves in the deep ocean

Abstract: Energetic pressure fluctuations at periods longer than 30 s are a ubiquitous feature of pressure spectra from instruments sited on the deep seafloor in both the Atlantic and the Pacific oceans. We show these pressure fluctuations are caused by freely propagating ocean surface waves. The waves are generated in the near shore region along the entire coastline of an ocean basin through nonlinear transfer of energy from short-period waves. This view contrasts with some earlier work, which described these long-period pressure fluctuations as trapped waves tied to groups of short waves. We have constructed a model based on the average energy in the short (wind driven and swell) wave band along the North Atlantic coast to predict the energy in the long wave band at a site in the Atlantic. Maximum likelihood wave number-frequency spectra calculated on data from an 11 element array in the North Pacific confirm that the long wave energy is confined to wave numbers corresponding to the surface gravity wave dispersion relation. We have used the wave number spectra to isolate particular regions of the Pacific Ocean which are sources of long wave energy. Energetic short-period waves are incident on the coastline in these regions. Long waves are detected at the army which originate in the Gulf of Alaska, the northwestern Pacific, and at the southern tip of South America.

Effects of the Gulf Stream on ocean waves

Abstract: In the present study a third-generation numerical wave model is used to study effects of a straight Gulf Stream ring on ocean waves in swell and storm conditions. The model accounts for all relevant processes of propagation, generation, and dissipation of the waves (including current effects) without imposing a priori restraints on the spectral development of the waves. The dominating mechanism affecting the waves appears to be current-induced refraction even though the short-crestedness of the incoming waves tends to mask its effects (also in swell conditions). Depending on wind and wave conditions, refraction may trap locally generated waves in the straight Gulf Stream or it may reflect wave energy back to the open ocean. In the Gulf Stream ring, refraction induces a considerable variation in significant wave height and short-crestedness, but it hardly affects the mean wave direction. In storm conditions the processes of generation and dissipation are considerably enhanced in countercurrent situations and reduced following-current situations.

Frequency downshift in narrowbanded surface waves under the influence of wind

Abstract: It is well known that the spectral peak of wind-induced gravity waves on the sea surface tends to shift to lower frequencies as the fetch increases. In past theories the nonlinear dynamics subsequent to Benjamin–Feir instability has been found to initiate the downshift in narrow-banded waves in the absence of wind. However, these weakly nonlinear theories all predict the downshift to be only the first phase of an almost cyclic process. Limited by the length of a wave tank, existing experiments are usually made with relatively steep waves which often break. Although there is a theory on how breaking adds dissipation to stop the reversal of the initial trend of downshift, the details of breaking must be crudely characterized by semi-empirical hypotheses. Since the direct role of wind itself must be relevant to the entire development of wind-wave spectrum, we examine here the effect of wind on the nonlinear evolution of unstable sidebands in narrow-banded waves. We assume that the waves do not break and consider the case where the nonlinear effects that initiate the downshift, energy input by wind and damping by internal dissipation all occur on the same timescale. This means that not only must the waves be mild but the wind stress intensity must also lie within a certain narrow range. With these limitations we couple the air flow above the waves with Dysthe's extension of the cubic Schrodinger equation, and examine the initial as well as the long-time evolution of a mechanically generated wavetrain. For a variety of wind intensities, downshift is indeed found to be enhanced and rendered long lasting.

Groundwater-Table Responses to Wave Run-up: An Experimental Study From Western Australia

Abstract: Groundwater-table responses to wave fun-up were observed on a natural sandy beach at South City Beach, Western Australia. The run-up spectrum was dominated by a broad band of swell energy. In contrast the groundwater spectrum was dominated by low-frequency energy. Thus the beachface and sediment matrix effectively filter input swash oscillations as they are transmitted through to the groundwater-table. The filtering appears to be that of a band-pass filter in which oscillations with a frequency of 0.013 Hz (77 s) are less attenuated than either longer or shorter period fluctuations. Despite intense filtering, groundwater-table oscillations at incident swell frequencies were still detected. These oscillations were closely related to swash motions on the beachface. Low-amplitude run-up did not induce a detectable response in the groundwater-table, and the groundwater-level continued to decline. Swashes with moderate run-up resulted in the transmission of a pressure force, via the saturated sands, which induced a temporary stabilizing of the falling groundwater-level. Swashes that extended beyond the mean groundwater-table level caused the groundwater-table to rise. The water-table rise and rate of rise were directly related to the amplitude of swash run-up. The groundwater-table rise was caused by swash water infiltration and in part by the reversed Wieringermeer effect. A groundwater-table response asymmetry was detected whereby the groundwater-level rises more rapidly than it falls.

