Why Does the Water Level in a Lake or Harbour Slowly Rise and Fall, Even With No Wind?
― A 19th-Century Swiss Doctor Measured a Whole Lake Rocking Like a Seesaw
The water in a lake or bay can slowly swap its tilt, like one big seesaw. This rocking has a fixed rhythm, and the rhythm depends only on the lake's length and depth. The person who confirmed this was a doctor who lived on a lake shore.
It is a calm, windless day. You are standing on a jetty on a lake. You look at a post by your feet. A spot that was dry a moment ago is now under water.
After a while, the water draws back again. No waves have rolled in. The surface has stayed as flat as a mirror the whole time.
A lake has almost none of the tides you see at sea. So where does this rising and falling come from?
There are only two reasons
When the water rises on one shore, it falls on the opposite shore. The middle hardly moves. The whole surface is slowly swapping its tilt.
The rocking repeats once for each round trip from shore to shore and back. That time depends only on the lake's length and depth. In a big lake it can be more than an hour.
This phenomenon is called a "seiche". The name is said to come from a word long used around Geneva in Switzerland. Local people had known for a long time that the water level of Lake Geneva sometimes rose and fell in a strange way.
A doctor on the lake shore kept measuring the water level
The person who uncovered what this rocking really was is a Swiss man named François-Alphonse Forel. His main field was medicine, and he taught anatomy and physiology at a university.
Forel grew up in Morges, a town on the shore of Lake Geneva, and made the lake the subject of his life's research. From the 1870s, he is said to have set up an instrument on the shore that drew the water level on paper automatically, and he kept records with it.
The same wave shape appeared again and again in the recorded line. The lake's rocking along its long direction is said to have taken about 73 minutes per round trip. Its size changed with the weather, but this period hardly changed at all.
That the period stayed the same was a big clue. A swing takes the same time for one round trip whether you push it hard or gently. If something has a fixed period, that is a sign it is swinging at its own "natural rhythm".
Look at Figure 1. It shows a lake cut through from the side. The water surface tilts up and down on the left and right in turn, with the middle as the pivot. Use the slider to change the lake's depth and see how the time for one round trip changes.
Deeper means faster, longer means slower
The seesaw's rhythm is the time the rocking takes to travel from shore to shore and back. When a lake is much shallower than it is long, the speed of this rocking depends only on the depth. It travels faster in a deep lake and slower in a shallow one.
The person who put this relationship into a formula was Merian, a scholar from Basel in Switzerland, in 1828. Forel compared this formula with his measurements on Lake Geneva, and confirmed that the rocking is a back-and-forth motion of all the lake's water.
When you actually calculate it, Lake Geneva comes out at about 62 minutes. That is off from the measured 73 minutes, because the lake is not a simple box shape. The rocking is slowed in shallow and narrow places, so a real lake takes a little longer.
So why does it start rocking on a windless day? The trigger is a change in air pressure passing over the lake, or wind that blew far away. If the water on one side of the lake is pushed down slightly, it keeps rocking at its own rhythm for a while, even after the push is gone.
The same rocking happens in harbours and bays. In Japan, the tide is treated as the "main" movement, and the short-period rocking on top of it is called "fukushindō". In the early 1900s, Kotaro Honda, Torahiko Terada and others gathered records from harbours across the country. They are said to have shown that each bay has its own fixed period.
If the mouth of the bay is open, the rocking changes
A lake is closed by shore at both ends. A bay, though, is open to the sea on one side. At the mouth of the bay the water level hardly changes, and that spot becomes a node. The biggest rise and fall is at the very back of the bay (Figure 2).
In a bay like this, one round trip takes about twice as long as in a lake of the same length. This is because the distance from the mouth to the back of the bay matches, in a lake, the distance "from the middle to the shore".
Here the swing comes back into the story. If you push a swing in time with its rhythm, even a small force makes it swing high. If the period of the rocking arriving from the open sea happens to match the bay's own fixed period, the water level at the back of the bay rises and falls a great deal.
