Is the water pressure below ocean waves constant?

[Treva31]

If you are stationary say 10m below the ocean surface does the water pressure at your location vary with the waves.

For example:

When a wave crest is above you than means perhaps 12m of water is above you.
Then a few seconds later a trough is above you so only 8m of water is above you.

So you might expect your pressure reading to be going up and down with the waves?

 

[Bystander]

What wavelength?

 

[Merlin3189]

I hadn't considered wavelength. I assumed a water depth very much greater than wavelength and amplitude.

 

[davenn]

What wavelength?

wouldn't matter
the point is that the head of water above you is varying depending if it is a peak or trough

 

[anorlunda]

I tried to find a graphic that illustrates @davenn 's correct answer. I found this. It's pretty extreme, but the principle applies to all waves, big and small.

 

[jbriggs444]

I tried to find a graphic that illustrates @davenn 's correct answer. I found this. It's pretty extreme, but the principle applies to all waves, big and small.

View attachment 203791

And what is the wavelength of a tsunami?

The point is that if the pressure at depth varies according to the depth below the peak or trough of surface waves then the water at depth must be moving due to the resulting pressure gradients. If the water at depth is not oscillating back and forth due to this effect, the pressure at depth must not be changing due to the surface waves.

In a shallow water wave, water at depth is indeed moving under the effect of the wave. In a deep water wave this is not the case. It may be surprising, but a tsunami is a shallow water wave.

 

[anorlunda]

The point is that if the pressure at depth varies according to the depth below the peak or trough of surface waves then the water at depth must be moving due to the resulting pressure gradients.

I'm sorry but I don't understand your point. Water is incompressible for practical purposes. Why is movement at depth necessary to have pressure change?

I also don't see why wavelength is relevant to the question.

I could understand an argument including the speed of sound in water that pressure oscillations fan out and merge with adjacent crests at very deep depths (the tsunami sensor was 19800 feet deep). But the OP specified only 10m depth.

 

[Svein]

That reminds me - in the start of the 1980s my research company were hired to do the instrumentation of the collapsed oil platform "Alexander Kielland" before attempting to turn it right side up. I was asked to create a backup system (in the case that the expensive measurement system crashed). The main function of my system was to show the depth of one of the flotation pods.

When I asked what precision they wanted on the depth, they more or less automatically answered "1 cm". To which I answered "below what?" This was in a rather large inlet, with waves seldom below half a meter. The answer: "Below sea level". No use in asking any further. I got a very precise pressure sensor, measured the sensor output frequency, calculated the apparent depth, did some low-pass filtering and presented the answer - they got a number and they were happy.

Back to the original question - is the pressure at, say, 10 m below the surface, independent on the amplitude of the waves on the surface? I still do not know, but my low-pass filter was meant to minimize any such effect. AFAIK, the frequency spectrum of sea waves is in the 0.1Hz - 1Hz band, so my filter could not be all that effective.

 

[anorlunda]

@Svein , even sea level (neglecting tides, waves, seasons, and weather) is dynamic, depending on your time scale.

 

[Svein]

@Svein , even sea level (neglecting tides, waves, seasons, and weather) is dynamic, depending on your time scale.

Yes, but they were trying to turn it around in a couple of days... Seriously, since the platform was floating in the same water, I was only supposed to inform the turnaround guys of the position of the pod in relation to the current sea level. My take on it was purely as a measurement guy - with the huge size of the platform a precision of half a meter would be more than precise enough.

I have a list of such anecdotes regarding silly requirements - I try to use them sparingly.

 

[tech99]

And what is the wavelength of a tsunami?

The point is that if the pressure at depth varies according to the depth below the peak or trough of surface waves then the water at depth must be moving due to the resulting pressure gradients. If the water at depth is not oscillating back and forth due to this effect, the pressure at depth must not be changing due to the surface waves.

In a shallow water wave, water at depth is indeed moving under the effect of the wave. In a deep water wave this is not the case. It may be surprising, but a tsunami is a shallow water wave.