Two-station measurements of Rayleigh wave group velocity along the Hawai'ian Swell

Abstract: Two-station measurements of Rayleigh wave group velocity between Midway Atoll and O'ahu provide a useful constraint on lithospheric thickness along the Hawai'ian Swell. Comparison of the observed dispersion curve with age-dependent, regionalized dispersion curves suggests that the swell acts as 50–110 m.y. old lithosphere, and not as 20–50 m.y. old lithosphere as is predicted by the currently favored hypothesis for the swell's formation. A preliminary isotropic shear velocity model for the swell suggests that the lithosphere may be as thick as 100 km. This value is difficult to reconcile with the lithosphere being substantially thinned during its passage over the Hawai'ian hotspot.

Field measurements of wave-induced pressure over wind-sea and swell

Abstract: Results of two field experiments in the North Sea are presented. Pressure was measured at two fixed heights above the mean water level and correlated with simultaneous wave height measurements. Roughly 90 hours of data have been analysed and the results are in agreement with earlier results obtained by Snyder et al. (1981). Measurements over swell give no indication of wave decay or growth for waves travelling faster than the wind or against the wind.

Joint environmental model for reliability calculations

Abstract: A joint environmental model for a long term response calculations is proposed. The model is based on experience gained from measurements and hindcast data from the Norwegian Continental Shelf. The model is an extension of an existing joint environmental model for Haltenbaken (off central Norway). The present model includes the following environmental parameters: 1-hour mean wind speed, current speed, significant wave height, spectral peak period, main wave direction (wind and current are assumed to be collinear with the main wave direction), and water level. Additionally, a simultaneous description of wind sea and swell is also introduced. The model is expected to be a useful tool for long term reliability calculations of offshore structures, especially as dynamics and/or other frequency dependent loading mechanisms become important. The model accounts for the lack of full correlation among the various environmental processes and it can be used for assessing the conservatism of the traditional design approach. Herein, as an illustration, the model is is applied in connection with reliability analysis of an idealised structural system, where the degree of dynamics is varied artificially. A first order reliability method (FORM) is used for this purpose.

Strain in shore fast ice due to incoming ocean waves and swell

Abstract: Using a development from the theoretical model presented by Fox and Squire (1990), this paper investigates the strain field generated in shore fast ice by normally incident ocean waves and swell After a brief description of the model and its convergence, normalized absolute strain (relative to a 1-m incident wave) is found as a function of distance from the ice edge for various wave periods, ice thicknesses, and water depths The squared transfer function, giving the relative ability of incident waves of different periods to generate strain in the ice, is calculated, and its consequences are discussed The ice is then forced with a Pierson-Moskowitz spectrum, and the consequent strain spectra are plotted as a function of penetration into the ice sheet Finally, rms strain, computed as the incoherent sum of the strains resulting from energy in the open water spectrum, is found The results have implications to the breakup of shore fast ice and hence to the floe size distribution of the marginal ice zone

Bottom friction for wind sea and swell in extreme depth-limited situations

Abstract: A severe depth-limited storm and a case of extreme swell, which both occurred in the southern North Sea, are hindcasted with a regional version of the third-generation WAM model. This is done using different expressions for the bottom-dissipation source term: an empirical expression, the Hasselmann and Collins drag-law expression and an expression based on the eddy-viscosity concept. An efficient approximation to this eddy-viscosity model is presented, which is easy to compute and which yields accurate results. It is proposed to take a constant roughness value kN = 4 cm in this model, which corresponds to small sand ripples. The validity of this assumption is investigated. The hindcast results are compared with measurements from different stations and an estimate is made of the influence of the tide on the wave dissipation in the southern North Sea. The eddy-viscosity model is found to be a promising alternative to the empirical expression, which is used now in the WAM model.

