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Paper presented at the Modelling the Offshore Environment: Proceedings of an International Conference, April 1–2, 1987
Paper presented at the Modelling the Offshore Environment: Proceedings of an International Conference, April 1–2, 1987
Paper presented at the Modelling the Offshore Environment: Proceedings of an International Conference, April 1–2, 1987

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Proceedings Papers

Publisher: Society of Underwater Technology

Paper presented at the Modelling the Offshore Environment: Proceedings of an International Conference, April 1–2, 1987

Paper Number: SUT-AUTOE-v12-343

... of momentum between the current at different depths. Usmg a theorehcal wmd-wave drectional

**spectrum**, results are presented whch are m reasonable agreement wth observahons The model WIU be suitable for mcorporahon mto three-dunensional numencal hydrodynarmc models for ocean current slrnulahon. Advances m...
Abstract

For realistic numerical modelling of ocean currents with the zone of wave influence, the effect of the waves on the current should be accounted for in a dynamically consistent manner. The following phenomena are relevant: The wave-induced Stokes drift, which is a result of the water particle orbits due to the wave motion not being closed. The transfer of momentum from the wind into the waves, instead of Into the current. The transfer of wave momentum to the current as a result of wave dissipation. The vertical transfer of momentum due to turbulent motions. The effect of the Earth's rotation. This includes a Coriolis force due to the wave-induced Stokes drift. A theoretical model has been developed which takes account of the above effects. It uses a perturbation expansion technique in a Lagrangian coordinate system (a coordinate system m which a water particle's coordinates remain constant throughout a wave cycle). Vertically varying eddy viscosities are used to parameterise both the wave dissipation and the turbulent transfer of momentum between the current at different depths. Using a theoretical wind-wave directional spectrum, results are presented which are in reasonable agreement with observations. The model WIU be suitable for incorporation into three-dimensional numerical hydrodynarmic models for ocean current simulation. INTRODUCTION Engineering requirements The current near the sea surface has an influence on offshore oil-related activities m the following ways: it gives rise to an extra force on offshore structures and other objects in the water m addition to the wave forcing, and it causes oil slicks and other forms of pollution near the sea surface to move around. Eulerian and Lagrangian mean currents There are basically two ways of defining the current with the wave zone. The first way is to take a vector average (over many wave cycles) of the fluid velocity at fixed points m space, to obtain the Eulerian mean current The second way is to follow water particles for a tune corresponding to many wave cycles: the average velocity over such a tune period 1s the Lagrangian mean current. The vector difference between the two types of current is the Stokes drift, which is dependent just on the wave field and can be calculated directly from the directional wave spectrum. Forces on structures due to near-surface currents The current causes of its own accord forces on objects m the water, but its most important forcing effect is a result of the combination of wave and current forces, since the orbital velocities in large waves are generally considerably larger than the maximum current velocities, and the drag force on an object m the water has a non-hear dependence on the fluid velocity, being in general proportional to the square of the velocity The current which is relevant for calculating forces on structures is the Eulerian mean current, since the Stokes drift part of the current does not given rise to any extra forces over and above those due to the wave motions themselves.

Proceedings Papers

Publisher: Society of Underwater Technology

Paper presented at the Modelling the Offshore Environment: Proceedings of an International Conference, April 1–2, 1987

Paper Number: SUT-AUTOE-v12-089

... shallow water december 1985 wave hmdcast model hiswa wave data wave model shallow-water wave model deep water area 4 gnd wave measurement

**spectrum**Wave Data in Shallow Waters Provided by the HISWA Numerical Model P. -E. S0r&, P. Schplberg and A. Thendrup, OCEANOR (Oceanographic Company...
Abstract

