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Copyright Tim Lovett © April, Oct, Dec 04, Apr 05 

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Sunk by waves the same length as the ship... More than 40 people died when the MV Derbyshire was lost in a typhoon in the South China Sea in 1980. The 294m Derbyshire had been at sea for only 2 years. An inquiry ruled that a hatch cover had failed as huge waves buffeted the 160,000 tonne bulk carrier. Further research indicated the ship failed because the waves were exactly the same length as the vessel. Dr Janet Heffernan who analyzed the wave patterns explained; "If the wave is smaller than the ship, then the vessel can cope with it. If the wave is much bigger, then the ship bobs on top of the wave, but if the wave is the same length then the ship picks up the frequency of the sea..."  BBC article.  Technical Report

CONTENTS

Wind Generated Waves

Rogue Waves

Tsunamis 

Waves of the Flood

Developing Seas 

Definitions

References

How Big and How Bad?

The size and nature of the waves during the deluge dictates the strength of the ark. The Korean safety study concluded that the ark was capable of riding out 30m waves if the structure had 30 cm walls and 50cm framing timbers. With stronger construction, the ark could survive 47.5 m waves before water reaches the corner of the roof (heeling angle 31^o).  Such waves have never been recorded in the ocean today, the highest has been measured at  26m in the notorious North Atlantic. 

The ark in a beam sea (sideways to the incoming waves). This is the most dangerous state for a ship in high seas and could lead to capsize.

Wind Generated Waves

Generation of wind waves of such magnitude would require a constant gale over a considerable distance (fetch). This is why waves are limited in a small lake. If the wind changes direction, the wave pattern can be reduced by interference with a new wave system. Generally speaking, strong winds are of relatively short duration, making very large waves a rare event.

Thirty meters is a big wave, a significant wave height H _1/3 of 15m approaching the upper limit in samples of tabulated data of North Atlantic waves. (Principles of Naval Architecture CH8 (Vol III), Section 2). At such a height, weatherships in the North Atlantic (PNA VIII, Section 2, Fig 20 Roll) recorded wavelengths of around 300m. (A height/length ratio of 1:20). These observations were from regions experiencing very severe weather compared to even the North Atlantic. In a more generalized study, Hogben and Lumb compiled over 1 million observations spanning 10 years, where wave heights in the highest range (11 to 12m) accounted for only 0.0013% of world-wide observations (or 0.007% of observations in the Northern North Atlantic). 

For a wave with H _1/3 of 14m to develop in the open sea, a sustained wind speed of 63 knots (117 km/h) is required. (PNA VII, S2, Tables 6 & 7). (Measured at 19.5m above water surface). It was also found that observed recordings slightly overestimated the actual measured wave heights in the upper ranges by around 13%.  According to Guinness Book of Records, the highest wave ever officially recorded was observed at 34m during a hurricane, but the record for an instrumentally measured wave is 'only' 26m.

Woodmorappe mentions the damping effect of flood debris as a factor in limiting wave development. Floating in the middle of a large mat of vegetation, the ark would be effectively shielded from wind generated waves. Of course, one could always assume such a floating island of organic material would become waterlogged and sink to the bottom prior to burial by sediment from continental runoff in the late flood stages. Not a bad explanation for the formation of oil reserves in the middle east. 

Data for waves up to 12m are listed with their most probable modal wave period in Principles of Naval Architecture V3 Ch8 S2.10 Fig 26. Curve fitting to this data appears to be a 2nd order polynomial (parabolic) function as follows;

Wave Height = 0.0663*period^2 - 0.5168*period + 2.5765   (Which fits the data reasonably well; R² = 0.9993.)  Then by extrapolation, we get the periods for the 30m wave = 25 secs, 47m wave = 30 secs. (Obviously a rather dubious extrapolation given that we just extrapolated to 300% of the actual data.) 

Assuming a sinusoidal waveform, equation 16 Section 2.2 gives; L_w = g * T_w^2 / (2 * P), which yields wavelengths of 944m for the 30m and 1424m for the 47m high wave. (Length to height ratios of approx 30:1). Such long wavelengths were probably not employed in the Hong study since the ark would ride comfortably over a 50m swell with a 1.5km wavelength. 

Compiled from Ref 1: Table 6.17a and 6.17b after Henschke. A photo of each sea state can be seen at http://www.crh.noaa.gov/lot/webpage/beaufort/#

Developed Sea data compiled from Ref 7

Hong paper 1994	40.1	78	Structural limit	30	1160
Hong paper 1994	50.5	98	Stability limit	47.5	2560

Extrapolated data for the 30 and 47.5m waves as described in the Hong study. Wave height is related to 2nd power of wind speed, the Henschke data yielding longer wavelengths than the PNA data extrapolation - obviously influenced by the 20m x 600 hurricane . 

Rogue Waves

There is plenty of wave data based on averages, but values such as significant wave height do not indicate the highest wave likely to be encountered. The fact that different sets of waves can be superimposed gives rise to the possibility of a freak wave appearing. These rogue waves are unusually high and unusually steep, often breaking on top of a vessel. Images: http://www.tv-antenna.com/heavy-seas/

"There is really no available measurement of freak waves per se. Academic interests may be satisfied by the theoretical simulation of an event of rogue wave occurrence ... but the present (lack) of actual field measurements of rogue waves (means) even the best formulated theories remain unverified."  Paul C. Liu, Research Physical Oceanographer, NOAA/Great Lakes Environmental Research Laboratory, http://www.glerl.noaa.gov/res/Task_rpts/ppliu02-3.html 

Dr Frank Gonzalez describes the current theories for rogue wave generation in the quote below. "Rogue Wave vs Tsunami?". They are principally wind generated, possibly a statistical freak between multiple wave sets or a perfect shape to catch the wind. There is also a theory of interplay between wind and currents, which obviously doesn't explain how rogue waves can form in the absence of significant water current. There is considerable research underway on rogue waves, and some argue for a tightening of shipping rules (esp. increase of wave bending moment, wave slamming loads). Very large ships normally ride several waves at once, but freak conditions such as the Derbyshire incident attest to the danger of the wavelengths equal to the length of the hull.  

