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Gulf of Mexico Shallow-Water Wave Heights and Forces OTC 4586 Gulf of Mexico Shallow-Water Wave Heights and Forces Downloaded from http://onepetro.org/OTCONF/proceedings-pdf/83OTC/All-83OTC/OTC-4586-MS/2032343/otc-4586-ms.pdf by guest on 28 September 2021 by R.G. Bea, PMB Systems Engineering Inc.; N.W. Lai, Woodward Clyde Consultants; A.W. Niedoroda, Dames & Moore; and G.H. Moore, McMoRan Offshore Exploration Co. This paper was presented at the 15tb Annual OTC in Houston, Texas, May 2-5, 1983. The material is subject to correction by the author. Permission to copy is restricted to an abstract of not more than 300 words. ABSTRACT tinental Shelves. General guidelines for setting environmental criteria (e.g., API RP 2A) have Storm waves tend to be attenuated by a variety been developed in the past to provide broad ranges of processes as they propagate across the relatively of possible design values. These guidelines, shallow depths of the Texas and Louisiana Continental however, have generally neglected detailed considera­ Shelves. Present shallow water wave force guidelines tions of shallow water effects on storm waves. contained in API RP 2A were developed as a very simplified, judgment-based interpolation into water In late 1981, McMoRan Offshore Exploration depths less than 300 feet. Shallow water design Company initiated a study of environemtnal criteria wave force levels adopted by many companies generally which could be applied to platforms in relatively reflect the conservative adjustments made after shallow depths in the western Gulf of Mexico. many platform losses and significant damages were This study was organized in two parts. The objective incurred during Hurricane Hilda in 1964. Subsequent of the first part was to develop and calibrate tests of the new generation of shallow water platforms a procedure for determining the amount of storm by other hurricanes indicates acceptable performance wave height reduction due to dissipation of wave of the structures. However, costs associated with energy through fluid shear stresses acting on these structures, as well as results of some of the seafloor of the continental shelves. The the more recent studies, indicate that there may prime consideration was wave attenuation due to have been some degree of over-correction in the the effects of bottom friction, although some process of revising the industry's shallow water attention was given to the effects of refraction, criteria after Hurricane Hilda. shoaling, energy loss due to flow within the bottom sediments, and other effects. The purpose of this study was to develop a rational procedure for establishing environmental The second part of this study consisted of design conditions for platforms in relatively shallow a wave force parameterization procedure. The water in the Gulf of Mexico. This paper discusses objective of this part of the study was to quantify two parts of this study. The first part is that the recurrence intervals of storm-related events of developing and calibrating a procedure for determin ngn terms of the resultant base shear and overturning the amount of storm wave height reduction due to moments on typical 8-leg, steel jacket structures dissipation of wave energy through fluid shear stresse in representative areas of the western Gulf of acting on the seafloor of the Continental Shelves. Mexico. A study of the base.shear and overturning The second part is that of developing and justifying force data with the input environmental data on a wave force parameterization procedure to quantify waves and currents, resulted in the development wave force levels on typical jacket structures in of a series of guidelines for determining the the Gulf of Mexico. environmental loadings on future platforms to be sited in these regions. INTRODUCTION This paper has been released by McMoRan as The development of a rational system for esta­ general interest and to suggest the need for future blishing environmental design criteria for platforms research to develop more definitive shallow water in relatively shallow water in the Gulf of Mexico criteria. requires an investigation of the phenomenon related to storm wave propagation over Continental Shelves. DEEP WATER WAVES It is known that storm waves tend to be attenuated by a variety of processes as they are driven across The maximum wave height which can reasonably the shallow depth of the Texas and Louisiana Con- be expected to affect a structure during its life­ time is one of the most critical factors which References and illustrations at end of paper. influences the design of an offshore structure. 