Environmental investigations supporting site selection and providing design values have to consider the wave climate as one of the important factors. In most cases the available time does not allow for wind and wave measurements over the time span required to give reliable statistics. Alternative studies are thus necessary, utilizing the sparse amount of data collected in the vicinity of possible sites combined with long-term wind and wave statistics collected at some distance in deep water major efforts during recent years to develop models describing the energy redistribution as the wave approaches shallow waters have resulted in more and more sophisticated models. One of these is the shallow-water wave model HISWA. A brief description of HISWA is given, together with some practical information demonstrating how o use the model. HISWA has been extensively used to compute the wave conditions in the coastal areas of mid-Norway. Some selected cases are given to test the model, illustrating how to choose the input data. The experience so far is that the calculated results deviate within 10% of the measured significant wave height close to potential sites. The mean wave period is over-estimated in parts of the integration area. These encouraging results strongly suggest extensive use of the model combined with short-term wind and wave measurements, providing more reliable wave data for various purposes. INTRODUCTION Increased human activity both in the open sea and in coastal waters results in an increasing need for environmental data for design purpose. In this chapter we will concentrate on a method to provide shallow-water data. Wave data for shallow waters are needed for the construction and design of, e.g., harbours and terminals, and fish farms, and for studies of areas for pipeline landfall. Due to the great number of physical processes influencing the wave conditions in shallow water, the various wave-measuring programs carried out along the Norwegian coast do not give sufficient wave data for the above-mentioned purposes. Some wave-measuring programs have been carried out in shallow waters too, but these data are normally valid within a very limited area. Hence only dedicated wave measurements or wave modelling can provide sufficient wave data for the various purpose mentioned. If wave measurements are chosen, these will have to continue for quite a while to give sufficient data coverage to give a satisfactory statistical estimate of design values. Normally, there is not enough time or money available to carry out a sufficient wave-measurement program, especially during the early planning stages. Wave modelling therefore ranks as an interesting alternative. Using wave models, wave data both for planning and for design and construction purposes could easily be provided. In this way, the sparse amount of data collected in the vicinity of interesting areas combined with long-term wind and wave statistics collected at some distance in deep water can be combined. OCEANOR has gathered encouraging experience using the HISWA numerical shallow-water wave model, and believe that the use of this model will support various planning and design need with necessary wave data in a most efficient way.

Proceedings Papers

Publisher: Society of Underwater Technology

Paper presented at the Modelling the Offshore Environment: Proceedings of an International Conference, April 1–2, 1987

Paper Number: SUT-AUTOE-v12-073

... energy to the water m dlrections on either side of the mean hection, which Itself may fluctuate dunng the penod of wave generahon. To mcorporate t h s effect m the model, components of the total wave directional

**spectrum**are calculated for vanous dlrections on elther side of the mean. A welghted average...
Abstract

There are a considerable number of wave records around the coastline of the United Kingdom and elsewhere, but all too often the engineer is faced with a short data set which is situated too far from his particular area of interest to be of use. With this in mind, a wave predication model has recently been developed at Hydraulics Research. It has wide applicability, is easy to use and can produce a long data sequence without the need for large computer storage. The techniques used in the model are not sophisticated but they do allow the effective use of any wave data which may be available. The model, called HINDWAVE, can estimate the mean annual wave climate at a site or produce a time-history of wave height, period and direction. It can be used in the absence of measured wave data or, equally well, it can extend an existing short wave record to a longer, more representative period. The model does not require a complex description of the wind field; instead it uses hourly averaged wind speeds and directions from the nearest coastal anemometer station. The results may be produced hour by hour, month by month, or as seasonally averaged values. A certain amount of calibration can be done by adjusting the land-based wind speeds for use over the sea. With quite minor changes, i.e. an increase in land-based data of say 10%, very good agreement with measured wave data is usually obtained. INTRODUCTION The HINDWAVE model was developed to meet the needs of coastal engineers requiring large wave data sets at specific sites, quickly, and at low cost. The input to the model consists of two sets of variables, one representing the shape of the wave generation area and the other the hourly averaged wind velocities in that area. The programs are written in an efficient way enabling long sequences of wind data to be processed rapidly. The model may be used on its own in order to estimate a directionally dependent wave climate distribution, or it may be used in conjunction with measured wave data. Alternatively, it can be calibrated against wave recordings, and then used at other nearby locations and with other or longer periods of wind data. For example, this procedure can be used to put a single year of wave records into a longer-term perspective, or to extend the effective length of sequences of wave records, or to predict wave conditions at a point nearby which has a different exposure to wave action. In addition, the model adds the important wave direction parameter which is not usually available with wave measurements. This is particularly valuable for coastal or harbour engineering projects. The model has been used successfully on about 20 recent studies at various sites around the British coast, and in several cases has been calibrated and proved against measured wave data. It has been used in conjunction with a refraction model, a beach plan shape model, and a method for extremes analysis.

