As I understand it, tides result from the attraction of the moon’s gravity, upon the oceans waters. Since the North Pole represents a point where the moon’s gravitational attraction is weakest, I would expect no tides in the Arctic Ocena there.
Is this correct? Has any tidal variation been seen at the North Pole?
The point where the moon’s gravitational attraction is weakest is directly opposite the moon. The North Pole is never directly opposite the moon, therefore it is never the point on earth where the moon’s gravitational attraction is weakest.
The tidal variation would tend to be smallest at the poles if the Moon orbited at the plane of the equator. It doesn’t orbit in that plane exactly, however, so I’d expect there would be small tidal variations at the North pole.
If the Earth were uniformly covered in water, and if the Moon orbited in the plane of the Earth’s equator, and if the Earth’s orbit around the Sun (which also causes significant tides) were also in the equatorial plane, then there would be no tides at the North Pole. None of those is the case, though, so there will be.
But the point directly opposite the moon does have tides (Right?). Isn’t that why there are 2 rides a day?
Right. Here’s the way it was explained to me back in school. The arrows represent the strength of the gravitational attraction of the moon experienced at the far, center, near side of the Earth
--> ---> ----> o (Moon)
But when one looks at the differential gravitation attraction with respect to the center of the Earth:
<- - -> o (Moon)
Which leads to tidal bulges directly towards the Moon and directly opposite.
On a theoretically perfect globe, there would be no daily tidal cycle at the Poles, because the rotation of the earth doesn’t introduce any daily variation in the altitude of the Sun or Moon.
Instead there would be (somewhat weak) monthly and annual cycles, with tide being highest at full and new moon near the solstices.
On the real globe there are currents and uneven bottoms and ice effects so I don’t know how the real water level behaves at the North Pole.
good question! I am researching something similar at the moment. I don’t actually know the answer to this question. I will investigate further tomorrow and report back. (no, I am not going to the North Pole. We build oceanographic models and are presently working on incorporating tides into the models).
The OP didn’t ask this, but there are certainly tides in the Arctic Ocean in case anyone doubted that. The question is, is there a tidal node at the geographic pole? And if there is, does it have anything to do with the pole?
Judging from the responses, there are a lot of factors to consider. Maybe we should ask Bill O’Reilly, and settle this once and for all.
Another factor would be whether the Moon’s altitude in the sky varies at the Pole. I suspect you have a mental picture of the Moon’s orbit neatly aligned with the Earth’s equator; it isn’t, by a long way. Another factor is the influence of the Sun on the tides; the Sun rises and sets at the Pole, so the tidal bulge raised by the Sun doesn’t have a permanent null point at the Pole either. I’d expect lesser tides at the Pole, but certainly not none.
And you are correct.
I looked into the problem. It is sufficiently interesting to me that I will be pursuing this further.
There are certainly tides at the North Pole and throughout the Arctic Ocean. We certainly do not know what those tides are. There are no measurements available. As this post points out the inclination of the moon and sun relative to the earth’s axis means there will be forces at the pole. And internal tides will travel through as everywhere else in the ocean.
With the OP answered, the interesting question is what are the characteristics of the arctic tides? A tide is defined by the forcing-amplitude and phase of the gravity forces, the rotation of the earth, and bathymetry. So each location is different and in general it is impossible to derive the tidal motion from just the forcing. But in the open ocean, we can make good progress toward that goal. We can’t get all the way there, but we can hope to approximate reality. At least in the open ocean (like the North Pole) bathymetry is only a factor, not a dominant factor as it is in coastal areas.
There are about 120 pelagic tide stations around the world to provide measurements to help in modeling the global tides. Unfortunately, none are in the arctic. Something about conditions being a bit extreme. Being way down south I don’t really understand, but that is what I hear. 
In episode 2 of the latest Bruce Parry tv series on the BBC, he’s up past Qaanaaq (Thule) in northern Greenland hunting with the locals. At one point there’s a shot of the ice in front of them undulating up and down as the tide comes in and they all have to retreat back to land because it’s too dangerous to stay on the ice.
Not the North Pole, but getting on for 80 degrees North…