In Nagasaki Bay, this rocking has long been called "abiki". On 31 March 1979, the water level in Nagasaki Harbour is said to have risen and fallen by about 2.8 metres. The trigger was a small change in air pressure moving across the East China Sea. It is thought to have grown bit by bit over the sea, then matched the bay's rhythm and become large.
In the abiki season, boats moored in the harbour can be swept away, and water can overflow low shorelines. The meteorological observatory issues information about "fukushindō". Near a harbour, it is wise to keep an eye on that information too.
Summary
The water level of a lake or harbour rises and falls slowly on a windless day because the whole body of water is rocking like a seesaw. Its period is set almost entirely by the length and depth of the lake or bay. Forel saw this from the "unchanging period" that showed up on the recording paper.
A puddle, a lake, a bay ―
each has a "rhythm of rocking" set by its shape alone.
You can read about the same thing happening in a small container in "Why does coffee spill when you walk with it?", and about long waves arriving from far away in "Why does a high wave suddenly come when there's no wind?". For the story of someone who chased a wave along a canal instead of a lake, see this article.
- Pour water about 2 cm deep into a rectangular tray or shallow container. Measure the length of the container.
- Lift one end of the container just slightly and put it straight back. Watch the water surface move back and forth like a seesaw.
- Time 10 round trips with a stopwatch and divide by 10. Then make the water 4 cm deep and measure again.
With a length of 30 cm and a depth of 2 cm, one round trip should take a little over a second. If you make the water deeper, one round trip gets shorter. The same formula as for a lake works just as well for a kitchen container.
For those who want to know more ― terms, formulas, and links to textbooksIt shows which level each part belongs to, from junior-high science to university courses
- Junior highCovered in junior-high science
- High schoolCovered in high-school physics
- High school+Advanced high-school material, or textbook sidebar content
- UniversityUniversity-level courses (fluid mechanics, physical oceanography) not taught in high school
- ResearchTopics researchers are still working on, not yet taught even at university as settled
Junior highTerms: this phenomenon has a name
- Seiche: a phenomenon in an enclosed body of water such as a lake or bay, in which all the water rocks at a fixed period.
- Fukushindō (secondary oscillation): a water-level change with a period of a few to several tens of minutes, on top of the tide in a harbour or bay. Nagasaki's "abiki" is a typical example.
- Natural period: the "time for one easy round trip" that each object has, such as a swing or a lake.
Junior highHigh schoolChecking with a formula: the round-trip time on Lake Geneva
Treat the lake as a long, thin box of constant length and depth. The time for the rocking to go from shore to shore and back is exactly the time for one round trip.
| In symbols | T ＝ 2L ÷ √( g × h ) (if one side is open, like a bay, T ＝ 4L ÷ √( g × h )) |
| In words | Time for one round trip ＝ distance of the round trip (twice the lake's length) ÷ speed of the rocking. The speed is the square root of "gravitational acceleration × depth" |
| Where it comes from | For shallow-water waves, the speed is fixed at √( g × h ) by the balance between gravity, which tries to return the water to level, and the momentum (inertia) of the moving water. Applying that to the round-trip distance gives "Merian's formula" |
| T | Time for one round trip (period). Unit: seconds |
| L | Length of the lake. Unit: metres |
| h | Mean depth. Unit: metres |
| g | Gravitational acceleration. About 9.8 m/s² |
| Length of Lake Geneva (long direction) | About 72 km ＝ 72000 m |
| Mean depth | Said to be about 154 m |
| Gravitational acceleration | 9.8 m/s² |
| Measured period (Forel and others) | Said to be about 73 minutes |
| Gravitational acceleration × depth | 9.8 × 154 ≒ 1509 |
| Speed of the rocking | The square root of 1509 is about 38.8 (38.8 m per second) |
| Round-trip distance | 2 × 72000 ＝ 144000 |
| Time for one round trip (seconds) | 144000 ÷ 38.8 ≒ 3711 |
| Converted to minutes | 3711 ÷ 60 ≒ 61.9 |
Treating the lake as a simple box gives about 62 minutes. That is the same order as the measured 73 minutes: "about an hour". The rocking moves at about 140 km/h, roughly half the speed of a bullet train. Even so, the lake is so long that one round trip takes an hour.
