Ocean Waves: Linear & Schoenbergers Wave Formulas

[Governor]

RE: Ocean Waves:
1. Linear Wave Formula - What is the average sea state that is capable of producing a 20 ft. wave?
2. Schoenbergers Wave Formula – What is the smallest average sea state that is capable of producing a 20 ft. wave?

 

[bm0p700f]

The amplitude of the wave will be determined by the amount of energy put into the system. What you mean by sea state is unclear.

 

[Governor]

You're right.

I believe the formula(s) needs to be worked "backwards" to arrive at an answer.

What I mean by sea state is in effect "energy". By energy in this example I mean wave height in feet, a 3' to 4' sea state, 3' to 4' waves = wave energy.

With the linear wave formula I am trying to prove that a 20' wave is not possible from a 3' to 4' sea state (energy), or that a 20' wave is not possible from an average of 3' to 4' waves (energy). I believe the linear wave formula restricts or prohibits abnormal waves (rogue) from existing.

With Stroenberger's wave formula I would like to know what "energy" (in wave height, feet) or average sea state (energy) or size the average wave would need to be to generate a 20' wave. I believe Stroenbergers formula proves that from some average sea state (average wave height), An abnormal (rogue) wave can be formed that that can be more than 3X the size of the average wave height and that this abnormal wave takes energy from the waves in front and behind to create it.

 

[stewartcs]

RE: Ocean Waves:
1. Linear Wave Formula - What is the average sea state that is capable of producing a 20 ft. wave?
2. Schoenbergers Wave Formula – What is the smallest average sea state that is capable of producing a 20 ft. wave?

If you know the significant wave height for a given sea state, you can determine the extreme wave height based on the spectrum used and the number of wave cycles. There is a statistical relationship between these.

For example, if we assume the wave spectrum is a Pierson-Moskowitz, then the maximum wave height that can exist is equal to 1.86 times the significant wave height (for 1000 cycles).

Hence, if the significant wave height is equal to 4-ft, then the maximum wave height that will occur in 1000 wave cycles is 1.86 x 4 = 7.44-ft.

Hope this helps.

CS

 

[Governor]

Very helpful, THANK YOU!

From your explanation and formula, it is reasonable to state that a 20' wave is not possible from a 4' sea state.
Excellent. Something in the order of an 11' wave sate would have existed to have created the 20' wave.

Would energy from an underwater current moving in the opposite direction to the wave add to the wave height?

.

Also: Can you please lend some clarity to Stroenberger's formula to possibly determine the smallest wave(s) height that could cause a 20' high rogue wave?

 

[stewartcs]

Very helpful, THANK YOU!

From your explanation and formula, it is reasonable to state that a 20' wave is not possible from a 4' sea state.
Excellent. Something in the order of an 11' wave sate would have existed to have created the 20' wave.

Would energy from an underwater current moving in the opposite direction to the wave add to the wave height?

.

Also: Can you please lend some clarity to Stroenberger's formula to possibly determine the smallest wave(s) height that could cause a 20' high rogue wave?

Based on a PM sea spectrum I would agree with that statement. However, depending on how the energy of a given sea state is distributed (which is based on the spectral frequency) it may be possible to get a slightly higher extreme wave height. This of course depends on the spectrum used as stated previously.

Regarding the underwater current moving in the opposite direction, I'm not entirely certain (off hand) whether or not it would add to the wave height. I would suggest reviewing some of the literature on the subject for more insight. I would recommend anything by T. Sarpkaya if you have access to his work.

Now that I've type this, I see that you are referring to rogue waves. In fact, rogue waves and extreme waves are two different phenomena. Regarding rogue waves (aka freak waves) neither the probability of occurrence nor their physics is well understood. It has been suggested that freak waves can be generated by mechanisms like wave-current interaction, combined seas, and wave energy focusing. However, no consensus has been reached.

Hope this helps.

CS

 

[Governor]

Thanks.
I watched this program when it first aired and it addresses most of my questions but does not provide the formulas or the answers.

