George Z. Forristall

Evolution and kinematics of a loop current eddy in the Gulf of Mexico during 1985

The large eddy that broke off from the Loop Current in July 1985 was the most extensively studied eddy ever to appear in the Gulf of Mexico. Other investigators have described its early evolution based on Lagrangian drifters and its later evolution using moored current meters in the western gulf. This paper provides additional insight on the early evolution of the eddy using results from air dropped expendable bathythermographs and air dropped expendable current profilers in early May, a hydrographic ship survey in mid July, and a detailed ship survey in August using expendable bathythermographs and a current profiler. The May survey established a center of circulation at about 26°N but showed that the eddy had not separated from the Loop Current. A maximum velocity of 171 cm/s was observed near the northern edge of the feature. The evidence suggests that a large elongated eddy then separated from the Loop Current and later split into two smaller eddies. The July hydrographic cruise showed a clear separation of the large eddy from the Loop Current to the southeast. Two weeks later, the August survey showed an asymmetric eddy, with the maximum surface current 178 cm/s south of the center of circulation and 132 cm/s to the north. A western eddy named Ghost Eddy then separated from an eastern eddy named Fast Eddy. Using the current profiles and data from the drifters, we constructed a simple kinematic feature model for eddies in the Gulf of Mexico.

Worldwide Measurements of Directional Wave Spreading

Abstract The directional spreading of waves is important for both theoretical and practical reasons. Enough measurements have now been made to draw conclusions about the behavior of wave spreading at sites in different climatic regimes. The measurements presented here of the directional spreading of fetch-limited waves agree in general with those of M. A. Donelan et al., but additional evidence is also found to support the conclusion of I. R. Young et al. that the spreading function is bimodal at high frequencies. The spreading factor ϕ is defined to be the square root of the in-line variance ratio defined by R. E. Haring and J. C. Heideman. This spreading factor gives an integrated measure of the degree of directional spreading in the wave spectrum and predicts the reduction in the in-line particle velocities under waves due to direction spreading. The value of ϕ is 1 for unidirectional waves and 0.707 for omnidirectional waves. For fetch-limited conditions, ϕ is essentially constant at 0.906. Results fr...

Irregular wave kinematics from a kinematic boundary condition fit (KBCF)

Abstract Calculation of the kinematics of random waves above the mean water line presents great difficulties. The kinematic boundary condition fit (KBCF) method approximates the solution through the numerical calculation of a potential function which fits the kinematic boundary condition on a specified surface. Comparisons with a high order regular wave show that the method converges to the true solution when the surface is accurately specified. Tests of the method for irregular waves were made with measurements from a laser-Doppler current meter in the Delft wave tank. These tests showed good agreement between theory and measurement when the surface evolution was calculated correct to second order. Stretched linear theory was also compared to the measurements. The stretched velocities were reasonably good when the phases of the component wavelets were measured but somewhat low when the phases were selected from a uniform distribution.

Wave Crest Sensor Intercomparison Study: An Overview of WACSIS

The Wave Crest Sensor Intercomparison Study (WACSIS) was designed as a thorough investigation of the statistical distribution of crest heights. Measurements were made in the southern North Sea during the winter of 1997-1998 from the Meetpost Noordwijk in 18 m water depth. The platform was outfitted with several popular wave sensors, including Saab and Marex radars, an EMI laser, a Baylor wave staff and a Vlissingen step gauge. Buoys were moored nearby to obtain directional spectra. Two video cameras viewed the ocean under the wave sensors and their signals were recorded digitally. The data analysis focused on comparisons of the crest height measurements from the various sensors and comparisons of the crest height distributions derived from the sensors and from theories. Some of the sensors had greater than expected energy at high frequencies. Once the measurements were filtered at 0.64 Hz, the Baylor, EMI and Vlissingen crest height distributions match quite closely, while those from the other sensors were a few percent higher. The Baylor and EMI crest distributions agreed very well with the statistics from second order simulations, while previous parameterizations of the crest height distribution were generally too high. We conclude that crest height distributions derived from second order simulations can be used with confidence in engineering calculations. The data were also used in investigations of crest and trough shapes and the joint height/period distribution INTRODUCTION Knowledge of the statistical distribution of crest heights given the wave spectrum is central to the problem of setting deck heights. Unfortunately, there is still considerable uncertainty about the form of this distribution. The empirical evidence is confusing, since different types of instruments have tended to give different results. The theoretical problem is difficult since it is essential to account for the non-linearity of the waves. The participants at the E&P Forum (1995) Workshop on Uncertainties in the Design Process felt that there was a need to

Statistics of Wave Crests From Models vs. Measurements

In this paper we first describe comparisons of the crest height distributions derived from the sensors (radars, wave staffs, laser) and from simulations based on 3D second order irregular wave models. These comparisons permit us to make conclusions on the quality of these models and to qualify the ability of some sensors to measure the crest heights accurately. In the second part two new parametric models of the crest height distributions are discussed and their superiority to standard parametric models is demonstrated.

