r8_wavespectra - 13.42 Design Principles for Ocean Vehicles...

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13.42 Design Principles for Ocean Vehicles Reading # 13.42 Design Principles for Ocean Vehicles Prof. A.H. Techet Spring 2005 1. Ocean Wave Spectra 1. Wave energy spectra. Red text indicates wave generation mechanisms and blue text indicates damping/restoring forces. The majority of ocean waves are wind generated. Other wave generating mechanisms include earthquakes and planetary forces. Planetary forces drive tides and cause long ©2004, 2005 A. H. Techet 1 Version 3.1, updated 2/24/2005
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13.42 Design Principles for Ocean Vehicles Reading # period waves on the order of 12 to 24 hours. Earthquakes are the major cause of tsunamis which, while rare, can be catastrophic if the earthquake occurs near or on the coast. Waves also encounter forces that tend to restore them to a flat surface. For small wavelength (high frequency) waves surface tension plays a large role in damping out these waves. The majority of waves are restored by gravity and longer period waves are damped by the Coriolis force. As wind begins to blow (between 0.5 - 2 knots) on a calm surface small ripples, capillary waves or “cat-paws”, tend to form. These small waves are on the order of less than 2 cm. As the wind becomes stronger wave amplitude increases and the waves become longer in order to satisfy the dispersion relationship. This growth is driven by the Bernoulli effect, frictional drag, and separation drag on the wave crests. Wind must blow over long periods of time and large distances to reach a fully developed sea state. When the phase speed of the wave crest matches the wind speed non-linear interactions stop (except friction) and the phase speed is maximized. The limiting frequency of the waves can be determined by the equation for phase speed and the dispersion relationship: w kg C » U =/=/ w (1) p w g w » (2) c U w where U is the wind speed and w is the limting frequency. Once wind stops viscosity w c erodes the waves slowly. The smallest wavelengths decay the fastest. Sample spectrum shapes are shown in figure 2. ©2004, 2005 A. H. Techet 2 Version 3.1, updated 2/24/2005
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13.42 Design Principles for Ocean Vehicles Reading # For a storm with wind speed, U , the effects of the storm can be felt at a distance from the w e storm, R . The number of wave cycles between the storm and the observation location is - g t 2 4 2 NR =/ l . The amplitude of the waves decays as where g = 2 n k = 2 nw / g (from Landau and Lifshitz). The development of storms can be tabulated. Fetch is the length over which the wind must blow to have fully developed seas (given in standard miles), and the storm duration, given in hours, is the time the storm must last to result in a fully developed sea. Wind warnings Beaufort scale Wind speed (mph) Fetch (miles) Storm duration (hr) 3-4 12 15 3 small craft 5-6 25 100 7 35 400 28 gale 9 50 1050 hurricane 70+ ©2004, 2005 A. H. Techet 3 Version 3.1, updated 2/24/2005
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13.42 Design Principles for Ocean Vehicles Reading # 2. Typical Wave Spectra Researchers have studying ocean waves have proposed several formulation for wave spectra dependent on a a number of parameters (such as wind speed, fetch, or modal frequency). These formulations are very useful in the absence of measured data, but they
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