How Would Tides Affect an Island Lake Connected to a Distant Ocean?

[Artlav]

Let's say we have an island in the middle of an ocean, and there is a lake on the island located at sea level.

If the lake is isolated from the ocean, then it's level would stay constant while the tides go up and down in the ocean.

If the lake have an underground connection to the ocean nearby, then the level would rise and fall with the tides in the ocean, right?

Now, imagine that there are caves that link the lake with the same ocean several thousand kilometres east from the island, instead of right near to it.
What would happen to the level of the lake?

Would it follow the tides at the island, or the tides at the point where the cave meets the ocean?

 

[tiny-tim]

Hi Artlav!

Now, imagine that there are caves that link the lake with the same ocean several thousand kilometres east from the island, instead of right near to it.
What would happen to the level of the lake?

(caves? why not just a pipe? )

Let's assume that the sea floor is at a constant depth (if it isn't, then decreasing depth increases the height of the tidal wave, and this has nothing to do with the tidal effect itself).

Because the waters are connected, the two surfaces will be on the same gravitational equipotential surface.

 

[sophiecentaur]

I think he's making the point that there is continual change in height at either end which is not in phase. There is a lag in the tide from place to place, besides what the position of the Moon / Sun in the sky would suggest. The equipotential is only part of the issue in a 'real' ocean which is not on a water-covered planet as the tidal wave travels on various paths and at different speeds.
I think the answer is that you would get a flow of water through the pipe, backwards and forwards from the different points in the ocean (with or without the lake).
I have a feeling that it would constitute the ultimate in `Tidal Energy Schemes'.

 

[AlephZero]

I think the answer is that you would get a flow of water through the pipe, backwards and forwards from the different points in the ocean (with or without the lake).

I agree. The answer would certainly depend on the size of the lake compared with the diameter of the "pipe", for example.

I have a feeling that it would constitute the ultimate in `Tidal Energy Schemes'.

Probably not, because the height of the tides in deep oceans is quite small (about 0.5m). The highest tides are large estuaries where the water flows into a confined space (like the Bristol Channel in the UK with tides of up to 15m), or where the sea is the right size and shape to create a resonant standing wave at the same frequency as the tide.

 

[Studiot]

Probably not, because the height of the tides in deep oceans is quite small

That's no reason in itself to disbar energy generation from horizontal tidal flows.

 

[Artlav]

The problem i see is what makes the water rise in a tide?
Is it compression or water flow?

With the long pipe and island in ideal conditions there should be the same level in the lake as in the nearby ocean - the pressure is proportional to gravity, so less gravity on the distant site would result in higher water level producing the same pressure.
At the lake position same pressure would be generated by less water - two pipe ends at different gravity with same pressure. So the level would follow the ocean.

But what makes the level rise? With large lake and small pipe, where would the water come from?
It would have to flow across the pipe, right?
Thus, there would be different level in the lake, but what kind of - out of phase, smoothed, etc?

 

[sophiecentaur]

Compression?

Of course the lake volume and pipe resistance would impose a 'time constant' on the process (RC analogy).
Your model is not far different from that of a river estuary and tidal changes always occur in that situation.
I could also make the point that a simple model of an ocean of constant depth doesn't apply here as the lake must be part of a land mass. I guess you could have the land mass situated at one of the Poles, though, where it may not impede tides much.