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Home , Airy wave theory

Ocean Environment

Sep. 2014

Kwang Hyo Jung, Ph.D

Assistant Professor Dept. of Naval Architecture & Engineering Pusan National University Introduction

Project 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, , Salinity and Temperature

Temperature • The largest 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 . 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 • (long-period waves) generated by distant storms • Surface current also generated from the local storms • Energetic deep water currents associated with low , large basin circulation • Non-storm-related currents, which are site-specific, such as in the Gulf of Mexico or coastal current in the Norwegian northern North Sea. Water Waves

• Water waves on the 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 theory : The first-order Stokes, small-, or Airy wave theory

• Nonlinear wave theories : Cnoidal, Solitary, and Stokes theories

Regular waves • Relative depth d/L • H • Wave period T • L • Angular or frequency  = 2/T • Wave number k = 2/L • Relative wave height H/d • or wave celerity C = L/T = /k • Still Water Level (SWL), Mean Water Level (MWL), Mean (MSL)

Regular waves Regular waves

Small-amplitude or linear wave theory (Airy, 1845) Assumptions • The is homogeneous and incompressible; therefore, the density is a constant. • can be neglected. • effect due to the earth's rotation can be neglected. • 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 with depth Regular waves

• per unit length of wave crest for a wave defined with the linear theory

• 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 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 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 .

• 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 , 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

• Rice’s (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 Spectrum

Definition of

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 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. Mean Sea Level

The average of all the low water heights observed over the National Tidal Datum Epoch. For stati MLW ons with shorter series, comparison of simultaneous observations with a control tide station is ma Mean Low Water de in order to derive the equivalent datum of the National Tidal Datum Epoch. The average of the lower low water height of each tidal day observed over the National Tidal Dat MLLW* um Epoch. For stations with shorter series, comparison of simultaneous observations with a contr Mean Lower Low Water ol tide station is made in order to derive the equivalent datum of the National Tidal Datum Epoc h. LAT The elevation of the lowest astronomical predicted tide expected to occur at a specific tide statio Lowest Astronomical Tide n over the National Tidal Datum Epoch. TIDAL DATUMS Currents

Common categories of current • Wind-generated currents, • Tidal currents (associated with astronomical ). • Circulational currents (associated with oceanic circulation patterns) • Loop and currents • currents.

The vector sum of these currents is the total current, and the speed and direction of the current at specified depths are represented by a current profile. Currents

Steady Uniform Current

• In most cases current is turbulent, but is generally approximated by the corresponding mean flow. For the design value, a 100 yr current is often chosen. The environmental conditions in design are obtained from the site-specific data.

• In areas where the current speed is high, and the sea states are represented with small wave heights, e.g. West Africa, an environmental condition represented by 100-year wind and current speeds combined with a sea state with a return period of 10-year should be considered.

• If the current statistical data is not available, the velocities at the still water level may be computed from the 1 h mean wind speed at a 10 m elevation as Currents

Steady Shear Current • While current is often uniform with depth, they may vary with water depth. The shear current is generally considered linear with depth or bilinear. • In deep water, the current disappears near the bottom. Near the sea floor in shallow water the current profile is logarithmic due to bottom shear.

Combined Current and Waves • Modifications are needed in computing the wave and associated loading from waves propagating on a superimposed steady current. • The wave period is modified to an apparent period by the free-stream current velocity. A current in the wave direction stretches the wavelength and opposing current shortens it. Currents

Comparison of horizontal water particle velocity in waves with uniform current (Ismail, 1984) Currents

• The Gulfs circulation is dominated by the loop current.

• The loop current is of warm subtropical water that enters the Gulf through the Yucatan Strait, extends northward, then loops around to the south and ultimately exits the Gulf through the Florida Strait.

• The strength of this loop current exhibits large variability and can be high. The loop current system passing from the Caribbean Sea to the Straits of Florida through the eastern Gulf has maximum speeds sometimes reaching the order of 3.0 m/s.

• The loop current may extend far north, often reaching Mississippi Delta, where the circulation closes off and a large warm-core loop current eddy is shed. These eddies also possess strong currents, but unlike the loop current, they are not constrained to the eastern Gulf and typically drift westward. Often, the westward drift can interfere with offshore operations. Currents

Loop Current • The Loop Current flow northwards into the Gulf of Mexico. Every 6-11 months, a bulge in the current cuts off into a clockwise- rotating eddy that then drifts slowly west-southwestward towards Texas at about 3-5 km per day.

Image credit: NOAA

Storm

Hurricane Katrina(2005) Storm Surge? Storm Grade

미국 한국 Category 5: 70.0 m/s 이상 매우 강: 44.0 m/s 이상 Category 4: 58.3 m/s 이상 강 : 33 m/s 이상 Category 3: 49.4 m/s 이상 중 : 25 m/s 이상 Category 2: 42.5 m/s 이상 약 : 17 m/s 이상 Category 1: 32.7 m/s 이상 Trajectory: Hurricane Katrina(2005) Katrina vs sea surface height Broken Offshore Plant by Huricane Katrina(2005)

USA road bridge over the Mobile An oil rig broken from its River, Alabama moorings rests on the beach at Fort Morgan, Ala.

Mars Platform at water depth of 896 m (2940 ft) 태풍 매미(2003)

Wave Hindcast Model Domains for U.S. Coasts

What is ?

Rogue waves

 Freak waves, Extreme waves, Giant waves

 H> 2HS (Dean,1990, etc)

Hc/Hs>1.25 (Olagnon and Iseghem, 2001)  Rogue waves are not

 Holes in the sea

 Just like a mountain, a wall of water coming against us

61

Reported encounters

Norwegian tanker Wilstar, Esso Languedoc, 1974 South Africa, 1980

62 Reported encounters

Draupner oil rig, North Sea, 1995

Wave height as a function of time, measured at the Draupner oil rig on 1/1/95.

63 More Frequent than Rare

1. Explorer, 2. Grand Voyager 3.Norwegian Dawn, 4. Kalk Bay, 5. Blue Bay,

6. Maracas Beach, 7. Blake de Pastino, 8. Port Orford, 9. Petit Havre 64