Wind-Wave Nonlinearity Observed at the Sea Floor. Part I: Forced-Wave Energy

Abstract: This is Part 1 of a study of nonlinear effects on natural wind waves. Array measurements of pressure at the sea floor and middepth, collected 30 km offshore in 13-m depth, are compared to an existing theory for weakly nonlinear surface gravity waves. In this depth, free surface waves (obeying the linear dispersion relation) an weakly attenuated at the sea bed at sea and swell frequencies (0.05–0.3 Hz) but very strongly attenuated at frequencies higher than about 0.35 Hz. Only nonlinearly driven motions can reach the sea floor at these high frequencies. Nonlinear interactions between free (primary) waves of about the same frequency, travelling in nearly opposing directions, theoretically excite long-wavelength, double-frequency forced (secondary) waves that are only weakly attenuated at the sea door and form a mechanism for the generation of microseisms at great depth. In 13-m depth, wind-generated free waves and corresponding long-wavelength, high-frequency forced waves can be simultaneously obse...

Bubble noise and wavelet spills recorded 1 m below the ocean surface

Abstract: A remote instrument has been used to record the sound and environment of small surface spills in light winds from a depth of approximately 1 m in the open ocean. Recordings from the instrument indicate that these small breaks have no correlation with the amplitude or phase of long-period swells moving faster than prevailing winds. The sound from the spills, which is composed of a number of distinct resonant bubble oscillations, is very similar to that described by Medwin and Beaky [J. Acoust. Soc. Am. 86, 1124–1130 (1989)] for windless artificial wave breaks. Peak oscillation source pressures range up to 1.2 Pa. The average of several acoustic spectra from a single energetic spill has shown a slope of −5 dB per octave over the frequency range of the instrument, roughly 500–8000 Hz. The unique frequency for each oscillating bubble within a spill indicates that bubbles are “rung” as they are formed during entrainment, die out exponentially within milliseconds, and then no longer contribute actively to the acoustic record. Analysis of the acoustic energy generated by a number of bubbles versus frequency suggests that the −5 dB per octave wind-dependent ambient noise slopes of the Knudsen curves [J. Mar. Res. 7, 410–429 (1948)] are caused by the shorter lifetimes of high-frequency bubbles, rather than significantly lower peak pressures.

Observation of wave refraction at an ice edge by synthetic aperture radar

Abstract: In this note the refraction of waves at the ice edge is studied by using aircraft synthesis aperture radar (SAR). Penetration of a dominant swell from open ocean into the ice cover was observed by SAR during the Labrador Ice Margin Experiment (LIMEX), conducted on the marginal ice zone (MIZ) off the east coast of Newfoundland, Canada, in March 1987. At an ice edge with a large curvature, the dominant swell component disappeared locally in the SAR imagery. Six subscenes of waves in the MIZ from the SAR image have been processed, revealing total reflection, refraction, and energy reduction of the ocean waves by the ice cover. The observed variations of wave spectra from SAR near the ice edge are consistent with the model prediction of wave refraction at the ice edge due to the change of wave dispersion relation in ice developed by Liu and Mollo-Christensen (1988).

Sand bodies and sand transport paths at the English Channel-North Sea border: Morphology, hydrodynamics and radioactive tracing

Abstract: Surficial sediments and detailed submarine morphology of the southern Strait of Dover have been mapped using different complementary techniques: side-scan sonar survey, bottom sediment sampling, and bathymetry. The geometry and regional pattern of sand bodies - sand waves, megaripples, sand ribbons, etc. - as well as current-meter data and eight radioactive tracing experiments in different settings, are presented and analyzed. The mean regional net sand transport is 0.2 m super(3)/linear metre/day. The strong tidal currents of the region studied are considered as the main factor responsible for sand transport, while the swell plays an important but local role in maintaining particulate matter in suspension.

