Showing papers on "Wave height published in 1994"

An improved model of the ocean surface wave vector spectrum and its effects on radar backscatter

Abstract: Images of the ocean surface taken with active microwave sensors often contain much information on near-surface and subsurface processes. However, their interpretations may depend on a detailed understanding of the physics of electromagnetic scatter. In scattering theory, the surface hydrodynamics enters the equations via (1) the probability distribution function for either wave heights or slopes, and (2) the two-dimensional wave height/slope autocovariance or its Fourier transform, the wave vector spectrum. This paper advances an improved model for the ocean surface wave vector spectrum based on recent work by M. A. Donelan, by M. L. Banner, and by B. Jahne and their collaborators. The model addresses the range of surface wavelengths from fully developed wind waves to the gravity-capillary region. For gravity-capillary waves, the spectral equation satisfactorily represents the observational data of Jahne et al. taken in tanks at large fetches, in the range from approximately 50 to 1500 rad/m to within the accuracy of the data. From the spectrum, the two-dimensional autocovariance of the sea surface is computed and correlation lengths and curvatures obtained. When used with a modification of Holliday's formulation of microwave radar backscatter from a Gaussian sea, it quantitatively reproduces observational cross section data taken at vertical polarization from aircraft and spacecraft over the open ocean, with differences from the field data having a mean of −0.2 dB and a standard deviation of 1.7 dB, The range of parameters for which satisfactory fits are obtained includes: wind speeds from 1.5 to 24 m/s; frequencies from approximately 5.5 to 35 GHz; and incidence angles from 0° to greater than 60°. For horizontal polarization, the scattering calculations fail rather badly for larger incidence angles, as do all theories based on the Kirchhoff approximation. Additionally, in spite of the incorporation of an anisotropic angular distribution of wave energy, the observed azimuthal variation of radar scatter is not captured, indicating that the source of that variation lies elsewhere.

Roll waves on a shallow layer of mud modelled as a power-law fluid

Abstract: We give a theory of permanent roll waves on a shallow layer of fluid mud which is modelled as a power-law fluid. Based on the long-wave approximation, Karman’s momentum integral method is applied to derive the averaged continuity and the momentum equations. Linearized instability analysis of a uniform flow shows that the growth rate of unstable disturbances increases monotonically with the wavenumber, and therefore is insufficient to suggest a preferred wavelength for the roll wave. Nonlinear roll waves are obtained next as periodic shocks connected by smooth profiles with depth increasing monotonically from the rear to the front. Among all wavelengths only those longer than a certain threshold correspond to positive energy loss across the shock, and are physically acceptable. This threshold also implies a minimum discharge, viewed in the moving system, for the roll wave to exist. These facts suggest that a roll wave developed spontaneously from infinitesimal disturbances should have the shortest wavelength corresponding to zero dissipation across the shock, though finite dissipation elsewhere. The discontinuity at the wave front is a mathematical shortcoming needing a local requirement. Predictions for the spontaneously developed roll waves in a Newtonian case are compared with available experimental data. Longer roll waves, with dissipation at the discontinuous fronts, cannot be maintained if the uniform flow is linearly stable, when the fluid is slightly non-Newtonian. However, when the fluid is highly non-Newtonian, very long roll waves may still exist even if the corresponding uniform flow is stable to infinitesimal disturbances. Numerical results are presented for the phase speed, wave height and wavenumber, and wave profiles for a representative value of the flow index of fluid mud.

Reflection of Ocean Surface Gravity Waves from a Natural Beach

Abstract: The energy of seaward and shoreward propagating ocean surface gravity waves on a natural beach was estimated with data from an army of 24 bottom-mounted pressure sensors in 13-m water depth, 2 km from the North Carolina coast. Consistent with a parameterization of surface wave reflection from a plane sloping beach by Miche, the ratio of seaward to shoreward propagating energy in the swell-sea frequency band (0.044–0.20 Hz) decreased with increasing wave frequency and increasing wave height, and increased with increasing beach-face slope. Although most incident swell-sea energy dissipated in the surf zone, reflection was sometimes significant (up to 18% of the incident swell-sea energy) when the beach face was steep (at high tide) and the wave field was dominated by low-energy, low-frequency swell. Frequency-directional spectra show that reflection of swell and sea was approximately specular. The ratio of seaward to shoreward propagating energy in the infragravity frequency band (0.010–0.044 Hz) v...

