Wave loads - particle velocity from 0-360° 1

[LR11]

With wave loads, is it a real thing that forces are equal in the opposite direction with a phase difference of 180°?
I saw this diagram online.
So if you had a structure much longer than the wavelength, would the net load be zero?
Or is that velocities/accelerations are higher for the phase 0-90°?

 

[1503-44]

Of course. They are real as covid 19.

The applied wave force is equal in both directions and algebracially sums to zero.
The structure to which the wave is applied may not experience equal loading in both directions, because the wave is higher at 0 and applies its load to a greater height of the structure.

Don't forget the current load. Design conditions are usually applied with a simultaneous current loading. The combination of wave and current will make the load in one direction considerably higher than the opposite. If waves and currents are considered to be omnidirectional, as more often than not, the net effect on the design of the structure may ultimately be the same in all directions.

 

[LR11]

Thanks for responding.
Do you know of a link or spreadsheet as to how to calculate the velocities and accelerations?

 

[1503-44]

You will find the necessary equations in the 2nd, 3rd and fourth pdf on this list,

https://duckduckgo.com/?q=wave+load+calculations&t=fpas&ia=web

Note that your diagram is for linear Airy wave theory, mostly valid for depths greater than 1/2 the wave length. You must use different wave shapes for lesser depths and where waves are subject to shoaling effects.

 

[1503-44]

And

http://web.mit.edu/fluids-modules/

http://www/potential_flows/LecturesHTML/lec19bu/node3.html

 

[WARose]

So if you had a structure much longer than the wavelength, would the net load be zero?

I don't think so....because aside from lift, it should also be thought of as a drag force. (Ergo it can't be zero.)

 

[1503-44]

In the context of a wave cyclic load, the velocity and resulting drag is first applied in one direction through Π/2 - 3Π/2 then reverses for during 3Π/2 - Π/2. Net orbital particle velocity at any depth is zero, but the drag vectors applied load to the structure are not zero, because the position of the load vector applied to the structure raises and falls with the height of the wave. But drag load is the same for equal velocities and drag sums to zero as there is no net movement of any water particles between cycles. The load vector components applied to the structure are sinusoidal functions, as are the vector's placements.

A cork (length =0) floating on a pure Airy wave, with no superimposed current, will orbit, but not experience any net movement forward or reverse,

(Assuming the structure is exposed to full wave height...)

A structure with length equal to that of the wavelength will have equal drag force applied in both forward and reverse directions at any given time.

A structure of half wavelength has a net forward force for a time equal to 1/2 the waves period, then a net reverse force for the next half period.

However those forward and reverse drags always create an overturning moment because the height of the wave applies the forward and reverse components at different heights.

 

[Settingsun]

For a cylinder that extends from bed to above water surface, whose diameter is equal to the wavelength, the inertia coefficient in the Morison equation is approx 0.3, compared with approx 2.0 for a cylinder that is small compared to the wavelength. So not zero force even when the structure exactly captures the full wave length.

 

[1503-44]

Yes, the Morison equation defines the design condition. But that was not the question. My understanding is that the Morison equation is not the result of integrating through the wave period from 0 to 2Π. It is the instantaneous maximum horizontal force. Likewise, instantaneous horizontal force is 0 at Π/2 and 3Π/2. I can't say I've ever done this, why would you, as it does not result in a design condition to have net force =0, but if you integrate the values of the Morison equation over the wave period, that will sum to zero, provided the drag factor is equal in both the forward and reverse directions. But like I said, the design condition occurs at t=0, so use the Morison equation to get the design force.

 

[Settingsun]

1503-44, I'm not sure I understood you but you don't integrate the Morison results over the wave period when using the 0.3 inertia coefficient I quoted. You apply it to the instantaneous water particle acceleration profile that gives maximum inertial force. If the cylinder is that large and there is no significant steady current, the inertial force will dominate the drag force so the inertial force is the ~maximum horizontal force. If the steady state current is large enough that the drag force becomes significant compared to the inertial force, you would add the two maximum values (conservative) or do a more rigorous analysis.

