What causes tides?

During low tides, the island of Mont Saint Michel connects to mainland France. At the highest tides, it's an island. What causes tides?

Below are graphs of the sea level in San Diego over a six-day period and over a thirty-day period. The difference in sea level is about 2 meters from the highest high tide to the lowest low tide. There are two high tides and two low tides each day, a stronger cycle followed by a weaker one. The time intervals between the strong high tides is the time it takes for the moon to return to the same point in the sky each day. .

Plot of tides in San Diego over a six-day period.

Plot of tides in San Diego over a thirty-day period.

When there is either a full moon or a new moon, the tides have very large daily variations. When the moon is at first or third quarter, the variations are much smaller.

This animation shows changing water levels in the Earth's oceans caused by the tidal flows. The water flows in a number of cyclical paths within the ocean basins. The strength of the tides varies from place to place depending on the size of the ocean basin, the depth of the water, and how the water interacts with the local coastline geography.

Tidal forces

Tides arise from tidal forces. A tidal force happens when an object free falls in a gravitational field that varies in strength from place to place, such as the strengthening gravitational pull of a star or planet as one moves closer to it.

Skydiver falling in a standing position

Imagine a skydiver in free fall, feet first. She is tiny compared to the size of the Earth. There is little variation in the Earth's gravitational field from head to toe. A kilogram of her head experiences the same force as a kilogram of her leg.

Suppose she goes skydiving on a massive, but very tiny planet. She's tall enough compared to the size of the planet that her feet experience a stronger gravitational attraction than her head. She is "light headed" and "heavy footed." She feels this discrepancy as a stretching force, as if she was stretched on a rack. This stretching force is called a tidal force.

Free fall in a uniform gravitational field and in a non-uniform gravitational field

A planet orbiting a star or a moon orbiting a planet is also being stretched by the gradient of the gravitational force from the other body.

Ocean Tides

First, let's think about how the sun contributes to ocean tides. To keep it simple, think of the Earth as a solid sphere completely covered with a thin layer of water that can quickly flow around in response to forces.

The Earth being stretched into an oblong shape by the gradient of the gravitational field of the sun

The Earth's gravity is by far the most powerful force acting on the water, causing the water to hug the Earth as tightly as possible. With no other forces, the surface of the water would level out into a perfect sphere. The sun's gravitational pull keeps the Earth in its orbit. The attractive effect of the sun's gravity and the repulsive effect of the centrifugal force from the Earth's orbital motion are in balance.

But the sun's gravity gets weaker as one gets farther from the sun. On the day side, it's a bit stronger than the centrifugal force, causing the water to flow toward the sun. On the night side, the centrifugal force is a bit stronger, causing the water to flow away from the sun. Tidal bulges form both at the noonday point and the midnight point.

Now let's look at the moon's contribution to the tides, which are stronger than the sun's contribution.

The moon

At the Earth's surface, the gravitational force from the moon is about 150 times weaker than that of the sun. So how can the moon's tidal force be stronger? The cause of the tides is the gradient of the gravitational force, or how much the gravitational force changes as you go from the nearest side of the Earth to the opposite side. The moon is much closer than the sun, so it produces a gradient that is about twice as strong as the sun's.

The second ingredient for a tidal force is being in free fall or in an orbit. But if the moon orbits the Earth and not the other way around, how can the moon produce tidal forces at all? The answer is that the Earth and moon orbit each other, both circling their common center of gravity. So this creates a centrifugal force that competes with the moon's gravitational attraction in the same way as we described for the sun.

At full moon and new moon, the solar and lunar tidal forces reinforce each other, as the Earth is stretched by both along the same direction. This is called spring tide.

Spring tide occurs when the sun and the moon are on opposite sides of the Earth.

Spring tide also occurs when the sun and the moon are on the same side of the Earth.

At first and third quarter they partially cancel; the stretch directions are perpendicular. This is the neap tide.

Neap tide occurs at quarter moons

This explains the pattern we see in the thirty-day San Diego graph above. But why is a strong tide followed by a weaker one 12 hours later? The Earth is tilted with respect to the plane of the moon's orbit. The picture below shows what can happen. A man on an island experiences a high tide at point A, where the moon is directly overhead. Twelve hours later, he's at point B. Again, there's a high tide, but it's not as high because the tilt of the Earth causes him to miss the highest part of the tidal bulge. This effect is the source of the daily pattern we see in the six-day San Diego graph above.

The tilt of the Earth with respect to the plane of the moon's orbit causes two unequal ties during a 24 hour day.

Finally, let's look at a few complicating factors.

The water

Tidal bulges in the ocean create waves. Waves have their own rather complicated physics. Inertia limits the speed at which the wave travels. There is friction as the water flows against irregular ocean bottoms. There is also friction between layers of water when one layer flows past another (which is called viscosity). The depth of the ocean varies from place to place, from zero at the beach to over six miles at the Mariana Trench. Waves slow down when the water gets shallow because of their interactions with the bottom.

The continents

Blocked by large land masses, the water is confined within ocean basins. The daily cycle of tidal forces tends to produce standing waves as the waves reflect off the continents and the water sloshes back and forth within the ocean basins.

The Coriolis effect

When you're on a spinning merry-go-round and try to throw a ball, you will observe it taking a curved trajectory. This is the Coriolis effect. Look at any weather map, and you see the telltale signs of the Coriolis effect produced by the Earth's rotation. Winds flow clockwise around high pressure centers in the northern hemisphere and counterclockwise in the southern hemisphere. The same effect happens with the tidal waves in ocean basins. Instead of sloshing back and forth, they slosh around looped paths.

Map of the lunar contribution to the tides.

Above is a map of the main contribution of the lunar tidal force to the 12-hour cycle. The colors show sea level height at a particular time. The white lines show the locations of high tides at 1-hour intervals. At the points where the white lines converge, the sea level stays constant. The tidal bulges circle either clockwise or counterclockwise around these points.