How Tides Form · TideLab

Ebb and Flow

Spend a whole day at the seashore and you will see the water come in and go out: the highest level is high tide, the lowest is low tide. In Chinese the daytime rise is called chao and the night-time one xi; together they make chaoxi, the tides.

Most of China's coast has two high tides and two low tides a day, and each day high tide comes about 50 minutes later than the day before — exactly how much later the Moon rises each day. The small window at the bottom right always shows the water level at the observation site.

Tide-Generating Force

The Moon's gravity differs in size and direction across the Earth: the near side is closer and is pulled harder; the far side is farther away and is pulled less.

The Earth and Moon revolve around their common centre of mass, so every point on the Earth feels the same inertial centrifugal force, equal to the Moon's pull on the Earth's centre and pointing away from the Moon.

Together they give the tide-generating force: at the points facing toward and away from the Moon it points outward with almost the same strength, while on the two sides it points toward the centre. It is inversely proportional to the cube of the Earth–Moon distance — halve the distance and it becomes 8 times stronger.

Two Tides a Day

Under the tide-generating force the water piles up toward the sub-lunar point and the antipodal point, forming two tidal bulges; the ring between them is the low-water belt.

The bulges follow the Moon and barely move; underneath, the Earth rotates from west to east. Each time the golden observation point passes a bulge it meets a high tide, and in the low-water belt a low tide — two high tides and two low tides a day.

The Moon moves about 13° east along its orbit each day, so the Earth needs 24 h 50 min to face it again: high tide comes about 50 minutes later each day, and two high tides are about 12 h 25 min apart.

Spring and Neap Tides

The Sun is enormous but very far away, so its tide-generating force is only about 0.46 times the Moon's; it raises a smaller pair of bulges.

At new moon (lunar day 1) and full moon (day 15) the Sun, Earth and Moon are roughly in line, the two pairs of bulges point the same way and add up, and the tidal range is largest: spring tides. At first quarter (day 8) and last quarter (day 23) the Sun and Moon are at right angles; the Sun's bulges fall on the Moon's low-water belt and weaken each other, so the range is smallest: neap tides.

In the Tang dynasty, Dou Shumeng already described this change with the Moon's phases in his Haitao Zhi (Treatise on Tides).

Diurnal Inequality

The Moon's orbit is tilted to the equator, so its declination swings north and south about every 27.3 days. When the Moon is above the equator the two bulges are symmetric about it, and the two daily high tides at a given latitude are equally high.

When the Moon is north, the near bulge shifts into the Northern Hemisphere and the far bulge into the Southern. An observation point on the golden latitude circle turns once a day, crossing one bulge through its thick part and the other near its edge, so the two high tides are one higher and one lower: this is diurnal inequality. The higher the latitude and the larger the declination, the stronger the effect; some seas get only one high tide a day.