Are There Really Waves Over 100 Metres High Inside the Ocean?
― The surface barely moves, yet huge waves roll through the deep
Yes, there are. Inside the ocean, waves travel along the boundary between light water and heavy water, not along the surface. In the South China Sea, some have been measured at 170 metres high. Even so, they are almost invisible from a ship. The key is that the water above and below differs in weight by only a tiny amount.
Gently rock a bottle of salad dressing from side to side. The boundary between the oil on top and the vinegar below swells into slow, big waves. Yet the surface of the oil at the very top stays almost flat.
The same thing happens in the sea. Ocean water is usually warm and light near the top, and cold and heavy in the depths. This boundary slowly heaves up and down in great swells.
And the waves can be as tall as a skyscraper. How can these "invisible giants" of the deep grow so large?
Just two reasons make waves inside the ocean so huge
The weight difference between the water above and below is only about 0.2%. Lift the boundary and it hardly feels any pull to fall back, so a small push makes it swing a long way.
With every rise and fall of the tide, water across the whole sea sloshes back and forth. When that flow crosses an undersea mountain range, it shoves the boundary up by tens of metres and sends out a giant wave.
The first reason is about how far the same push can shake the boundary. The second is about where that push comes from. Let's take them in turn.
Reason 1: When the weight difference is small, the same push shakes it 20 times more
Think first of waves on the sea surface. Above the water is air, and air weighs only about 1/800 as much as water. So when the surface is lifted, the water soon falls back under its own weight. That is why surface waves stay at a few metres at most.
At a boundary inside the sea, things are completely different, because what lies above is also water. The water above and the water below differ in weight by only about 2 grams per litre. Lift the boundary, and the water below is only "slightly heavier than its surroundings". The force trying to pull it down is a few hundred times smaller than at the surface.
When the pull-back force is weak, a wave of the same energy swings much higher. By calculation, a wave with the same energy as a 1-metre wave on the surface makes the boundary swing by about 23 metres. Try changing the weight difference with the slider in Figure 1. The smaller the difference, the bigger the swing of the boundary.
There is one more thing: waves inside the sea travel very slowly. Because the pull-back force is weak, it takes time for the motion to pass to the next patch of water. Where a long surface wave would race along at 30 metres per second, a wave on the boundary moves at only about 1 to 3 metres per second. These giants, moving at roughly walking pace, cross the ocean over many days.
Reason 2: Tides make waves over undersea ridges
So where does the push that raises such a giant wave come from? Mainly from the tides. With every flood and ebb, the sea's water swings widely back and forth.
When this flow hits an undersea mountain range, the boundary is thrust upward along the slopes. When the flow turns around, the raised boundary spreads outward as a wave. The Luzon Strait, between Taiwan and the Philippines, is a classic site. Two ridges run along its seafloor, and the waves born there cross the South China Sea to the west. Observations have reported heights of up to 170 metres.
What about the surface? Even when the boundary moves more than 100 metres, the surface height is said to change only slightly. But over the wave, bands where the water flow converges and bands where it spreads apart form. As a result, the surface shows stripes of "rippled bands" and "smooth bands" side by side. Satellite photos show these stripes stretching for tens of kilometres.
In 1893 the ship Fram, led by the Norwegian explorer Nansen, suddenly stopped making headway in Arctic waters. The wind and engine were fine, yet it was recorded as feeling as if something had caught hold of the ship. There, light water from rivers and ice lay in a thin layer on top of heavy seawater. The ship's power was being drained into making waves on the boundary below. The Swedish researcher Ekman later confirmed the mechanism in tank experiments. Sailors called the phenomenon "dead water".
When the giant waves inside the ocean break, they stir the deep cold water together with the water above. Deep water is rich in nutrients. For that reason, plankton and fish are thought to gather where internal waves strike often. They have also been reported to carry cold water to coral reefs in hot summers and protect them.
Summary
Ocean water is a "two-storey" building, light on top and heavy below. At the boundary between the storeys, the weight difference is small, so the pull-back force is very weak. That is why the same energy shakes it more than 20 times as much as the surface, and why it moves slowly. When tidal flow crosses an undersea ridge, waves more than 100 metres high are born.