The Use of Satellite Altimeter Data to Estimate the Extreme Wave Climate

Abstract Since 1986, nine years of wave data derived from satellites have been accumulated, and this database will expand dramatically in the next two years as two more satellites are added. Several researchers have begun using this data to estimate extreme value statistics for waves. However, one potential problem with satellite data is space–time resolution, which is a poor match for the scales of storms. Satellites only revisit a site once every 10–35 days, and their tracks are separated by 100–200 km. With this coarse sampling, the satellite may miss storms since they have characteristic length and time scales as short as a few hours and tens of kilometers. The purpose of this paper is to explore the impact of this undersampling on the calculated 100-yr wave height. This is accomplished by running Monte Carlo simulations of simplified but realistic storms sampled by a simulated satellite and site. The authors study the sensitivity of the calculated 100-yr wave to variations in storm type, radius, and ...

KINEMATICS IN THE CRESTS OF STORM WAVES

More than 150 tests have been analyzed in order to describe the dynamically stable profiles of rock slopes and gravel beaches under wave attack. Relationships between profile parameters and boundary conditions have been established. These relationships have been used to develop a computer program. This program is able to predict the profiles of slopes with an arbitrary shape under varying wave conditions, such as those found in storm surges and during the tidal period.This paper investigates the utility of winds obtainable from a numerical weather prediction model for driving a spectral ocean-wave model in an operational mode. Wind inputs for two operational spectral wave models were analyzed with respect to observed winds at three locations in the Canadian east coast offshore. Also, significant wave heights obtainable from the two spectral models were evaluated against measured wave data at these locations. Based on this analysis, the importance of appropriate wind specification for operational wave analysis and forecasting is demonstrated.

NEW INSIGHTS IN EXTREME CREST HEIGHT DISTRIBUTIONS (A SUMMARY OF THE 'CREST' JIP)

The objective of the CresT JIP was ‘to develop models for realistic extreme waves and a design methodology for the loading and response of floating platforms’. Within this objective the central question was: ‘What is the highest (most critical) wave crest that will be encountered by my platform in its lifetime?’ Based on the presented results for long and short-crested numerical, field and basin results in the paper, it can be concluded that the statistics of long-crested waves are different than those of short-crested waves. But also short-crested waves show a trend to reach crest heights above second order. This is in line with visual observations of the physics involved: crests are sharper than predicted by second order, waves are asymmetric (fronts are steeper) and waves are breaking. Although the development of extreme waves within short-crested sea states still needs further investigation (including the counteracting effect of breaking), at the end of the CresT project the following procedure for taking into account extreme waves in platform design is recommended: 1. For the wave height distribution, use the Forristall distribution (Forristall, 1978). 2. For the crest height distribution, use 2nd order distribution as basis. 3. Both the basin and field measurements show crest heights higher than predicted by second order theory for steeper sea states. It is therefore recommended to apply a correction to the second order distribution based on the basin results. 4. Account for the sampling variability at the tail of the distribution (and resulting remaining possibility of higher crests than given by the corrected second order distribution) in the reliability analysis. 5. Consider the fact that the maximum crest height under a complete platform deck can be considerably higher than the maximum crest at a single point.Copyright

West Africa Swell Spectral Shapes

Wave spectra measured at sites off West Africa are dominated by the constant presence of one or several swell wave systems. The West Africa Swell Project (WASP JIP) was carried out to propose and assess parametric models for the shap es of the swell components. Bias, variability, and dispersionof estimates are affected by the length/stationarity comprom ise of the record lengths and the window-tapering used to reduce th eir variability. In particular, shapes with sharp angles are st rongly smoothed, for instance a triangular peak would appear round and reduced by 15 to 25% with rectangular or Tuckey windowing. Models that consider each wave system individually, an d an arbitrary number of those, were preferred to global ones. Pa rtitioning of directional spectra is thus a prerequisite, an d needs to be tuned taking account some prior knowledge of the swell characteristics. Triangular, log-normal, Gaussian and Gl ennJonswap shapes were considered. Sampling variability make s it difficult to distinguish between those shapes as far as swell s are concerned. The models also indicate that the width of the spe ctrum in frequency should be inversely proportional to the pe ak frequency. Directional spreading width shows a similar tre nd.

THE WEST AFRICA SWELL PROJECT (WASP)

The responses of floating systems are sensitive to the detailed shape of the swell portion of the wave spectrum. Knowledge of swell is particularly important for sites off West Africa. The West Africa Swell Project (WASP JIP) was formed to analyze the available data on West African swell. Measurements were obtained from Shell, Ifremer, Chevron and Marathon. Hindcast data came from Oceanweather and the NOAA Wavewatch model. Sites ranging from Nigeria to Namibia were considered.Modeling the dispersion of swell over long distances indicates that the resulting power spectrum will have a triangular or lognormal shape. Sampling variability makes it difficult to distinguish between those shapes or Jonswap or Gaussian forms, but lognormal spectra generally provided good fits. The models also indicate that the width of the spectrum in both frequency and direction should be inversely related to the peak frequency. Fits to the measurements established detailed relationships for each location.Calculating the response of single degree of freedom oscillators to the measured and hindcast spectra produces response spectra which give the maximum response as a function of natural period and damping. Extreme values of system response can be calculated from the response spectra. The largest responses come from uni-modal spectra, and design spectra can be estimated by inflating them.Copyright