I. The Depth of the Bulge
The original movie ends with the caveat, "The stretch of the tidal bulge and the depth of the ocean are greatly exaggerated." Some numbers may put this in context. The radius of the Earth (the brown circle in our movie) is 6378 km. The average depth of Earth's oceans is 3.790 km, a thin skin on top of the rocky/metallic "solid" Earth. The size of the tidal bulges induced in this layer of water is about 2 meters (see note1). That is, the ocean depth is about 1 m (0.001 km) deeper at high tide and about 1 m shallower at low tide.
Think of this in percentages. The Earth's oceans represent about 3.79 km / 6378 km = 0.00059 or 0.059% of the Earth's total radius -- a thin skin indeed! The Earth's tidal bulges represent only 0.002 km / 3.790 km = 0.0005 or 0.05% of the ocean's average depth -- a small variation, and an even tinier variation in the total diameter of the Earth.
If tides have such a very small influence on the size and shape of the Earth, why do we bother? Two reasons: (i) 2 m is significant on a human scale, and (ii) to maintain the bulge, water does have to flow, and the speed of the water flow can be significant on a human scale.
II. Maintaining the Bulge: Tidal Flow
In watching the movie, you may have developed the idea that the solid (brown) Earth spins while the water stays fixed with respect to the moon. This can not be true; if it were, the yardstick would have to plow through the water at a high rate of speed (see note2). Instead, the water rotates along with the solid Earth, mostly.
To maintain the tidal bulge, the water does have to flow, but in a more subtle way. Watch the movie below. In the top panel, you see the same movie as before, but with an arrow showing how the water is flowing past the yardstick (imagine the stick is fixed to the solid Earth under the water, or is a buoy anchored to the sea floor). During the first 6 hours of the movie, the water flows slowly past the yardstick, toward the bulge opposite the moon. Typical speeds are only about a km/hr, but over several hours, a lot of water has shifted position and has "piled up" into the bulge. At 6 hours, the yardstick finds itself in the deeper water, or "high tide", of this bulge.
During the next six hours, the yardstick sees the water change direction and flow the other way past the stick (notice that the water is still flowing toward the bulge: the differential tidal force on this, the "far side" of the Earth "pushes" the water away from the moon). Flow speeds are about the same as before, just in the opposite direction past the yardstick/buoy.
At time=12 hours, the water has flowed away from the region of the yardstick, and it is at "low tide". But fear not! During the next six hours, the water direction shifts again as the water is pulled by differential tidal forces toward the bulge on the (right) side of the Earth facing the moon.
At t=18 hours, the yardstick is at high tide again, and the water flow has stopped, about to change directions yet again. During 18 to 24 hours, the water flows in the opposite direction (still toward the bulge facing the moon), and at 24 hours we are back to the low tide at which we started.
To summarize, over the course of one rotation (day), the water flows East past the yardstick for about 6 hours, then West for 6 hours, then East for 6 hr, then West for 6 hrs, "sloshing" back and forth past the yardstick as it rotates along with the solid Earth below it. Looking globally, we see that as the water rotates along with the solid earth, the water on the side of Earth nearest the moon (right side) always feels a weak tidal pull that causes it to flow toward the moon, building up the bulge on that side of Earth. On the side of Earth away from the moon (left side), the equal but opposite tidal "push" causes the water to flow away from the moon, into the bulge on the left (see note3).
III. Shorelines, Tides, and Tidal Currents
Most of us don't experience tides in the deep ocean (though NOAA and other agencies do maintain buoys anchored in the deep ocean for monitoring tides, weather, tsunamis, etc.). Instead, we see it along shorelines, particularly at seaside beaches. The bottom two panels of the movie show (left) a side-view of a dock at a beach, with a yardstick that is more realistic than in the upper panel, and on the right, a birds-eye view of a bay. This is not unlike the harbor at Nantucket, MA, where the tides in our activity were measured. The ruler reads "2" at low tide in our movie, which corresponds to the MMLW ("mean lower low water") benchmark shown in the NOAA tide plots for Nantucket.
Notice that during times 0-6 hr of our movie, the water flows into the harbor, and the level of the water rises up the yardstick. We say the tide at this point on the Earth is "flooding." The speed is fastest at about 3 hours (half way to the bulge), slowing, and going "slack" as we reach high tide at 6 hours.