What sets the size of a wave is not the amount of water, but the difference in weight.
The smaller the difference at the boundary, the bigger, quieter and slower the wave.
How high surface waves can get is covered in "How high can ocean waves get?", and waves that travel without changing shape are covered in "Why do waves that keep their shape travel on and on without breaking up?". Many of the giant waves inside the ocean belong to this family of "unbreaking waves".
- Fill a clear plastic bottle halfway with water in which you have dissolved plenty of salt.
- Gently pour water coloured with food dye on top, letting it run down the back of a spoon. If it separates into two layers, you've succeeded.
- Cap the bottle, lay it on its side, then slowly tilt it and return it. Watch how the boundary keeps swinging in big, slow waves, and compare that with the surface.
Use less salt to make the weight difference smaller, and the boundary swings even more slowly. You can also try water and oil. Since they don't mix, the shape of the wave shows up clearly.
For those who want to know more ― terms, equations and links to textbooksFrom middle-school science to university courses, with each level clearly marked
- Middle schoolCovered in middle-school science
- High schoolCovered in high-school physics or earth science
- High school+Advanced high-school material, or a textbook sidebar
- UniversityNot taught in high school; university courses (physical oceanography, geophysical fluid dynamics)
- ResearchNot taught even at university as settled knowledge; researchers are still working on it
Middle schoolTerms: this phenomenon has names
- Internal wave: a wave that travels not along the surface but along the boundary between waters of different density (weight), or within the water itself.
- Pycnocline: a layer in the ocean where density changes sharply with depth. It lies between warm surface water and cold deep water.
- Internal tide: an internal wave with the same period as the tide, produced when tidal flow crosses seafloor terrain.
- Dead water: a phenomenon in which, in a sea with a thin layer of light water on top, a ship's thrust is drained into making internal waves and the ship struggles to move forward.
Middle schoolHigh schoolChecking with equations: how far does the boundary swing for the same energy?
Compare the potential energy of the lifted water in the wave. At the surface it is "water and air"; at the boundary it is "heavy water and light water". The weight difference sets how hard it is to lift.
| In symbols | ½ × Δρ × g × a² ＝ ½ × ρ × g × a₀² so a ＝ a₀ × √( ρ ÷ Δρ ) |
| In words | Boundary swing ＝ surface swing × square root of (water density ÷ density difference between upper and lower water) |
| Where it comes from | The potential energy needed to move an interface by a height a is proportional to the density difference across it. Give the surface and the boundary the same energy and set the two equal: that is this balance equation. The speed slows for the same reason: c ＝ √( g × (Δρ ÷ ρ) × h ). |
| Symbol | Meaning and unit |
| ρ | Density of seawater (kg/m³) |
| Δρ | Density difference between upper and lower water (kg/m³) |
| g | Gravitational acceleration (m/s²) |
| a₀, a | Surface swing, boundary swing (m) |
| h | Thickness of the upper light layer (m). An approximation for a very deep lower layer |
| Density of seawater | about 1025 kg/m³ |
| Density difference between upper and lower water (a typical value) | about 2 kg/m³ |
| Gravitational acceleration | 9.8 m/s² |
| Thickness of the upper light layer | 100 m |
| Surface wave swing (the baseline for comparison) | 1 m |
| Density ratio | 1025 ÷ 2 ＝ 512.5 |
| Its square root | The square root of 512.5 is about 22.6 |
| Boundary swing (same energy as 1 m at the surface) | 1 × 22.6 ＝ 22.6 m |
| Weight difference as a fraction | 2 ÷ 1025 ≒ 0.00195 |
| "Gravity" felt by the boundary | 9.8 × 0.00195 ≒ 0.0191 m/s² |
| Speed squared | 0.0191 × 100 ＝ 1.91 |
| Speed of the boundary wave | The square root of 1.91 is about 1.38 m/s |
| Comparison: long surface wave (depth 100 m) | 9.8 × 100 ＝ 980 → square root is about 31.3 m/s |
| Speed ratio | 31.3 ÷ 1.38 ≒ 22.7 |
The boundary wave swings about 23 times higher than a surface wave and travels about 23 times slower. Both come from the same "√(ρ ÷ Δρ)", so the factors match.