I agree with this reply. A wave is held up by the dynamics of movement, its inertia, and the pressure effect must die out when we get a few wavelengths below the surface. We only see seaweed waving in fairly shallow water. It is rather like the situation when an airliner flies overhead - we are not all crushed by an increase in pressure.

 

[anorlunda]

I agree with this reply. A wave is held up by the dynamics of movement, its inertia, and the pressure effect must die out when we get a few wavelengths below the surface. We only see seaweed waving in fairly shallow water. It is rather like the situation when an airliner flies overhead - we are not all crushed by an increase in pressure.

An airliner is a poor comparison because air is so compressible.

Of course I can always be wrong. You and @jbriggs444 could be right. I tried looking it up. https://en.wikipedia.org/wiki/Wind_wave#Physics_of_waves talks about the motion but not the pressure.

If I had a hollow cylinder, sealed at the base, and anchored to the sea bottom, with a hole in the side just barely deep enough to stay submerged. Its level would go up and down as waves pass (not as high as the waves, but some) but horizontal motion would be blocked. What about pressure in the bottom of that cylinder, constant or oscillatory?

 

[tech99]

An airliner is a poor comparison because air is so compressible.

Of course I can always be wrong. You and @jbriggs444 could be right. I tried looking it up. https://en.wikipedia.org/wiki/Wind_wave#Physics_of_waves talks about the motion but not the pressure.

If I had a hollow cylinder, sealed at the base, and anchored to the sea bottom, with a hole in the side just barely deep enough to stay submerged. Its level would go up and down as waves pass (not as high as the waves, but some) but horizontal motion would be blocked. What about pressure in the bottom of that cylinder, constant or oscillatory?

The water particles near the surface execute a circular motion as a wave passes, and the tube would alter their motion to an up-and-down one. It seems like a waveguide carrying energy down to the sea floor.

 

[jbriggs444]

I'm sorry but I don't understand your point. Water is incompressible for practical purposes. Why is movement at depth necessary to have pressure change?

The reasoning runs the other way. If there is a pressure difference between the water under the crest and the water under the trough then water will flow under that pressure gradient. If we do not observe such a flow then we can infer the lack of a gradient. We do not, in fact, observe such a flow (for deep water waves).

 

[berkeman]

The reasoning runs the other way. If there is a pressure difference between the water under the crest and the water under the trough then water will flow under that pressure gradient. If we do not observe such a flow then we can infer the lack of a gradient. We do not, in fact, observe such a flow (for deep water waves).

But the tsunami wave is wide enough that an ocean floor monitor can pick it up? That might make sense.

 

[jbriggs444]

But the tsunami wave is wide enough that an ocean floor monitor can pick it up? That might make sense.

Yes. Tsunami waves have huge wavelengths, huge enough that the ocean depth is smaller than the wavelength. Accordingly, they qualify as shallow water waves.

[Mind you, my education in the details of tsunamis is limited to what I could Google up in a few minutes]

 

[berkeman]

Yes. Tsunami waves have huge wavelengths, huge enough that the ocean depth is smaller than the wavelength. They are shallow water waves.

Interesting. Learn something new every dang day here at the PF!

 

[anorlunda]

If there is a pressure difference between the water under the crest and the water under the trough then water will flow under that pressure gradient.

I feel like I'm being denser than water because I still don't see it. Yes water does flow under that pressure gradient. Isn't that what causes the circular motions of the molecules in the wave?

I would like a link to a tutorial on the math of the pressure-motion interactions in those water waves. As I said, the Wikipedia article doesn't even talk about the pressure.

 

[jbriggs444]

I feel like I'm being denser than water because I still don't see it. Yes water does flow under that pressure gradient. Isn't that what causes the circular motions of the molecules in the wave?

Yes, near the surface, water moves in a circular pattern under the wave. But water farther from the surface does not move that much. Otherwise, the energy in a wave of small amplitude and small wavelength in deep water would be enormous.

If you drop a rock off the back end of an ocean liner, it makes waves. That proves that the deep water does not move appreciably.

 

[anorlunda]

Yes, near the surface, water moves in a circle under the wave. But water farther from the surface does not move that much. Otherwise, the energy in a wave of small amplitude and small wavelength in deep water would be enormous.

