[chris (OP)]

The Atlantic coast of Portugal and Spain have large tides, but the Mediterranean has a tidal reach of only a few feet if that. Why? Wouldn't the water rushing across the Atlantic all get trapped in the Med and "build up" because there's no way out?

Chris

[yor_on]

"Tides are most pronounced along the coastline of the oceans and in bays where tidal range (the difference in height between low tide and high tide) is increased due to the topography and other factors. "Tidal bulges" which are the focus of attention in many textbooks, are in fact not due to rotation, but are simply due to the gravitational field of the moon, and the fact that this field has varying direction and strength over the volume of the Earth.

These bulges distort the shape of the solid Earth, and also distort the oceans. If the oceans covered the entire Earth uniformly, this would almost be the end of the story. But there are land masses, and ocean basins in which the water is mostly confined as the Earth rotates. This is where rotation does come into play, but not because of inertial effects, as textbooks would have you think. Without continents, the water in the ocean would lag behind the rotation of the Earth, due to frictional effects. But with continents the water is forced to move with them. However, the frictional drag is still important. Water in ocean basins is forced to "slosh around", reflecting from continental shelves, setting up ocean currents and standing waves that cause water level variations to be superimposed on the tidal bulges, and in many places, these are of greater amplitude than the tidal bulge variations.""

The last from Tidal Misconceptions.

[Geezer]

I think there might be a simpler answer.

The Mediterranean is really just a very big lake, big enough that it actually has tidal action, but nowhere near as much as the major oceans. It is connected to the Atlantic, but the connection is so restricted that tides in the Atlantic have little effect on the Mediterranean.

[B4Real]

Yup- No need calling Bill Nye for this one! 👍

[alancalverd]

Indeed there is no way out for the Atlantic tide. But equally, there's no way in.

[evan_au]

As the following map shows, the Mediterranean basin actually consists of several smaller basins, each of which have relatively small tidal range. The center of the white areas are called amphidromic points, which have effectively no tide, while the surrounding blue areas have very little tide. (Unfortunately, this map splits the Mediterranean across the left and right edges.)

https://en.wikipedia.org/wiki/File:M2_tidal_constituent.jpg

There are other, smaller tidal constituents which will have different amphidromic points, but these will also be affected by the multiple small basins in the Mediterranean.

[evan_au]

Another thread is talking about Chladni's plates - patterns formed when sand is sprinkled on a vibrating plate. The sand will move away from areas with high amplitude vibrations (anti-nodes), and migrate to areas with little vibration (nodes).

The amphidromic points are the places in the ocean where the amplitude of tide variation is minimal (you could call them nodes).

Of course, the mode of vibration is very different in a solid and a liquid - stiffness plays a major part in the resonances of a solid, while stiffness does not really apply to the sloshing of a liquid like the ocean or a sea.

[rmolnav]

"Tidal bulges" which are the focus of attention in many textbooks, are in fact not due to rotation, but are simply due to the gravitational field of the moon, and the fact that this field has varying direction and strength over the volume of the Earth.

Sorry, but that´s wrong. The varying gravitational field of the moon is one of the causes, but NOT "simply" that. Revolving (rather than rotation) of the Earth around Moon/Earth barycenter is also one of the root causes. And other local factors hinder or enhance tidal locally. You can see it if you have a look at most thorough work on tides, published by experts of most important institution in the field:
https://tidesandcurrents.noaa.gov/publications/Tidal_Analysis_and_Predictions.pdf

[rmolnav]

And the answer to the question "Why are the tides in the Mediterranean so small?" is pretty clear. Surely you can find it in the NOAA linked work, but I´m going to put it here in my own words.
On the one hand, the so called bulges are relatively very, very small deformations of sea surface, not more than only a few meters from high to low tide, some 10,000,000 meters apart (along the equator). And the Mediterranean size, even in the sense W-E, is pretty small in comparison to that distance.
And on the other hand, bulges require the supply of huge amounts of water, which have to come not only from low latitud areas where medium and low tides, but also from higher N and S latitud areas. There the Moon pull, and centrifugal forces at farthest hemisphere, have tangential components , not in opposition to water weight, and water displacement is easy ... But the average size of the Mediterranean in meridian sense is very, very small.
Where could the water necessary for the bulges come from?   