 

[1503-44]

I believe we agree. That's what I said...One does not integrate the Morison equation. It gives the maximum instantaneous design value as is, which is exactly what we should use.

I'm just saying that I think if you did integrate the Moriso equation, the result would be zero. Its just an interesting fact of no practical use. It's zero. The unintegrated Morison equation is indeed the maximum instances design value that we need.

Same with the Airy wave drag forces. They are max at values of 0 and pi/2, but integrating over the wave period, sum to zero. But we are interested in the maximums, hence there is no need or value in integrating them to obtain values of zero. But I think that was the question that the OP was asking. If integrated over the wave length, would it =0. I think Yes, it integrates to zero.

I find the max instaneous design force using the Morison equation too. I dont integrate it, so I think we agree.

Add Note: The Morison equation is valid only for diameters very much smaller than the wave length.

https://www.sciencedirect.com/topics/engineering/morison-equation

And good refs

http://www.coastalwiki.org/wiki/Shallow-water_wave_theory

http://publications.lib.chalmers.se/records/fulltext/151295.pdf

https://ft-sipil.unila.ac.id/dbooks/S P M 1984 volume 2-2.pdf

 

[LR11]

Thanks for the responses.
What prompted me to ask the query, was that I was observing someone else's output from what I think was a Stream Wave calculation and I think it showed velocities and accelerations only for the first 90°. After that it was Zero. I don't know if the range was 0-180° or 0-360°.

The structure I had in mind was a jetty with piles. Some piles would have forward forces, some in the other direction (this is what I'm not sure of). So hypothetically, if jetty is long, and piles were at a smaller spacing than wavelength, then was net zero? I do understand the part about the current, in this scenario it was assumed there is no current.

I will review the references posted then.

 

[Settingsun]

LR11, you are correct that not all piles will experience the maximum load at the same time, and some will have reverse loading. The overall lateral system doesn't need to deal with a simple sum of maximum force on a pile multiplied by number of piles. If the jetty can experience side-on waves (wave crest parallel to the jetty), the effect would be fairly marginal, but the dominant wave crest is oblique to the average jetty.

For pile-size elements, drag is probably dominant rather than inertia, so my earlier comments not so useful to you.

A jetty is also quite likely not in deep water as far as waves are concerned, so the Airy (linear) wave theory not quite correct as 1503-44 said before.

 

[LR11]

OK thanks.
I will have to sort out why I only saw velocities/accelerations for the first 90° only.

 

[Settingsun]

I will have to sort out why I only saw velocities/accelerations for the first 90° only.

The other three quadrants can be determined from the first quadrant for linear wave theory (mirror and/or negative of the first quadrant), so maybe only the first quadrant is calculated.

 

[1503-44]

For practical design, you may find these even more helpful than those above.

https://www.publications.usace.army...Xc316Jvw2I=&tabid=16439&portalid=76&mid=43544

https://www.publications.usace.army...L4oDlcbwvc=&tabid=16439&portalid=76&mid=43544

https://www.publications.usace.army..._W_L_2eCpg=&tabid=16439&portalid=76&mid=43544

https://www.publications.usace.army...eJoIhP0JEo=&tabid=16439&portalid=76&mid=43544

https://www.publications.usace.army...eOFzCUhCck=&tabid=16439&portalid=76&mid=43544

https://www.publications.usace.army...vxhTbX2AhA=&tabid=16439&portalid=76&mid=43544

https://www.publications.usace.army...vo0IdvqjW8=&tabid=16439&portalid=76&mid=43544

 

[WARose]

Another reference I'd highly recommend is 'Structural Dynamics: Theory and Application', by: Tedesco. That's one of the better treatments of rolling waves I've seen. (Most texts, they are built around breaking waves.)

 

[LR11]

OK thanks for additional references, I will look at in the next few days.