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It's clear that on a smooth surface of a massive sphere $M$, covered with water, two bulges of water appear when it's rotating in sync with a satellite (a massive sphere with a substantially smaller mass as the mass $M$) around their center of mass.

Now in the case of the Earth, its surface can't be said to be smooth, to say the least. There are huge pieces of land sticking out above the water on about 30% of the Earth and almost all landmass above the water is situated on one side. The water covered surface varies from 11$km$ deep near Japan (the Marian trog) to more shallow waters.

What (if so) will be the influence of this rugged surface on the form of the two tidal bulges in contrast to a smooth Earth surface?

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  • $\begingroup$ Seems more appropriate to Earth Science SE. $\endgroup$ Commented Apr 29, 2020 at 11:02

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This is just a very brief answer; wikipedia (https://en.wikipedia.org/wiki/Theory_of_tides) would be a place to start for more details.

The general idea is the following: For a uniformly water-covered sphere, ideally you would have two opposing high-tide waves. However, you can immediately see two complications:

  • For the earth, the tidal potential comes from moon and sun (and in priciple other planets, but that's negligible). The positions vary, but you can decompose the potential into modes with specific duration. The major modes have durations around 12 hours and around 24 hours.
  • What's more, the tidal bulges interact with the continents. For example, in the Atlantic, the wave gets scattered and reflected on the American coast, the returning wave gets again scattered and reflected off Europe and Africa, interferes with the next wave etc. In the end, you have a complicated resonator (the ocean) that gets excited with a broad signal. The response (i.e. the actual tides) are then determined by the eigenfrequencies of the system.

More or less separate parts of the ocean have their own tides; e.g., the pacific generally has tides around 24 hours length, while the Atlantic has 12-hourish tides. The North Sea is too small to have "own" tides; it's just the Atlantic sloshing iin aand out. The Baltic sea has a too small connection to the Atlantic, so it has no significant tides at all.

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