Science Channel - Last night - 8/23/2009 - "Killer Waves"
Science Channel - 9/07/2009 (my birthday-must be some significance there) - "Killer Waves"

As I understand it, the program suggests that what mariners have called "rogue waves", tall tails, are actually not Rogue but rather fall into extreme category as suggested by Schoenberger and you.

Schoenberger basically states that "a wave" robs the energy from the waves in front of and behind and uses the energy from these neighboring waves to generate and become a giant wave. It was an unproven theory until the 1995 New Years Day Wave that was recorded at a Nordic oil platform in the North Atlantic (I think), North Sea maybe. The wave was video taped and recorded with instrumentation to be 95' or so feet tall in a 30 to 40' sea state, more than 2X the avg. sea state. This was hard evidence of Schoenbergers theory and formula. A study was then done using satellites/radar/imagery in an attempt to identify these not so "rogue" waves in seas around he world and during a period of one week they found something like eleven 100' waves in oceans around the world. The scientists are able to differentiate waves by 5' increments or less, failrly accurate imagery it seems.

Prior to this study they proved the occurrence of 100' waves off the southern and south western tip of Africa was due to the combination of High North Winds directly opposing a seasonal strong southerly current and shipping companies now change their shipping routes during these seasons.

I am attempting to apply this information and anything elso I can find to gain an understanding of what created the 20' wave that came from "no where" (3-4' sea state) and almost swamped my boat. What these captains on the show describe is exactly what I saw, the wave rose up in front of me as if it were an elevator and I slid down a deepening trough into it. I'm somewhat obsessed with trying to learn where it came from.

Thank you for your interest and thoughts and taking the time to respond. I'll try to find some info on T.S.

Try to catch the show, it's very interesting and goes into some interesting scientific and physical concepts.
Bryan

 

[Integral]

Let's clear up something, I to watched the show you saw, but it was some time ago. I do not know where you came up with Schoenberger, what I heard was Schrödinger. The Schrödinger wave equation originates in Quantum Mechanics. The physicists that they were talking to never went into any useful detail on how the Schrödinger wave equation was modified for application to the surface of the ocean.

The predictions of the rouge waves was through numerical solutions to the modified Schrödinger wave equation. You need knowledge of how the equation was formulated and a program to solve it numerically before any predictions can be made.

This is a nonlinear phenomenon, to understand it you must accept that the surface of the ocean is a very complex system, being driven by wind and water. They are indeed "rogue" waves that are predicted. Essentially the energy contained in several small waves combine to form a single huge wave. The linear model fails to predict them simply because a linear model has been simplified to the point that nothing unusual can possibly be predicted. The non linear system however is able to capture more interesting events, such as rouge waves. They are very real, the trouble is there is no way to predict when the surface of the ocean will behave in this manner, but we know it can happen.

 

[Integral]

stewartcs,
I think you are speaking exactly like all the conventional oceanographers. This is the predictions given by the linear model. While watching this show I was literally yelling at the oceanographers talking about how their LINEAER model did not predict such waves therefore they could not exist. The trouble is the surface of the ocean is not a linear system, so you can expect phenomenon not predicted by the simplified linear models.

edit:
According to the show there are areas, specifically off the south eastern coast of Africa, where current and winds combine to produce random huge waves. These are a bit different then the open sea rouge wave predicted by the nonlinear systems.

 

[stewartcs]

Thanks.

As I understand it, the program suggests that what mariners have called "rogue waves", tall tails, are actually not Rogue but rather fall into extreme category as suggested by Schoenberger and you.

Hi Bryan,

Just to be clear, as I said earlier, extreme waves and rouge (freak) waves are not the same thing. Integral has beat me to the explanation of why the two different waves are classified differently. However, there are multiple theories on how they are created and not just a combination of current and wind (refer to my earlier post on some other theories).

All most all of the literature and models we use when considering environmental loadings on our offshore structures are linear models and they behave really nice and are predictable. The extreme wave heights therefore have a statistical relationship with their significant heights as I noted previously. The relationship for an extreme wave height based on a significant wave height is given by:

$$H_m = \sqrt{\frac{1}{2}Ln(N)} \cdot H_s$$

Where N is the number of observed waves in a set.