| Gravitational acceleration × depth (depth 0.02 m) | 9.8 × 0.02 ≒ 0.196 |
| Speed of the rocking | The square root of 0.196 is about 0.44 (0.44 m per second) |
| Round-trip distance (length 0.3 m) | 2 × 0.3 ＝ 0.6 |
| Time for one round trip (seconds) | 0.6 ÷ 0.44 ≒ 1.36 |
High schoolHigh school+Seiches as standing waves
High schoolA seiche is a standing wave, formed when waves bounced back from the shores overlap. In a lake closed at both ends, both ends are antinodes. In the simplest rocking, the lake's length equals half a wavelength. The idea is the same as the natural vibrations of a string or an air column.
High school+A bay open on one side is like an air column closed at one end, and its length equals a quarter of a wavelength. That is why the period formula has 4L. There are also modes of rocking with two or three nodes, and each has a shorter period.
UniversityShallow-water wave theory, and how abiki grows
Waves whose wavelength is much longer than the water depth are called "shallow-water waves (long waves)", and their speed depends only on the depth. For a real lake with a complicated shape, the natural periods are found by solving, numerically, equations that include changes in depth and width. Chrystal of Scotland is said to have built a theory including changes in cross-section in the early twentieth century. Like abiki, when the speed of a pressure change moving over the sea matches the speed of long waves, the waves grow little by little. This is called "Proudman resonance".
📖 Derivations of the formula, and further reading: Fukushindō (Seiche) ― Wikipedia (Japanese) ／ Standing wave ― Wikipedia (Japanese)
ResearchWhat is still not well understood
- When and where can a big abiki be predicted? Small pressure changes slip easily through the gaps in observation networks, and it is still said to be difficult to give a reliable warning hours ahead.
- Effects on life in lakes. In a deep lake, it is not only the surface that rocks. The boundaries between layers of different temperature also swing greatly. How this affects the transport of nutrients and oxygen is being studied lake by lake.
- Will climate change alter the rocking? If pressure changes or the layering of water temperature change, how readily seiches occur could change too.
In other words, what this article says is also "an explanation within what is known today". The formula that sets the period is solid, but when a big rocking will happen is still being researched.
Links to textbooks (by level)
| Level | Subject / unit | Where in this article |
|---|---|---|
| Junior high | Science: "Sound and vibration" (period of vibration) | A swing's round trip, and the lake's rhythm |
| High school | Physics: "Waves" (standing waves, natural vibrations) | Nodes and antinodes in Figure 1 |
| High school+ | Physics: applying "air-column resonance" | The bay open on one side in Figure 2 |
| University | Fluid mechanics and physical oceanography (shallow-water waves, resonance) | Merian's formula, Proudman resonance |
| Research | Limnology and coastal disaster prevention | Forecasting abiki, rocking inside lakes |
| ― | Links to daily life | Mooring in harbours, changes in lakeshore water level |
- F.-A. Forel, Le Léman: monographie limnologique (1892–1904)
- Wikipedia, "Fukushindō" (副振動, in Japanese)
- Sanae Unoki (宇野木早苗), Kaiyō no Nami to Nagare no Kagaku (『海洋の波と流れの科学』, "The Science of Ocean Waves and Currents"), Tokai University Press (東海大学出版会)
- Rabinovich, A. B., Seiches and Harbor Oscillations, Handbook of Coastal and Ocean Engineering (2009)
*This article is a popular-science explanation for general readers. The figures given are rough guides to help you understand how things work. Near harbours and coasts, follow the information and instructions of the meteorological observatory and local authorities.