Ah, thanks @jbriggs444 , now the first light of understanding is beginning to penetrate. That's a clever argument.

I would still like to see the math.

 

[davenn]

It may be surprising, but a tsunami is a shallow water wave.

I agree with this reply. A wave is held up by the dynamics of movement, its inertia, and the pressure effect must die out when we get a few wavelengths below the surface. We only see seaweed waving in fairly shallow water. It is rather like the situation when an airliner flies overhead - we are not all crushed by an increase in pressure.

you are agreeing with incorrect comments, tech99

both these comments are incorrect as anorlunda pointed out with his comments

you cannot compare tsunamis with surficial waves caused by winds etc as you have done, tech99, they are very different beasts

wind etc waves are created at the surface and don't penetrate to any great depth.
The tsunami wave pulse(s) covers the full depth of the water that is in ... why ?
one reason is because they are, in general, created at depth

when a tsunami wave crosses the Pacific Ocean from say, Japan to Hawaii. The wave pulses can be measured at any depth from sea floor to the surface as they pass by

http://itic.ioc-unesco.org/index.ph...n-tsunamis-waves-reach&catid=1340&Itemid=2031

note the very first sentence ...

Once a tsunami has been generated, its energy is distributed throughout the water column, regardless of the ocean's depth.

Dave

 

[tech99]

you are agreeing with incorrect comments, tech99

both these comments are incorrect as anorlunda pointed out with his comments

you cannot compare tsunamis with surficial waves caused by winds etc as you have done, tech99, they are very different beasts

wind etc waves are created at the surface and don't penetrate to any great depth.
The tsunami wave pulse(s) covers the full depth of the water that is in ... why ?
one reason is because they are, in general, created at depth

when a tsunami wave crosses the Pacific Ocean from say, Japan to Hawaii. The wave pulses can be measured at any depth from sea floor to the surface as they pass by

http://itic.ioc-unesco.org/index.ph...n-tsunamis-waves-reach&catid=1340&Itemid=2031

note the very first sentence ...Dave

Sorry, I was agreeing with the wrong reply! I agree the Tsunami is a long wave where pressure will be felt at the sea bed, but pressure is not felt at the sea bed for the case of "short" waves in "deep" water.

 

[jbriggs444]

both these comments are incorrect as anorlunda pointed out with his comments

I stand by my comment. A tsunami is a shallow water wave. As you agree.

 

[NTL2009]

I stand by my comment. A tsunami is a shallow water wave. As you agree.

But it seems extremely relevant that, as davenn points out, a tsunami wave is created at the ocean floor, not at the surface.

I seem to recall that the surface wave of a tsunami is rather small while out in the far ocean, until it starts interacting with the shallow shelf near land, and this (drag?) causes it to increase in height near land.

 

[davenn]

I seem to recall that the surface wave of a tsunami is rather small while out in the far ocean, until it starts interacting with the shallow shelf near land, and this (drag?) causes it to increase in height near land.

exactly, and this is the important point
that article link I posted yesterday shows how that happens

 

[Crowxe]

let's take inputs to the extreme, say the pressure meter is just an inch under the trough hight, and in opposite extreme , presume it's 3km deep. I think it's obvious that whatever going on the water surface won't affect the readings at that depth. So, in your example , there will be fluctuation in pressure but not entirely equal to the wave hight. The deeper you go the less the fluctuation will be , wave length and speed could slightly contribute to the fluctuation value (remember that there's tons of dynamic involved)

 

[sophiecentaur]

I stand by my comment. A tsunami is a shallow water wave. As you agree.

If you are using the term 'shallow', referring to the depth with respect to the wavelength and the amplitude then I agree. The effect that you get with ordinary waves, breaking on a gently sloping beach is the same. The height of a Tsunami wave as it travels over the deep ocean may be very great and the effect on a boat out at sea will be relatively mild at all as the acceleration is very low. The path of the water particles is the same for all deep water waves - vertical circles with a radius that decreases with depth and the shape of the path becomes flattened and the motion is mostly forward and backward rather than up and down. This hyper physics link gives a simple model of a continuous wave. If the water at depth is moving in a closed curve then there must be acceleration and that implies there must be varying force (therefore varying pressure) at depth.