Proceedings Papers

Publisher: Society of Underwater Technology

Paper Number: SUT-AUTOE-v12-117

... that should be applied dumg the use of second- and thlrd-generation wave models. The good results obtamed dumg hgh wave condltlons are the result of the hgh drectlonal resolution of the model coupled wth the use of a reahstlc formula for the energy m the saturated wave

**spectrum**. INTRODUCTION Hydrodynamic...
Abstract

A ray tracing model that includes the effects of refraction in shallow water has been developed to allow the evaluation of a set of empirical formulae for the prediction of directional wave spectra. The formulae have been tested by hindcasting the waves at eight offshore sites in the North Sea during WHIST storms 3, 5 and 6. At the peak of a storm the model predicted significant wave heights that agreed with observed values to within the ±10% accuracy suggested by the Department of Energy. Although the model is first-generation and cannot resolve non-linear interactions, it is computationally efficient and may be suitable for many engineering applications. In particular, it could be used in sensitivity tests for determining the grid spacing and coastal wind correction factors that should be applied during the use of second-and third-generation wave models. The good results obtained during high wave conditions are the result of the high directional resolution of the model coupled with the use of a realistic formula for the energy in the saturated wave spectrum. INTRODUCTION Hydrodynamic models of the currents and surface elevations associated with tides and surges can give results of high accuracy (e.g. Heaps and Jones, 1979). This is because the physics of the problem is well understood, and the equations that describe the motion contain only a relatively small amount of empiricism (with empirical formulae being used to represent the surface and bottom stresses, and the vertical eddy viscosity in the case of a three-dimensional model), in contrast wave models contain a fair degree of empiricism. For example, the BMO model (Gloding 1983), which is a second-generation model, attempts to take account of the effect of the non-linear interactions by replacing the wind-sea part of the spectrum by a JONSWAP spectrum with the same energy. Consequently, the model results depend not only on the empirical formulae used to describe the wave growth, but also on the empirical constants that appear in the JONSWAP spectrum. The lack of our understanding of the true physics of wave generation is reflected in the predictions made by wave models which can show appreciable errors. The Department of Energy has suggested that a wave model should be accurate to±10% of peak wave height, and existing second-generation models have been evaluated by applying them to the WHIST storms (Department of Energy, 1986). Recent wave models (the third-generation models) are becoming even more complex as they attempt to solve explicitly the non-linear interactions, thus necessitating the use of high-powered computers. Ultimately, this may lead to a better understanding of the physics of wave generation, but it limits the work to those researchers who have access to parallel processing computers, and the computational costs are likely to be high. An alternative approach is to accept the empirical nature of much wave modelling, and to investigate the use of purely empirical methods for the practical prediction of wave spectra. This may not advance our understanding of wave dynamics, but may produce practical models that will be suitable for many engineering problems.

Proceedings Papers

Publisher: Society of Underwater Technology

Paper Number: SUT-AUTOE-v12-181

... procedure penod verification procedure wave propagation model

**spectrum**amphtude field data dalrymple shoal laboratory data whch wave height gnd spacmg refidif 1 wavelength usmg offshore bathymetry A Verification Procedure for Wave Propagation Models C. J. Martzn, Marex...
Abstract