Typically we observe a 3 hour storm which is around 1000 cycles (depends on the zero-crossing period). Hence, a factor of 1.86 is used to predict the maximum wave height with the linear assumption.

Rogue or freak waves are non-linear. In fact, ALL ocean waves are technically non-linear. However, most sea states behave rather well and can be approximated by linear means. I've always thought of rogue waves like this: An ocean wave has a certain amount of energy. This energy comes from different phenomena but is contained in the wave. Linear waves release their energy in a predictable manor. Rogue waves have sudden "bursts" that release the energy. This changes the sea surface elevation drastically as opposed to more suddenly as the linear wave does.

Again, there is no general consensus on the physics of rogue waves or their predictability. There is quite a bit of work in progress on this however.

Hope this helps.

CS

 

[stewartcs]

...This is a nonlinear phenomenon, to understand it you must accept that the surface of the ocean is a very complex system, being driven by wind and water. They are indeed "rogue" waves that are predicted. Essentially the energy contained in several small waves combine to form a single huge wave...

Indeed these are non-linear waves. However, rogue waves are not simply generated by wave interference as it seems you might be suggesting. The literature I've read on this subject suggests that rogue/freak waves can be generated by mechanisms like wave-current interaction, combined seas, and wave energy focusing.

Of course there are tons of opinions on how these things are generated. In fact, there are some websites dedicated entirely to this subject. If anyone cares to read more about them, a quick Google turned up this website: http://www.ifremer.fr/web-com/stw2004/rw/index.html

I have not reviewed any of the literature there so I can't say if it is valid or not but it seems at first glance to have some merit.

CS

 

[Governor]

Thank you for the information.

I apologize for the error "Schoenberger -v- Schrödinger. I was recently involved in an industrial accident (compressed air) and have some hearing loss.

Correction: Schrödinger...hope that is right.

I have one college Physics course under my belt some 25 years ago as part of my degree and I'm hanging on every word you guys say in an effort to understand "my wave".

I apologize in advance for my lack of Physics knowlwdge or mis-statements. In no way do I pretend to have any expertise in this field. It is not my intention to make anyone angry.

I found the example on the show "Killer Waves" regarding the 100' waves off of southern Africa to be relavent because the conditions that created them seemed to me to be similar to thoser that may have created "my wave". This occurred in the inlet at Oregon inlet. The wtar from the Pamlico sound leaves throough this inlet and Hatteras inlet. It was low tide so there was a strong out going current, 85' water depth, and a direct opposing NE incoming swell. These conditions seem similar on a smaller scale to the conditions that create the monster waves off southern Africa to me and so why I mentioned that example.

The outgoing current, my guess is a river of moving water (energy) that might be 75' deep that has it's own wave ocillations. Colliding into this outgoing energy is an incoming swell that is 3'4' tall, maybe 10' deep?, that has it's own energy and wave ocillations. When the two separate bodies of energy are in sinc, it seems you would get this fairly regular wave action but when the become out of sinc, it would seem that you might get something very unusal to happen...like the 20' wave I saw.

That inlet is usually like a washing machine and this day was no different. But then I had a fairly large wave lift the boat up and then I traveled down this big trough and into this big 20 footer. The inlet was not crashing with big waves and surf. There was no white water waves breaking anywhere. It looked just like the NOAA forecast, 3-4' waves.

After learning that the 1.86 X 4 could not give me the 20' wave. That proves to me that there must be some other explanation, possibly Schrödinger, or something else. It also proves that the inlet could not have been that "big" on that day, 10-15' waves. I have been criticized for goig on a day that was too rough...it was not.

I guess the only question I have would be, re: Schrödinger formula, what would the sea state need to be to produce a 20' wave? If a 20' wave could come from a 4' wave I guess it would all make sense.

Thank you again,
Bryan

 

[Governor]

http://www.ifremer.fr/web-com/stw2004/rw/index.html

Great resource!

Reading material for my upcoming vacation.

Thanks!