49 2 GULF OF MEXICO SHALLOW WATER WAVE HEIGHTS AND FORCES OTC 4586 The estimation of such maximum wave occurrences SHALLOW WATER WAVE HEIGHT ATTENUATION in the future must reflect the past history of storm wave occurrences. Thus, long-term historical data The maximum wave height statistics discussed bases are required to estimate these maximum wave in the earlier section have been restricted to height occurrences with meaningful reliability. deep water regions where the waves do not feel the effect of the ocean bottom. As the waves Characterizations of historical storm conditions propagate into shallow waters, the wave heights can be either based on measured or hindcast data. change due to wave transformation and bottom dissipa­ However, since only relatively small amounts of tion of wave energy. The wave transformation measured wave data are available in the Gulf of in shallow waters includes shoaling and refraction Mexico, hindcasting techniques are necessary to effects. The wave energy dissipation mechanism extend the data base. A hindcast is the reconstruc­ may consist either of bottom friction, percolation tion of an historic event or series of events to or soft-bottom interaction, or combinations of yield certain meteorological and/or oceanographic the three and other unknown factors. Downloaded from http://onepetro.org/OTCONF/proceedings-pdf/83OTC/All-83OTC/OTC-4586-MS/2032343/otc-4586-ms.pdf by guest on 28 September 2021 data for the study area. Through the reconstruction of these events, a series of data can be generated. Shoaling A statistical analysis can be conducted with the hindcast data to provide estimates of future occur­ As a wave propagates from deep to shallow rences. water, its height and length change. The transformed wave height, H, at shallow water dept relative The deep water maximum wave conditions obtained to the original deep water wave height, H , can in this study are based on historical hindcast studies be computed from: 0 of Gulf of Mexico hurricanes. The hindcast deep water wave heights are shown in Figure 1. The probabilistic distribution of expected deep water maximum wave heights has been based on where V is the group velocity of the waves, b results published by Bea (1974), Ward, et al (1978), is the distance between pairs of adjacent wave and Haring and Heideman (1978). The 100-year deep rays, and the subscript o refers to deep water water expected maximum wave height at an average condition. site in the northern Gulf of Mexico is indicated to fall in the range of 70 to 72 feet. This value The term (V /V)~ is also known as the shoaling is comparable to the API Reference Level Height coefficient, K •0 The shoaling coefficient is of 71 feet in a water depth of 400 feet for the given accordin~ to linear wave theory by open, broad, Continental Shelf of Western Louisiana and Eastern Texas (API, 1981). Characterizations of wave periods associated with maximum wave conditions are important as they can have significant effects on the computation where h is the water depth and k is the wave number. of wave forces on offshore structures. A study K' is then given explicitly as a function of wave of the joint probabilities of wave height and period l~ngth and water depth. in hurricane· conditions has been reported by Earle, et al. (1974). The study was based on a wave­ Wave Refraction by-wave analysis from data obtained during Hurricane Camille from the Ocean Data Gathering Program. Earle, The term (b /b)~ in the shoaling equation et al. reported that height-period joint probabili­ represents the rglative spacing of adjacent wave ties are time dependent, with large relative wave rays and is also defined as the refraction coefficient periods becoming less probable as the hurricane ~· Physically, the relative spacing between and its extreme waves pass the site. wave rays represents the local wave energy density. It is generally assumed that the wave energy contained The hindcast results of Haring and Heideman between wave orthogonals is conserved as the wave (1978) show that a representative wave steepness front progresses. Various graphical and numerical (ratio of wave height to length) of 1/13 for deep methods are available to compute wave refraction. water and 1/12 for relatively shallow water can In this study, the graphical procedure was adopted. be generalized for hurricane wave conditions. These However, most of the wave paths were near normal wave steepness ratios correspond to wave periods to the smoothed depth contours; thus, the wave of about 12 to 13 seconds. A wave steepness of refraction effects proved to be insignificant. 1/12 is also recommended in API RP 2A for the Gulf of Mexico area for the determination of design wave Bottom Friction periods associated with the API reference level wave heights. Wave energy lost through bottom friction results from the work done by the wave orbital Based on the above sources, the extreme wave velocity against bottom shear stress. The bottom heights are expected to be associated with "growing" stress can be expressed as: sea states in which waves are relatively steep with shorter wave periods. The longer period waves are usually associated with the more regular swells that have traveled some distance, but are usually lagging behind the peak of the storm.
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