Wind Waves and Moveable-Bed Bottom Friction

Abstract: Effects of moveable-bed bottom friction for wave observations and wave modeling are investigated using a state-of-the-art bottom friction model. This model combines the hydrodynamic friction model of Madsen et al. with a moveable-bed roughness model based on Grant and Madsen. Analyzing the present model for idealized swell cases, it is shown that swell might result in wave-generated sand ripples. The large change of roughness corresponding to initial ripple formation results in a preferred wave height for swell, related to bathymetric scales as generally occur in shelf seas away from the coast. The corresponding wave-generated bottom roughness is not defined by the local wave conditions, but is related to the overall energy balance of the wave field. Sediment data thus is imperative for the interpretation of observed decay rates and friction factors for swell. For idealized depth-limited wind seas, near-bottom wave motion is expected to generate partially washed-out ripples and moderate sheet-flo...

Wave scattering by submerged porous disk

Abstract: Linearized potential wave theory is applied in the present paper to investigate the phenomenon of wave scattering by a submerged porous disk. By means of the eigenfunction expansion method, harmonic expressions of the velocity potential in terms of unknown constants are obtained in two subregions of the domain by taking into account the boundary conditions on the free surface, the porous disk surface, and sea bottom surface, as well as the Sommerfeld condition at infinity. These unknown constants are then determined by the matching conditions. Variation of the wave height around the disk and the wave load on the disk versus the dimensionless disk radius, the relative water depth, and the porous-effect parameter is discussed. It is found that the wave scattering by a disk includes a process of focusing wave energy near the rear of the disk for small dimensionless porous-effect parameters. An increase of the dimensionless porous-effect parameter decreases the wave height, and the behavior of a porous disk is similar to that of a wave absorber that may lead to \Isetdown\N for a large disk radius.

Evaluation of Depth-Limited Wave Breaking Criteria

Abstract: Numerous criteria exists for predicting incipient wave breaking. These criteria were verified with a limited number of data sets or under limited number of data sets or under limited beach and wave conditions, and confusion exists as to which of the many criteria to use. In the present study, a large database of wave breaking parameters from 17 laboratory experiments with plane slopes was complied to yield 416 data points, of which 409 were used in empirical correlations to develop predective breaking criteria covering the widest possible range available of beach and wave conditions. Selected criteria were evaluated and empirical coefficients adjusted by iterative best-fit procedures involving bin averaging of widely scattered parameter values to reveal functional dependencies. High-predictive capability was obtained using simple criteria expressed in terms of beach slope and wave steepness, and new criteria were developed for three breaking wave ratios or breaker indices: wave height to water depth at incipient breaking; incipient breaking wave height to deep-water wave height; and water depth at incipient breaking to deep-water wave height.

The sea state bias in altimeter estimates of sea level from collinear analysis of TOPEX data

Abstract: The wind speed and significant wave height (H(sub 1/3)) dependencies of the sea state bias in altimeter estimates of sea level, expressed in the form (Delta)h(sub SSB) = bH(sub 1/3), are examined from least squares analysis of 21 cycles of collinear TOPEX data. The bias coefficient b is found to increase in magnitude with increasing wind speed up to about 12 m/s and decrease monotonically in magnitude with increasing H(sub 1/3). A parameterization of b as a quadratic function of wind speed only, as in the formation used to produce the TOPEX geophysical data records (GDRs), is significantly better than a parameterization purely in terms of H(sub 1/3). However, a four-parameter combined wind speed and wave height formulation for b (quadratic in wind speed plus linear in H(sub 1/3)) significantly improves the accuracy of the sea state bias correction. The GDR formulation in terms of wind speed only should therefore be expanded to account for a wave height dependence of b. An attempt to quantify the accuracy of the sea state bias correction (Delta)h(sub SSB) concludes that the uncertainty is a disconcertingly large 1% of H(sub 1/3).

