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Spectral Analysis Ocean Environment Sep. 2014 Kwang Hyo Jung, Ph.D Assistant Professor Dept. of Naval Architecture & Ocean Engineering Pusan National University Introduction Project Phase and Functions Appraise Screen new development development Identify Commence basic Complete detail development options options & define Design & define design & opportunity & Data acquisition base case equipment & material place order LLE Final Investment Field Feasibility Decision Const. and Development Pre-FEED FEED Detail Eng. Procurement Study Installation Planning (3 - 5 M) (6 - 8 M) (33 - 36 M) 1st Production 45/40 Tendering for FEED Tendering for EPCI Single Source 30/25 (4 - 6 M) (11 - 15 M) Design Competition 20/15 15/10 0 - 10/- 5 - 15/-10 - 25/-15 Cost Estimate Accuracy (%) EstimateAccuracy Cost - 40/- 25 Equipment Bills of Material & Concept options Process systems & Material Purchase order & Process blocks defined Definition information Ocean Water Properties Density, Viscosity, Salinity and Temperature Temperature • The largest thermocline occurs near the water surface. • The temperature of water is the highest at the surface and decays down to nearly constant value just above 0 at a depth below 1000 m. • This decay is much faster in the colder polar region compared to the tropical region and varies between the winter and summer seasons. Salinity • The variation of salinity is less profound, except near the coastal region. • The river run-off introduces enough fresh water in circulation near the coast producing a variable horizontal as well as vertical salinity. • In the open sea. the salinity is less variable having an average value of about 35 ‰ (permille, parts per thousand). Viscosity • The dynamic viscosity may be obtained by multiplying the viscosity with mass density. Density and viscosity vs. temperature of fresh and sea-water Metocean conditions Meteorological and Oceanographic Conditions • Local surface wind • Wind-generated local waves • Swell (long-period waves) generated by distant storms • Surface current also generated from the local storms • Energetic deep water currents associated with low frequency, large basin circulation • Non-storm-related currents, which are site-specific, such as loop current in the Gulf of Mexico or coastal current in the Norwegian northern North Sea. Water Waves • Water waves on the free surface of the ocean with periods of 3 to 25 s are primarily generated by wind. • Regular Waves : waves of constant height and period • Irregular Waves : successive waves differing periods and heights • Linear wave theory : The first-order Stokes, small-amplitude, or Airy wave theory • Nonlinear wave theories : Cnoidal, Solitary, and Stokes theories Regular waves • Relative depth d/L • Wave height H • Wave period T • Wavelength L • Angular or radian frequency = 2/T • Wave number k = 2/L • Relative wave height H/d • Phase velocity or wave celerity C = L/T = /k • Still Water Level (SWL), Mean Water Level (MWL), Mean Sea Level (MSL) Regular waves Regular waves Small-amplitude or linear wave theory (Airy, 1845) Assumptions • The fluid is homogeneous and incompressible; therefore, the density is a constant. • Surface tension can be neglected. • Coriolis effect due to the earth's rotation can be neglected. • Pressure at the free surface is uniform and constant. • The fluid is ideal or inviscid (lacks viscosity). • The particular wave being considered does not interact with any other water motions. • The flow is irrotational so that water particles do not rotate (only normal forces are important and shearing forces • are negligible). • The bed is a horizontal, fixed, impermeable boundary, which implies that the vertical velocity at the bed is zero. • The wave amplitude is small and the waveform is invariant in time and space. • Waves are plane or long-crested (two-dimensional). Wave Water Particle Trajectory Regular waves Particle velocity amplitudes with depth Regular waves • Kinetic energy per unit length of wave crest for a wave defined with the linear theory • Potential energy per unit length of wave crest for a linear wave • Total wave energy in one wavelength per unit crest width Regular waves Nonlinear wave theories • Wave steepness (H/L) is a measure of how large a wave is relative to its height and whether the linear wave assumption is valid. • Relative depth (d/L) determines whether waves are dispersive or nondispersive and whether the celerity, length, and height are influenced by water depth • Large values of the relative wave height indicate that the small- amplitude assumption may not be valid. • High Ursell number indicate large, finite-amplitude, long waves in shallow water that may necessitate the use of nonlinear wave theory