After t=6 hr, the tide starts to "ebb," slowly at first, fastest at 6+3 = 9 hrs, and going slack again at low tide (t=12 hr), when it again changes direction. The tide floods from 12-18 hours, is slack at high tide, then ebbs from 18-24 hours, getting us back to a low tide where we start the whole cycle again (see note4).
This flow of water across the ocean floor and into/out of the harbor is called a tidal current (not to be confused with currents in rivers that result from water flowing downhill, or ocean currents like the Gulf Stream that are driven by convection). In our simple model, they are well-defined and regular. In real life, things get messy because continents are large and break up the uniform flow of water into and out of the tidal bulges.
IV. Life is Messy: Toward Better Tidal Predictions
As a shoreline interacts with the ebbing and flooding of tidal currents, the water is forced to change direction and speed, flow into and out of harbors, up rivers, etc. Water can "pile up" along continental coastlines since there isn't time for it to flow around the continent before the "tide turns" a few hours later. The simple astronomical model of tides that we developed can no longer cope with this complexity, and we are forced to consider different models for predicting the tides.
One method is to use the physics principles of waves and oscillations, which also help us understand how musical instruments produce sound waves. For example, a violin string of a certain length, thickness, and tension will vibrate at a certain frequency when it is plucked or bowed. If you bow it faster, it still vibrates at the same frequency, producing the same note. Similarly, air in an organ pipe vibrates at a frequency that depends only on the length of the pipe. If you blow harder or softer, you change the loudness, but not the frequency or tone of the sound. In both cases, this is because the vibration is a "resonance" that is related to the size of the "resonant cavity" that is vibrating.
Oceanographers have found that different bodies of water can be treated as resonant cavities that resonate at preferred frequencies depending on their size. The "bowing" or "blowing" that excites a resonance comes from the astronomical model of tides that we developed: two high tides are "forced" on the body of water every 24h 48m. Some bodies of water are the right size to respond well to this forcing, and they develop strong and regular tides. Others are not the right size: the Great Lakes, for example, are too small, and do not resonate much, tidally. Some develop complex resonances that at first don't seem related to the astronomical forcing (for example, look at the tides in the Gulf of Mexico).
These bodies of water can not be treated as isolated resonant cavities -- they are connected and water can flow into and out of adjacent bodies, so complex mathematical models are used to track the interplay of the difference resonances. These models tend to do a much better job of predicting tidal behavior at different places on Earth. Again, we see this pattern of starting with simple models and improving them (Occam's Razor); here, we needed a "paradigm shift" to jump from the overly simplistic, astronomy-only model to the oscillations-based resonance models.
Endnotes
Note1: I took this value from our textbook. I've read other sources that indicate the bulge is less than one meter in the deep ocean. Either way, it is small compared to the depth of the oceans and the global size of the Earth.
Note2: Since velocity = distance/time, and we can think of the Earth's equatorial circumference as the total distance traveled in a day's rotation, we have d = 2*pi*R = 2*3.1415*6378 km = 40,074 km. There are 24 hours in a day, so v = d/t = 40,074 km / 24 hr = 1670 km/hr. For comparison, highway speed for a car is 100 km/hr. Imagine a yardstick plowing through the ocean at 1670 km/hr -- it would make quite a splash, and is not at all consistent with our experience with the real world. This is a nice example of how some simple math can impact your "critical thinking."
Note3: As the Earth rotates under the tidal bulge, you can think of the bulges as a pair of waves that flow over a fixed place on the Earth -- "tidal waves" (not to be confused with tsunamis, sporadic waves caused by earthquakes). This study of tides provides us with an interesting exercise in viewing a phenomenon from several view points: a "Gods-eye" view of the Earth as a planet rotating in space, a person looking at the entire planet but rotating along with it, and a person viewing a small patch of the planet from a human scale and perspective. Changing perspectives like this is an important tool in understanding all aspects of a complex phenomenon.
Note4: Well, not really. Remember from the activity answer page that we have to allow the moon to move in its orbit, and that makes the tide cycle a bit longer than one day -- actually about 24 hr 48 min.