The important of verifying the calibrating numerical models, before using them to predict design criteria, is well known. A verification scheme for wave refraction models has recently been developed. Two of the latest wave refraction models have been acquired and tested. The first is based on a parabolic approximation method, using a finite difference technique, which includes the effects of combined refraction/diffraction, wave-current interaction, partial and full wave breaking and non-liner effects. The second is a simpler model based on the wave action equations, and includes the effects of wave refraction, shoaling, partial breaking and bottom friction. The first model is most useful over coastal areas (up to 200 km 2 ) but is relatively expensive to run compared with the wave action model. The second model, although less rigorous in its solution of the physical equations, is more useful over much large areas (up to 200 km 2 ). The method has been carefully designed to test all aspects of model performance. This includes : Verification against laboratory data (where traditional ray techniques break down) Sensitivity tests against hypothetical bathymetries for several input/boundary conditions. Verification against two field data sets, both including the measurement of directional spectra This chapter outlines the test procedure and presents the results using the two models described above. It also highlights area where development work on the models was necessary, and where future work is required. Development of the modelling techniques is continuing. INTRODUCTION The designer of offshore and coastal structures requires local estimates of wave forces and elevations, while often the only available wave data are from offshore locations. It then becomes necessary to propagate waves from regions where they are known to areas of design interest. Numerous techniques have been developed to calculate the transformation of waves as they propagate from offshore generation areas to the coast. For a single wave train, ray tracing has been the most popular technique (e.g. Griswold, 193). This technique has two major disadvantages the wave rays do not often provide a uniformly dense grid of wave heights and directions; and the presence of caustics makes the interpretation of the results difficult. Recently, wave propagation models of various levels of sophistication have been produced. For example, in this project, a wave action model and a parabolic model, both of which produce wave information on a rectangular grid, have been examined. The aim of this study was to design and develop a verification procedure that could be systematically applied to any wave propagation model, in order to provide a thorough examination of the model's performance. The procedure, as developed, identifies the model's ability to include the relevant physical processes, such as wave refraction, diffraction, shoaling, wave breaking, non-linear effects and frictional attenuation. An end-product of the verification procedure is a guide to the setting-up and use of the model, including the selection of grid spacing, the value of variable coefficients, and the applicability of the model to various types of bathymetry.

Proceedings Papers

Publisher: Society of Underwater Technology

Paper Number: SUT-AUTOE-v12-133

... spectra amphtude phase

**spectrum**standmg second-order force sensitivity underwater technology wave**spectrum**platform sequence regular wave functlon**spectrum**wth penod subsea system frequency resolution response**spectrum**whch dnft force waste management The Sensitivity...
Abstract

This chapter examines the sensitivity of structure loads and responses, particularly those of compliant and dynamic systems, to changes in the environment model. The main parameters investigated are those associated with the wave: the use of regular and irregular wave models, long- and short-crested waves, sensitivity to wave spectral truncation frequency and resolution, and to the choice of the amplitude and phase spectra. The extraction of extreme loads from irregular wave data poses special problems. Low-frequency resonant systems, such as moored vessels or tension leg platforms, are often sensitivity to wave grouping and second-order processes, and to the way in which these are modelled. FIXDED STRUCTURES The choice of environmental modelling parameters is linked to that of design philosophy. Conventional jacket structure design does not try to represent the environment in a realistic way; indeed, the attempt to improve ‘realism’ may be dangerous, perhaps reducing an importing source of conservatism in the process. This approach aims to produce a safe and economic structure without unnecessary design effort, replying heavily on post experience. The traditional design package therefore has to seen as a single entity, some aspects of which are conservative, and others not so. It is this unity that makes it difficult to bring in new information, or to reconcile the design package with research data. The traditional approach is gradually being challenged by reliability-based methods, where parameter variations are considered as part of the design, and the whole approach may be reconciled more easily with research data and with the real sea. Some of the sources of conservatism or otherwise in the traditional design process will now be discussed, and the results indicate a few of the difficulties that may arise in introducing a more realistic model. Morison's equation Loads on a conventional jacket structure are invariably calculates using Morison's equation. The force per unit length on a structural member is expressed as the sum of drag and inertial components: Formula available in full paper Where u andû are components of fluid velocity and acceleration normal to the member, p is the water density, D and A are the member's effective diameter and cross-sectional area, and C d' , C m are drag and inertia force coefficients. Over the years, there has been much controversy among researchers about the values of C d and C m . Research has shown that these values depend on a complex range of parameters such as the Keulegan-Carpenter and Reynolds number, type and effective height of marine fouling- with C d reaching as high as 1.9 with only a small amount of marine roughness. Design practice has tended to ignore much of this variability. Very low values of the drag coefficient, in the range C d = 0.6–.08, continue to be used because there are other compensating factors in the design process which provide sufficient conservatism. One such factor lies in the research data itself: high values of C d tend to be associated with low value of C m representing a change in phase of the force on an individual member rather than a change in its magnitude.