The peakiness of a wave is brought about for high amplitude and also when the water becomes shallow. the speed gets slower for shallow water and the peaks overtake the troughs to make a breaking wave. The water flows backwards in front of the crest and accounts for the draining of water away from the coast just ahead of the breaking tsunami wave.

 

[anorlunda]

Don't forget that tides are also waves. And even seich waves in oceans with one year periods cause seasonal variations (see #9)

Go back to @jbriggs444 posts in this thread. I'm convinced that his is the right explanation, and his reasoning includes the wavelength between crests.

 

[olivermsun]

If you are using the term 'shallow', referring to the depth with respect to the wavelength and the amplitude then I agree. The effect that you get with ordinary waves, breaking on a gently sloping beach is the same. The height of a Tsunami wave as it travels over the deep ocean may be very great and the effect on a boat out at sea will be relatively mild at all as the acceleration is very low.

FWIW, the vertical displacement due to tsunamis traveling in the deep ocean is typically very small. According to Wikipedia, the 2004 Indian Ocean tsunami was observed 2 h after the earthquake in deep water with a height of 60 cm. Conservation of wave action/conservation of energy combined with the slowdown in wave group speed caused the tsunami to reach heights of 24+ m as it shoaled.

The path of the water particles is the same for all deep water waves - vertical circles with a radius that decreases with depth and the shape of the path becomes flattened and the motion is mostly forward and backward rather than up and down. This hyper physics link gives a simple model of a continuous wave. If the water at depth is moving in a closed curve then there must be acceleration and that implies there must be varying force (therefore varying pressure) at depth.

The (exponential) decay scale is in terms of wavelengths, so practically speaking it's very difficult to measure the bottom pressure fluctuation due to short/"deep water" waves. By contrast, long/"shallow water" waves are routinely observed with bottom pressure sensors.

 

[CWatters]

Google books found what looks like an equation for the pressure below a wave...https://books.google.co.uk/books?id...TAC#v=onepage&q=pressure below a wave&f=false

 

[olivermsun]

Thanks, CWatters.
Here's another useful resource as well: http://web.mit.edu/1.138j/www/material/chap-4.pdf

 

[sophiecentaur]

FWIW, the vertical displacement due to tsunamis traveling in the deep ocean is typically very small.

It's down to the total volume of water displaced, I suppose. If the deep water height is 1m and the wavelength is 1km then it stands on its end when entering shallow water. You can easily get tens of metres of height.
But, apart from the dimensions, the tsunami has to behave the same as small waves breaking on the shore. Water waves are only different at the very small scale, where surface tension dominates (capillary waves) there is no difference in the physics of straight 'gravity' waves.
Having observed many bow waves from ships as they meet a shallow shore, I have noticed the very same effect that tsunamis cause - once launched, the moderate bow wave carries on for a great distance and then peaks as it reaches the beach etc. etc.. Interestingly, the dissipation is not inverse square because the spreading is not over a sphere and it's not even 1/r because the wavefront of an established bow wave is more or less a straight line. I like to think in terms of Huygens construction (personal observation but justified, I think). A tsunami can be generated by a large aperture source like half an island appearing or disappearing so I imagine the source can be looked at as several wavelengths. Hence less dispersion of energy.

 

[pieselsoft]

If you are stationary say 10m below the ocean surface does the water pressure at your location vary with the waves.

For example:

When a wave crest is above you than means perhaps 12m of water is above you.
Then a few seconds later a trough is above you so only 8m of water is above you.

So you might expect your pressure reading to be going up and down with the waves?

No. It is rather complicated, because you have to include dynamic pressure, and not just the hydrostatic pressure (use Bernoulli's Equation). It's not static, if there are waves, and dynamic pressure comes from the fact that the water is moving and accelerating, which requires forces/pressure. How it behaves depends on the depth of the water. See here, e.g. http://web.mit.edu/2.016/www/handouts/Free-Surface-Waves.pdf