Infrared radiance and solar glint at the ocean-sky horizon.

Abstract: An analytic model is developed for the mean and clutter infrared radiance emitted from the ocean surface near the horizon and in the presence of solar glint. The model is based on the identification of a characteristic facet dimension over which the ocean surface is essentially flat. Fluctuations in the facet orientation generated by the water wave motion are modeled by a parameterized wave height power spectral density that provides the two orthogonal wave slope variances. The mean and root-mean-square facet radiances are calculated with Gaussian probability-density functions for the wave slopes. One can determine the number of facets within the field of view of a single detector by estimating the exposed ocean area and dividing by the facet area. This estimation takes into account shadowing effects of the swell wave, the swell wavelength, and the transverse detector field of view. The number of exposed facets together with the central-limit theorem permits computation of the radiance clutter as a function of look-down angle below the horizon. Vertical radiance profiles, parameterized by the azimuthal offset from the solar position, are calculated over a sensor look-down angle range of ±50 mrad about the horizon. The results of this analysis are compared with infrared radiance measurements of the ocean surface near the horizon and in the presence of solar glint. Agreement between the measured and calculated values of the mean and clutter radiances is good.

Correlated environmental corrections in TOPEX/POSEIDON, with a note on ionospheric accuracy

Abstract: Estimates of the effectiveness of an altimetric correction, and interpretation of sea level variability as a response to atmospheric forcing, both depend upon assuming that residual errors in altimetric corrections are uncorrelated among themselves and with residual sea level, or knowing the correlations. Not surprisingly, many corrections are highly correlated since they involve atmospheric properties and the ocean surface's response to them. The full corrections (including their geographically varying time mean values), show correlations between electromagnetic bias (mostly the height of wind waves) and either atmospheric pressure or water vapor of -40%, and between atmospheric pressure and water vapor of 28%. In the more commonly used collinear differences (after removal of the geographically varying time mean), atmospheric pressure and wave height show a -30% correlation, atmospheric pressure and water vapor a -10% correlation, both pressure and water vapor a 7% correlation with residual sea level, and a bit surprisingly, ionospheric electron content and wave height a 15% correlation. Only the ocean tide is totally uncorrelated with other corrections or residual sea level. The effectiveness of three ionospheric corrections (TOPEX dual-frequency, a smoothed version of the TOPEX dual-frequency, and Doppler orbitography and radiopositioning integrated by satellite (DORIS) is also evaluated in terms of their reduction in variance of residual sea level. Smooth (90-200 km along-track) versions of the dual-frequency altimeter ionosphere perform best both globally and within 20 deg in latitude from the equator. The noise variance in the 1/s TOPEX inospheric samples is approximately (11 mm) squared, about the same as noise in the DORIS-based correction; however, the latter has its error over scales of order 10(exp 3) km. Within 20 deg of the equator, the DORIS-based correction adds (14 mm) squared to the residual sea level variance.

Experimental study of three-dimensional wave breaking

Abstract: The present study investigates two cases of three‐dimensional wave breaking. In the first case, the wave field contains a single frequency with a uniform angular spreading within a given range {-α,α}. The wave field of the second case consists of a number of frequencies with a uniform angular spreading applied to each frequency. In both cases, the waves are designed such that the wave energy is focused at a given point. Surface elevation in the focusing region is recorded and parameters such as the breaking‐wave height and the crest‐front steepness are calculated. It is shown that the wave height, crest elevation, crest‐front steepness, and vertical asymmetry factor, at breaking, are strong functions of the angular spreading, while the crest‐rear steepness and horizontal asymmetry factor are little affected by the angular spreading. In general, the greater the spreading angle, the bigger are the breakers. It is hoped that the results obtained here will provide a useful preliminary assessment of the import...