The Steepness and Shape of Wind Waves.

Abstract: Variations are found in the shape and the steepness of wind-generated surface gravity waves between very young waves, such as seen in a laboratory tank, and larger waves of various wave ages encountered at sea as the result of wind stress over larger fetches. These differences in the characteristic shape of wind waves are presented as a function of the wave age. The wave steepness is also expressed as a function of wave age, the measurement of which is consistent with the 3/2-power law connecting wave height and characteristic period, normalized by the air friction velocity.

Laboratory measurements of modulation of short-wave slopes by long surface waves

Abstract: Hydrodynamic modulation of wind waves by long surface waves in a wake tank is investigated, at wind speeds ranging fro 1.5 to 10 m s-1. The results are compared with the linear, non-dissipative, theory, of Longuet-Higgins & Stewart (1960), which describes the modulation of a group of short gravity waves due to straining of the surface by currents produced by the orbital motions of the long wave, and work done against the radiation stresses of the short waves. In most cases the theory is in good agreement with the experimental results when the short waves are not too steep, and the rate of growth due to the wind is relatively small. At the higher wind speeds, the effects of wind-wave growth, dissipation and wave-wave interactions are dominant.

Field verification of acoustic Doppler surface gravity wave measurements

Abstract: A compact acoustic Doppler current meter, designed for nearshore surface gravity wave measurements, was field tested by comparison to a colocated array of pressure transducers. Both measurement systems were bottom mounted in a water depth of 7 m. Each of four acoustic beams, inclined 45° from vertical, measures the alongbeam velocity at a single range (1 m) about 1.5 m above the seafloor. These four velocity beams are used to estimate low-order moments of the frequency-directional wave spectrum and are compared to pressure measurements on four occasions. Predictions of the (nondirectional) bottom pressure spectrum at sea and swell frequencies (0.04–0.30 Hz), based on the velocity measurements and linear theory, are in excellent agreement with directly measured pressure. The general level of agreement (gain errors less than 5%) is somewhat better than results reported from similar (but spanning a much wider range of conditions ) intercomparison studies using conventional in situ current meters. Observed cross spectra between colocated pressure and horizontal velocity components, frequently used to separate turbulence and wave orbital velocities (assuming that the coherence of wave velocity and pressure is equal to 1), are compared to predictions based on the pressure array data and linear wave theory. The observed and predicted pressure-velocity cross spectra are in excellent agreement and show that large coherence reductions can occur in natural wind waves owing to wave directional spreading effects, despite relatively low turbulence energy levels. Wave radiation stresses, estimated from the velocity measurements, also agree well with estimates extracted from the pressure array data. Overall, the intercomparisons show that the present acoustic Doppler system has directional resolution comparable to a pitch-and-roll buoy, and they suggest that higher-order directional information as well as weak nonlinear properties of natural wind waves may be examined with a slightly modified compact system.

Wind Waves on the Great Lakes: A 32 Year Hindcast

Abstract: Information on winds and waves near the coast is critical to scientists and engineers working on a variety of problems on the Great Lakes. These include design of coastal structures, estimation of erosion rates, and aspects of navigational and recreational safety. Very few measurements of winds and waves are available along the coastlines of the lakes and none are of long duration. The Wave Information Study (WIS) at the Coastal Engineering Research Center (CERC) has addressed this lack of information by completlng a 32-year hindcast of wind and wave conditions at locations 10 miles apart along the shorelines of the Great Lakes. Results are summarized in reports for each lake. Wind speed and direction are available every 3 hours for the 32·year period from 1956-1987 over a 10 mile grid on each lake. Directional wave spectra also are available each 3 hours for the 32 years at each location near shore and other selected points over the lakes. The procedures used to produce this information are discussed and examples of verification against measurements are shown.