Tsunamis

"A tsunami is a series of ocean waves generated by any rapid large-scale disturbance of the sea water. Most tsunamis are generated by earthquakes, but they may also be caused by volcanic eruptions, landslides, undersea slumps or meteor impacts." NOAA 

How could a loving God allow this? See AiG article "Waves of Sadness" by Carl Wieland. Note: In reference to the 2004 Indian Ocean tsunami the article states "Korean naval architects showed that the Ark could have withstood waves 4–5 times taller than this tsunami (only about 20 feet or 6 metres high)". In deep water a tsunami has a gentle slope and is only a few feet high - passing under ships virtually undetected. In this case the wave was 50cm after several hours.[8] The more dangerous wave heights only apply as the wave approaches the shore. In some instances, ships are recommended to head out to deeper water if there is enough time before a tsunami arrives.  

"If you are on a boat or ship and there is time, move your vessel to deeper water (at least 100 fathoms - 600ft or 182m, ). Tsunami Safety Rules http://wcatwc.gov/safety.htm

In deep water a tsunami develops such a long wavelength that it is very low and virtually harmless (even unnoticed) to shipping. Wavelength is related to apparent speed (celerity), so the wave formation can attain speeds of up to 500 miles an hour, crossing the Pacific in a day. It is only as it approaches the shoreline that the tsunami begins to compress and rise higher, its momentum known to send the water far inland. Since the height of tsunamis in deep water is not dramatic, the run-up data is often quoted. This can be very misleading since the tsunami height can be amplified 20 times as the shallow water slows it down. Cynical imagery of the ark tossed around in 500m tsunamis (in deep water) would imply there was the potential for 10km (6 miles) of vertical runup when it hit the shoreline - not likely. Such a wave would break in the comparatively 'shallow' 1000-4000m water, dissipating its energy and settling down to a more realistic size. In fact, the 520m tsunami height of the 1958 landslide quoted by ark skeptics took place within a narrow Alaskan bay where there was no time for the wave to develop a standard profile. This is not a deep sea tsunami wave height.

So a tsunami generated by earthquake, landslide or volcanic activity could only pose a threat to Noah's Ark in shallow water. With an average depth of nearly 3km (2 miles) which is well over the NOAA recommendation, the world wide flood would actually protect the ark from tsunami shoreline effects. In the middle of an ocean where geological activity is concentrated on the perimeter (e.g. such as in the modern Pacific Ocean) the ark would safely ride over tsunami waves. 

More tsunami info: http://www.pmel.noaa.gov/tsunami/Faq/

Waves of the Flood

Wind: After the rainfall had ceased and the fountains of the deep subsided, God sent a wind. Genesis 8:1. The ark was still afloat at this stage, so the intensity and geographical scale of these winds hold the key to wave sizes. Record breaking waves (such as the Hong roll limit of 47.5m) would be unacceptable at the time of the ark coming to rest of the mountains, in fact waves of more then a few meters could pose a threat to a beached ark.  

In the open sea, a stability limit of 47.5m or a structural limit of 30m does not tell the full story, since the wavelength must also be specified. 

The following screenshot shows the ark in a beam sea. The waves have the more realistic 2nd order Stokes profile, and a very steep ratio of 1:10. For smaller waves a limit of around 1:7 is generally as bad as it gets before the wave will break on itself. This software was begun by Tim Lovett in an effort to reproduce the roll stability calculations in the Hong paper.

In closer detail, the ark is rolling in a double period with the Stokes waveform - with the roof beginning to dip into the water. Note the centre of buoyancy (B) which has not yet corrected the heel angle due to the angular momentum of the vessel generated by the passing wave crest. The wave is 'traveling' from left to right in this simulation, the vessel still rolling as it descends. If waves happen to coincide with the natural roll period of the ship, then roll is amplified. Immediate action is required, such as turning the vessel to change the frequency at which the waves meet the ship.  

A more probable ratio of wave-height to wave-length is around 1:30, which would looks more like this;   

Tsunami: (Based on the catastrophic plate tectonics model). Once the ark had landed the receding water level would minimize the risk of tsunami damage, especially since that ark was in a mountain range (Mountains of Ararat with other peaks visible). Hence the latter stages of the flood which involve high current velocities during continental runoff are irrelevant. 

During the voyage, a tsunami could only pose a threat if the source was nearby - such as a local exploding volcano. So the proximity to volcanic activity and its likely nature (explosive or continuous) hold the key to understanding the tsunami waves of Noah's flood. Essentially, the deeper the water and the more distant  the tsunami source, the safer the wave would be when it reaches the ark.

Developing Seas

WAVE HEIGHT vs  WIND SPEED AND DURATION

It is common knowledge that wind generates waves. Stronger wind gives bigger waves. (Ref 4) Initially the waves are close together and unsorted but with a steady wind over a long distance (fetch) the waves become well formed and further apart. A fully developed sea is one that has reached the full height and wavelength corresponding to a particular wind speed.

The following table shows the relationship between wind speed and duration (fetch) and the effect on wave height and period. The blue figures indicate typical values in a modern sea - very high wind speeds have a fixed direction for only a relatively short time. This table is a metric conversion based on http://www.stormsurf.com/page2/papers/seatable.html. (Ref 2)