Regular waves • Stokes finite-amplitude wave theory • In general, the perturbation expansion for velocity potential may be written as • Particle paths for Stokes waves are no longer closed orbits and there is a drift or mass transport in the direction of wave propagation. • Maximum wave steepness (Michell, 1893) Region of application of wave theories Irregular Waves • Ocean waves are, generally, random in nature. • Larger waves in a random wave series may be given the form of a regular wave that may be described by a deterministic theory. • Even though these wave theories are idealistic, they are very useful in the design of an offshore structure and its structural members. Irregular Waves • These individual components were generated by the wind in different regions of the ocean and have propagated to the point of observation. • If a recorder were to measure waves at a fixed location on the ocean, a non-repeating wave profile would be seen and the wave surface record would be rather irregular and random. • Definitions of wave height, period, and duration must be statistical and simply indicate the severity of wave conditions. Wave train (wave-by-wave) analysis • In the time-domain analysis of irregular or random seas, wave height and period, wavelength, wave crest, and trough have to be carefully defined for the analysis to be performed. Wave train (wave-by-wave) analysis Short term wave statistics • The probability that a wave of a given height will occur given that we know the statistics of the sea surface over a 16- to 60-min period. Long-term wave statistics • To obtain long-term wave statistics, a 15-min record may have been recorded every 3 hr for 10 years (about 29,000 records) and the statistics of the set of 29,000 significant wave heights compiled. Spectral analysis • Rices (1944-1945) work on signal processing was extended to ocean waves (Kinsman 1965; Phillips 1977). • E(f) or S(f) is actually a measurement of variance, it is often called frequency energy spectrum because (assuming linear wave theory) the energy of the wave field may be estimated by multiplying E(f) by g. • The wave energy spectral density, E(f) or S(f), simply the wave spectrum may be obtained directly from a continuous time series of the surface (t) with the aid of the Fourier analysis. Spectral analysis Spectral analysis Spectral analysis Spectral analysis • Zero-th moment of the spectrum (m0) • Moments of a spectrum • Approximate relations for most common wave parameters by the statistical analysis Spectral analysis • Bretschneider Spectrum Spectral analysis • Bretschneider Spectrum Spectral analysis Pierson-Muskowitz Spectrum Spectral analysis Pierson-Muskowitz Spectrum Spectral analysis JONSWAP(Joint North Sea Wave Project) Spectrum Spectral analysis F1 F2 1 1.00 1.0 2 1.24 0.95 3 1.46 0.93 3.3(1) 1.52 0.82 4 1.66 0.91 5 1.89 0.90 6 2.04 0.89 (1) Mean JONSWAP spectrum Spectral analysis JONSWAP Spectrum Spectral analysis Common form of spectral models applied to different regions Typical JONSWAP -values for various offshore locations around the world Qualitative Wave Power Spectrum Definition of Sea State Significant wave Wind speed (knots) Wave period(s) Sea state height(m) code Most Range Median Range Median Range probability 0-1 0 - 0.1 0.05 0 - 6 3.0 - - 2 0.1 - 0.5 0.30 7 - 10 8.5 5.1-14.9 6.3 3 0.5 - 1.25 0.88 11 - 16 13.5 5.3-16.1 7.5 4 1.25 - 2.5 1.88 17 - 21 19.0 6.1-17.2 8.8 5 2.5 – 4.0 3.25 22 - 27 24.5 7.7-17.8 9.7 6 4.0 – 6.0 5.00 28 - 47 37.5 10.0-18.7 12.4 7 6.0 - 9.0 7.50 48 - 55 51.5 11.7-19.8 15.0 8 9.0 - 14.0 11.50 56 - 63 59.5 14.5-21.5 16.4 >9 >14.0 >14.0 >63.0 >63.0 16.4-22.5 20.0 Tidal Constituents TIDAL DATUMS HAT The elevation of the highest predicted astronomical tide expected to occur at a specific tide stati Highest Astronomical Tide on over the National Tidal Datum Epoch. The average of the higher high water height of each tidal day observed over the National Tidal D MHHW* atum Epoch. For stations with shorter series, comparison of simultaneous observations with a con Mean Higher High Water trol tide station is made in order to derive the equivalent datum of the National Tidal Datum Epo ch. The average of all the high water heights observed over the National Tidal Datum Epoch. For stat MHW ions with shorter series, comparison of simultaneous observations with a control tide station is m Mean High Water ade in order to derive the equivalent datum of the National Tidal Datum Epoch. MTL The arithmetic mean of mean high water and mean low water. Mean Tide Level The arithmetic mean of hourly heights observed over the National Tidal Datum Epoch. Shorter se MSL ries are specified in the name; e.g. monthly mean sea level and yearly mean sea level.
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