Investigation of Long Waves in the Tsunami Frequency Band on the Southwestern Shelf of Kamchatka

Abstract: Two inexpensive cable bottom pressure stations were installed on the southwestern shelf of Kamchatka (Okhotsk Sea) in 1987 and two more in 1988 to provide longwave measurements in the tsunami frequency band, to investigate the generating mechanism of these waves, and to test the instrumentation. Microfluctuations of atmospheric pressure were recorded simultaneously. Two cable lines were torn off by ship anchors in March 1989 but others are still working in spite of highly dynamic activity on beaches and in hard ice regimes. Careful data analysis of two months of observations (September–October, 1987) showed that: (1) the atmospheric spectra were very stable and monotonic in the period range 2–50 min and corresponded to a power law of ω−2.3, (2) the direct generation of long waves by atmospheric pressure fluctuations was negligible, (3) there was high correlation between background longwave oscillations and sea state, (4) the structure of the offshore longwave field was in good agreement with theoretical estimates of standing waves for a linear slope.

Waves generated by a plunger-type wavemaker

Abstract: Based on a two dimensional linear water wave theory, the boundary element method (BEM) is developed and applied to study the waves generated by a plunger-type wavemaker. The computational domain is truncated by introducing two auxiliary boundaries at three times wave length distance away from the wavemaker. Radiation condition is used along the auxiliary boundaries. The accuracy of the numerical technique is demonstrated by comparing numerical results with previously published results, experimental and other techniques. However the actual wave height is smaller in the experiments than predicted by numerical models. The discrepancy between predicted and observed wave height can be attributed to the effects of leakage of wave energy under the plunger-type wavemaker. In order to predict waves generated by plungertype wavemaker accurately, the influence of leakage, under the plunger-type wavemaker, is included in the present study. The ratios between wave amplitude and stroke are established for two different...

Ocean wave spectral distortion in airborne synthetic aperture radar imagery during the Norwegian Continental Shelf Experiment of 1988

Abstract: C band radar images of ocean gravity waves off the Norwegian coast were processed into one-dimensional azimuth spectra. These spectra were used to measure the azimuth spectral (width) cutoff on the basis of a least squares fit to a Gaussian spectral shape. The widths were calculated for a range of wave heights (2–5 m) and wind speeds (2–18 m/s) during 3 days in March, 1988. Velocity smearing (συ) estimates were extracted, independent of R/V and incidence angle, based on an imaging model and the measured azimuth cutoffs with συ values varying from 0.4 to 0.7 m/s. Quantitative velocity smearing estimates are important as input to models describing the distortion in wave imagery. We propose a first-order model which neglects velocity bunching for ocean swell with peak wavelengths longer than about 250 m. This model is offered as a first estimate of when ocean wave swell will be detected by the C band SAR on board the ERS 1 spacecraft. The model predicts that this swell will be imaged under light winds of the order of 2–4 m/s. Higher wind speeds cause larger smearing, which may result in significant distortion of the imaged swell provided that the swell is traveling near the direction of the spacecraft ground track.

Macro-engineering process and system for all-weather at-sea wind-energy extraction

Abstract: A process and system for harvesting energy from wind action on the high seas ill all weather conditions, on a year-round basis. This process depends upon the use of seagoing platforms (FIG. 2+ FIG. 4) which themselves achieve stability in the presence of storms at sea, doing so through the selective extraction of wave energy. The selective wave energy extraction takes place in such a way that the prevailing ratio of sea height to swell height affecting a typical seagoing platform ((FIG. 2 or FIG. 4)) is reduced to a small fraction of the ratio of sea height to swell height which prevails at a distance from the platform. In short, this process and system stabilizes a plurality of seagoing platforms which support wind and wave energy conversion means, while simultaneously extracting and converting energy from the combined wind and wave action.