[Yusup Hizirov]

"Why are the tides in the Mediterranean so small?"

Tides is the result of the rotation of the Earth and whirlpools

There is a rigorous regularity; tides are formed not along the entire coast of the seas and oceans, but only on those shores where the high angular velocity of the currents. And the higher the velocity of currents, the higher the amplitude of the tidal wave. On the rectilinear banks, where the currents do not have angular velocity, tides and ebbs do not form.

The waters of lakes, seas and oceans of the northern hemisphere rotate counterclockwise, and the waters of the southern hemisphere rotate by the hour hand, forming giant whirlpools. https://en.m.wikipedia.org/wiki/Ocean_gyre

As is known, everything that rotates, including whirlpools, possess the property of a gyro (yule) to maintain the vertical position of the axis in space, regardless of the rotation of the Earth.

If you look at the Earth from the Sun, the whirlpools, rotating together with the Earth, turn over twice a day, due to which the whirlpools precess (swing by 1-2 degrees) and reflect the tidal wave around the entire perimeter of the whirlpool.
http://img-fotki.yandex.ru/get/9804/7837959.21/0_f6015_1eb816e5_orig https://goo.gl/images/URBn32

The waters of the White Sea rotate counter-clockwise, forming a huge whirlpool-gyroscope, which, precessing, reflects a tidal wave along the entire perimeter of the White Sea.
A similar pattern of tides is observed in all lakes, seas and oceanas.
http://tapemark.narod.ru/more/22.png

The waters of the Mediterranean Sea rotate counter-clockwise, forming tides 10-15 cm high. But in Gabes Bay, off the coast of Tunisia, the tides can reach three meters, and sometimes even more, and this is considered one of the mysteries of nature. But at the same time, in the Gulf of Gabes the whirlpool turns, precessing the reflecting additional tidal wave.
A tidal wave in the Amazon River creates a huge planetary maelstrom a few thousand kilometers in diameter, rotating between South America and North Africa, embracing the mouth of the Amazon River.
The scheme of motion of a tidal wave, along the perimeter of the North Atlantic planetary maelstrom.

The length of the tidal wave depends on the diameter of the whirlpool. And the height of the tidal wave depends on the rotation speed of the whirlpool of the orbital velocity of the Earth, and the time of the tilting of the whirlpool (12 hours).
A = V1 • V2 / t
where: A is the amplitude of the tidal wave (precession angle).
V1 - rotation speed of the whirlpool.
V2 is the orbital velocity of the Earth.
t - the time of tilting of the whirlpool (12 hours).

The vortex theory of tides can be easily verified by the connection between the height of the tidal wave and the rotation speed of the whirlpools. The height of the tidal wave can be determined by the location of the whirlpools. Drawing on a map of the depths and currents of the seas and oceans.
Comments: 
https://www.thenakedscientists.com/forum/index.php?topic=73127.0
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In the west of the Mediterranean Sea there are three whirlpools, four hundred kilometers in diameter each, which precesses create high tides with a height of 1.2 meters.
Whirlpools of the Mediterranean Sea
http://goo.gl/G9l71A

Also through the Strait of Gibraltar with a width of 14 km. and a depth of 53 m into the Mediterranean Sea tidal wave moves, precessing reflected by the North Atlantic planetary whirlpool .

The Mediterranean Sea is considered without tidal, but near Venice and on the Euricos Channel in eastern Greece, tides and ebbs are up to one meter or more. And this is considered one of the mysteries of nature, but at the same time, Italian physicists discovered in the east of the Mediterranean, at a depth of more than three kilometers of a chain of underwater whirlpools, ten kilometers in diameter each. From this we can conclude that along the coast of Venice, at a depth of several kilometers, there is a chain of underwater whirlpools.