Potential Energy in Steep and Breaking Waves

Abstract: We find that the RMS wave height (square root of the potential energy) rather than peak-to-peak wave height is a better experimental and analytic criterion for determining when a regular, two-dimensional deep-water wave will break. A spectral algorithm for two-dimensional potential flow is developed and used to compare breaking onset criteria for energy input from (i) converging sidewalls, (ii) a submerged disturbance, and (iii) wave focusing. We also find that wave-breaking criteria (potential energy or the more classical peak-to-peak wave height) are a function of the rate of energy input. Large plunging waves occur when energy input rates are large. As energy input rates become smaller there is a smooth transition to smaller spilling waves. The various energy input methods show similar breaking trends in the limit as the energy input rate becomes small - waves break when the potential energy becomes approximately 52 % of the energy for the most energetic Stokes wave, with the formation of a singularity immediately before the crest. The effects of wave modulation and reflection are briefly discussed and shown not to affect the potential energy breaking criterion significantly. The experimental scatter of the RMS wave height is shown to be half that of wave steepness during incipient breaking in wave packets.

Integral Equation Model for Wave Propagation with Bottom Frictions

Abstract: An integral equation method is developed to calculate wave propagation and runup in a two‐dimensional wave channel. First, the problem is formulated as a potential flow with nonlinear free‐surface boundary conditions. The effects of bottom friction are included in the model via a boundary‐layer approximation. Numerical solutions are obtained for the maximum runup heights of solitary waves and cnoidal waves on a constant slope. Numerical solutions are compared with available experimental data. A very good agreement is observed. The maximum runup height of a cnoidal wave is larger than that of an equivalent sinusoidal wave. However, the runup height of cnoidal wave is smaller than that of solitary wave with the same wave height. The runup height of cnoidal waves is not a monotonic function of the incident wavelength. Numerical solutions for the maximum runup heights confirm that the bottom frictional effects are important when the slope is less than 20°.

On the use of the Donelan wave spectral parameter as a measure for the roughness of wind waves

Abstract: The roughness of the sea surface has been investigated and described by many researchers. Up to now nearly all researchers considered the roughness to be a function of at least the wind speed and possibly of parameters which are related to the wave field such as significant wave height or wave age. This study is an investigation of how far the equilibrium range of the wave spectrum described by a characteristic parameter such as the Phillips' constant αP can define the roughness of wind waves. Comparing the Donelan and Toba expressions for the description of a wave spectrum, one could conclude that the Donelan parameter αD, a parameter similar to the Phillips' constant αP, is proportional to the nondimensional roughness of the waves. The KNMI-HEXOS data set is used to verify the hypothesis. It is concluded that the measurements do not contradict the suggested relationship between the nondimensional roughness and the Donelan parameter αD. Linear regression however suggests a stronger than linear dependence of the nondimensional roughness on the Donelan parameter.

Wave-energy distribution and hurricane effects on Margarita Reef, southwestern Puerto Rico

Abstract: Wave measurements at Margarita Reef in southwestern Puerto Rico show that wave height decreases as waves travel across the forereef and into the backreef. Wave spectra reveal the presence of two wave trains impinging on the reef during the study: trade-wind waves and locally generated seas. Significant wave height calculated from the spectra show an average reduction of 19.5% from 20- to 10-m isobaths and 26% from 20- to 5-m isobaths. The significant wave height decreases an average of 82% for waves traveling across the reef crest and into the backreef. Wave-energy reduction is 35% from 20- to 10-m isobaths and 45% from 20- to 5-m isobaths. Energy loss across the reef crest is 97% which translates into the formation of strong across-the-reef currents capable of moving coarse sediment. Refraction diagrams of waves impinging on the reef from the SE provide a display of wave energy distribution around the reef. The transmission coefficients calculated for trade-wind waves and locally generated seas have means of 18% and 39%, respectively. A wave height model with negligible energy dissipation, produces wave height estimates that are, in general, within the ±15% error bands. Results of wave-energy changes from this study were applied to waves representative of hurricane conditions at the reef. Aerial photographs of the reef before and after the passage of hurricanes were compared to assess the reef changes. Changes observed in the photographs are interpreted as products of sediment transport by hurricane-generated waves. The patterns of change agree with the refraction diagrams suggesting that waves were the main agents of change at margarita Reef during severe storms.

