# Is the water pressure below ocean waves constant?

• B

## Main Question or Discussion Point

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?

Related Other Physics Topics News on Phys.org
Bystander
Homework Helper
Gold Member
What wavelength?

Merlin3189
Homework Helper
Gold Member
I hadn't considered wavelength. I assumed a water depth very much greater than wavelength and amplitude.

davenn
Gold Member
2019 Award
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

Last edited:
anorlunda
Staff Emeritus
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.

davenn
jbriggs444
Homework Helper
2019 Award
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.

Last edited:
tech99
anorlunda
Staff Emeritus
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.

davenn and berkeman
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
Staff Emeritus
@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.

anorlunda
tech99
Gold Member
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.

Merlin3189
anorlunda
Staff Emeritus
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?

Merlin3189
tech99
Gold Member
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
Homework Helper
2019 Award
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
Mentor
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
Homework Helper
2019 Award
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
berkeman
Mentor
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
Staff Emeritus
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
Homework Helper
2019 Award
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.

Crowxe
anorlunda
Staff Emeritus
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
Gold Member
2019 Award
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
Gold Member
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
Homework Helper
2019 Award
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.

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
davenn
Gold Member
2019 Award
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