Measurements of Suspended Sediment Transport: Prototype Shorefaces

Abstract: Field measurements of local time-varying suspended sediment flux were obtained using rapid response velocity and sediment concentration sensors at a number of elevations under shoaling and breaking waves from similar water depths on both barred and non-barred shorefaces. Co-spectral analyses of velocity and concentration reveal that the net oscillatory transport across shore is dependant upon the relative contributions from: (i) wind waves (including swell) and (ii) low frequency waves (group-forced bound long waves). Time-averaged mean currents are invariably directed offshore (undertows) and increase in magnitude as waves break; coupled with increases in the average sediment concentration, this can result in sediment flux dominated by the mean transport. The overall transport balance (spatially and temporally) depends upon the relative contribution of each distinct transport component. The wind wave component is directed pedominantly onshore under the skewed shoaling waves; reversals can occur in response to bedform changes and the presence or absence of well defined separation vortices. The net transport can exhibit a distinct vertical structure reflecting changes in the contributions of opposing transport components at each elevation.

Numerical investigation of depth and current refraction of waves

Abstract: A numerical investigation of depth and current refraction of surface waves for several simple test cases is presented. The refraction scheme is incorporated into a third-generation wave prediction model. It models the effect upon wave propagation of the temporally and spatially varying sea surface elevations and mean currents associated with tides and storm surges. The scheme solves the transport equation for the wave action spectrum. The magnitude of bathymetric depth refraction is large for the lower frequency swell waves. The accuracy to which the proposed scheme can predict refraction is dependent upon the directional resolution of the spectrum. A directional resolution of at least 15° is required; the use of a higher directional resolution may be limited by computational resource restrictions. Current refraction effects are very significant for wave propagation across a simple current eddy. Refraction effects are not limited to just a turning of the waves, but also involve significant changes in the spectral shape. Some of the test results exhibit excessive numerical dispersion associated with the use of upwind differencing. The magnitude of this dispersion is much reduced by employing a simple hybrid differencing scheme in wave frequency-direction space. The high degree of numerical dispersion present in the model results is also a result of the nature of the simplified test cases. The magnitude of the numerical dispersion produced by the upwind differencing technique may not be significant when the model is used for storm simulation.

New Experimental Results on the Parameters Influencing Air-Sea Gas Exchange

Abstract: Gas exchange experiments from large linear and circular facilities are presented which provide some more insight into the influence of waves on the gas exchange process. The experimental data do not support models which closely link the gas exchange rate to the spectral density of capillary waves. The gas exchange rate is also not significantly influenced by swell. The key parameter is rather the instability of the wave field which can be expressed by the mean square slope of the waves.

Focusing of synthetic aperture radar ocean images with long integration times

Abstract: Synthetic aperture radar (SAR) images obtained in the SAR and X Band Ocean Nonlinearities: Chesapeake Light Tower (SAXON:CLT) experiment are processed with long integration times (6 s) and analyzed to study the effects of focusing. Two images with near-azimuth-traveling waves were chosen for the study. The first image consists of relatively short wavelength wind waves traveling in the same general direction as the aircraft. The second image consists of a long Atlantic swell traveling in the opposite direction to the aircraft. At these long integration times the image spectral intensities are found to be sensitive to the focus setting. The spectral intensity at the optimum focus is 400% of that at zero focus for the first image and 167% for the second image. The focusing curves for both images agree well with those predicted by a model developed by several groups and referred to here as the “consensus” model. This model predicts an optimum focus setting that is equal to one half of the effective phase speed of the dominant wave in the azimuth direction. The velocity bunching model underpredicts the optimum focus setting significantly. The study concludes that in long-integration-time SAR processing of surface waves, such as the spotlight mode, the image contrast is sensitively dependent on the focus setting and that the optimum focus setting is given by one half of the effective phase speed of the dominant surface wave.

Wave Propagation in Jettied Entrance Channels. I: Models

Abstract: A model for the propagation of sea and swell waves in a channel bounded by rubble‐mound jetties is presented. The model combines elements of earlier work on waves normally incident on a breakwater with a modified diffraction model based on the linear mild‐slope equation. For grazing‐angle (relative to the jetty axis) wave incidence, a parabolic approximation to the governing equation is used to obtain numerical solutions for monochromatic long waves propagating down the channel. An initially plane wave evolves into a spatially complex pattern as dissipation occurs along the jetties and energy is drawn from the channel interior by diffraction. Comparisons of the model to field observations are presented in a companion paper.