Variational Wave Data Assimilation in a Third-Generation Wave Model

Abstract: The adjoint of the wave model WAM, which runs operationally performing global wave forecast at the European Centre for Medium-Range Weather Forecasts, has been constructed. In this model, the nonlinear interactions are described by the discrete interaction approximation of Hasselmann et al., and the wind input and the dissipation are consistent with the theory of Janssen. The drag coefficient depends not only on the wind speed, but also on the wave-induced stress, reflecting in this way the dependence of winds on waves. The adjoint scheme constitutes a new (the first variational) method to assimilate arbitrary wave data into the WAM. Up to now, this had been done using an optimal interpolation technique (sequential method), and only for wave heights. The new assimilation scheme has been tested with a one-gridpoint version of the WAM. Assimilating only wave data-significant wave height and mean wave direction—is sufficient to reconstruct all wind fields, significant wave height, and two-dimensiona...

Deep Ocean Wave Measurements Using a Vertically Oriented Sonar

Abstract: A vertically oriented 200-kHz sonar is used to make estimates of (one-dimensional) surface wave spectra in the deep ocean. Two independent approaches are used to determine wave spectra from this system: a direct measurement of range to the surface and the vertical velocity estimate of the surface. Estimated wave spectra are compared with observations from a Datawell Waverider buoy positioned directly above the acoustic instrument. Comparisons are provided for relatively calm conditions and also during a period of mixed swell and wind waves forced by a 13 m s−1 wind. Wave spectra from the three estimates appear qualitatively similar and agree to within 10% in total wave energy density.

Hindcast Wave Information for the U.S. Atlantic Coast

Abstract: The Coastal Engineering Research Center (CERC) calculated wave information along the U.S. Atlantic coast for the period 1956-1975 in the late 1970’s. Calculations were made with a numerical wave hindcast model using wind speeds and directions calculated from atmospheric surface pressure records and ship observations. Measured wind and wave data became available in the 1980's from a number (If buoys located off the Atlantic coast. Comparisons of mean wind and wave parameters were made between the measurements of the 1980's and hindcast results for 1956-1975 assuming the mean wind and wave climates for the different time periods were the same. Mean wind climates compared well, but mean wave climates differed. The skill of recently developed wave hindcast models indicates that the hindcast wave results could be improved by using present model technology with the previously calculated winds. Comparison of hindcast results, using present technology to measurements for the year 1990 show little bias with respect to wave height and peak period at coincident locations and times. Typical root mean square differences are 0.5m and 2-3 sec for wave height and peak period respectively. The hindcast for 1956-1975 is improved by using higher resolution numerical grids to better represent the U.S. coastline, continental shelf bathymetry, and offshore islands and shoals in the Bahamas region and by using a more accurate wave model. Results are presented at locations and in a format appropriate for present coastal engineering studies.

Wave Height From Deep Water Through Breaking Zone

Abstract: For a large series of hydraulic model tests performed at Queen’s University, wave heights from deep water through the breaking zone can be described quite simply by linear shoaling, refraction, and friction, combined with a breaking criterion and one single-wave-decay calculation based on excess energy. This wave-decay model was verified with other hydraulic-model tests and applied to field results. Comparison with prototype results showed several inconsistencies. The field data indicated that nonlinear shoaling is sometimes required while linear shoaling is perfectly adequate for other cases. It was not possible to determine clearly when to use nonlinear shoaling. The energy dissipation rate for some field data was similar to that found in the hydraulic models, while for other field data sets the energy dissipation rate was much smaller. The difference in behavior of seemingly similar data sets cannot be readily explained by common parameters such as wave steepness and surf similarity. The field data also showed the need to incorporate spectral saturation in the calculations.

Evidence of surface wave enhancement in the southwest Indian Ocean from satellite altimetry

Abstract: Wave height data from Geosat over the period November 1986 to February 1989 were used to survey the occurrence of wave amplification/attenuation in the southwest Indian Ocean More than half of the wave profiles that were inspected revealed some enhancement in the Agulhas Current, with 17% of the profiles showing fractional amplification of more than 40% (relative to the background wave height) Other aspects that were considered included attenuation of wave height in the shelf region and the characterization of the Agulhas Return Current by wave height variations