| Largest height observed in the South China Sea | about 170 m |
| Converted to a surface wave | 170 ÷ 22.6 ≒ 7.5 m |
Roughly speaking, a boundary wave 170 metres high carries about as much energy as a surface wave 7.5 metres high (the real ocean is not two layers but changes density smoothly, so this is only a guide). These walking-speed giants carry as much energy as heavy storm waves.
High schoolHigh school+Wave speed is set by the balance of "restoring force" and "inertia"
High schoolIn high-school physics you learn that the speed of a wave on a string is the square root of "tension ÷ linear density". The stronger the pull-back, the faster; the heavier the thing being moved, the slower. Internal waves work the same way: the pull-back weakens in proportion to Δρ, but the weight of the water being moved stays the same, so the wave is slow.
High school+The speed of an internal wave is the shallow-water wave speed √(g × depth) with g replaced by the "reduced gravity" g × (Δρ ÷ ρ). Archimedes' principle (buoyancy) shows that water only slightly heavier than its surroundings feels a downward force equal only to that weight difference.
UniversityBuoyancy frequency and internal solitary waves
In an ocean where density changes continuously, water pushed up or down oscillates around its original depth. That frequency is called the Brunt–Väisälä frequency (buoyancy frequency), and internal waves can exist only at frequencies below it. Large-amplitude waves like those in the South China Sea are approximated as internal solitary waves (internal solitons), where nonlinearity and dispersion balance, using equations such as the Korteweg–de Vries equation. How energy passes from tidal flow to internal waves is studied as "internal tide generation".
📖 Derivations and further reading: Internal wave (Wikipedia, Japanese) ／ Soliton (Wikipedia, Japanese)
ResearchWhat is still not well understood
- Where and how do the giant waves finally break? Where internal-wave energy turns into heat and mixing varies greatly from place to place, and observations have not caught up.
- How much is the deep ocean stirred by internal waves? How much internal-wave mixing helps keep the slow overturning of the world's deep water going is a big question that also bears on climate prediction.
- How will warming change the ocean's "two storeys"? When the surface warms, the density difference between upper and lower water grows, and internal waves and mixing are thought to change too, but the size of the effect is still only roughly estimated.
So the content of this article is also "an explanation of what is known so far". The giant waves inside the ocean have only come into view in the last few decades, as satellites and deep-sea instruments have multiplied.
Links to textbooks (by level)
| Level | Subject / unit | Where in this article |
|---|---|---|
| Middle school | Science: density, buoyancy, how waves travel | The ocean's "two storeys", light on top and heavy below |
| High school | Physics: wave speed, potential energy / Earth science: layered structure of the ocean | Checking with equations (energy balance) |
| High school+ | Shallow-water wave speed, reduced gravity | Why boundary waves are about 23 times slower |
| University | Physical oceanography, geophysical fluid dynamics | Buoyancy frequency, internal solitary waves, internal tides |
| Research | Ocean mixing, climate | How giant waves break, and the overturning of deep water |
| ― | Links to daily life | Nutrients for fishing grounds, cooling of coral reefs, effects on ships and offshore structures |
- Alford, M. H. et al. (2015) The formation and fate of internal waves in the South China Sea. Nature 521
- Internal wave ― Japanese Wikipedia (内部波 ― ウィキペディア日本語版)
- Nansen, F. (1897) Farthest North (the Fram expedition narrative, including the account of dead water)
- Ekman, V. W. (1904) On dead water. The Norwegian North Polar Expedition 1893–1896, Scientific Results
- Gill, A. E. (1982) Atmosphere-Ocean Dynamics. Academic Press
※This article is a general-audience science explainer. The figures given are rough guides to help you grasp the mechanism. The real ocean changes density smoothly, so the two-layer calculation is only for getting a sense of scale.