The Physics of Tsunamis: When the Entire Ocean Moves

Not What You Think It Is

Most people picture a tsunami as a giant version of a normal ocean wave — a towering wall of water cresting and crashing onto shore. Hollywood likes this image. But it’s wrong in almost every way that matters, and the real physics is both more interesting and more terrifying.

A normal ocean wave is a surface phenomenon. The wind pushes the top few metres of water into oscillation, and a surfer rides the circular motion of water particles near the surface. Dive 20 metres down and you barely feel a storm wave passing overhead. The water at depth doesn’t move much.

A tsunami is fundamentally different. It’s not a surface wave. It’s a shallow-water wave — which is a confusing name, because it can travel across the deepest oceans. “Shallow” in wave physics doesn’t mean the water is shallow. It means the wavelength is much longer than the water depth. A tsunami’s wavelength can be 200 kilometres or more. The Pacific Ocean’s average depth is about 4 km. Since 200 km is vastly greater than 4 km, the tsunami “feels” the bottom at every point in the ocean. The entire water column — from surface to seafloor — participates in the wave motion.

That’s the crucial difference, and it explains everything else about how tsunamis behave.

How a Tsunami Starts

Most tsunamis are caused by submarine earthquakes — specifically, by vertical displacement of the seafloor along a fault. When one tectonic plate suddenly thrusts under or over another, the seafloor lurches upward or downward by metres. The water above it is displaced as well. An area potentially hundreds of kilometres long and tens of kilometres wide is suddenly at a different elevation than the surrounding ocean.

Gravity immediately starts restoring equilibrium. The raised water flows outward. The depressed water fills back in. These motions generate a series of long waves — the tsunami — that propagate away from the source in all directions.

The initial displacement is modest — typically 1 to 5 metres vertically over an area of perhaps 100 × 50 km. Spread across that enormous area, it doesn’t look like much. In the open ocean, the tsunami wave height is typically 30 to 60 centimetres. You could be on a ship directly above it and not notice. The wave passes beneath you as a very gradual rise and fall over 10–20 minutes, indistinguishable from normal ocean swell.

The energy, though, is colossal. The 2004 Indian Ocean earthquake released about 1.1 × 10¹⁷ joules into the tsunami — equivalent to about 5 megatons of TNT. That energy is distributed across the entire depth of the water column and the entire length of the wave. It’s dilute in the open ocean. It becomes concentrated at the coast.

The Speed Equation

Here’s where the physics gets clean and elegant. The speed of a shallow-water wave is:

v = √(g × h)

where g is gravitational acceleration (9.81 m/s²) and h is the water depth.

That’s it. The speed depends only on depth. In the deep Pacific (h ≈ 4,000 m), a tsunami travels at about 200 m/s — roughly 720 km/h, the cruising speed of a jetliner. In the Atlantic (average depth about 3,300 m), it’s slightly slower. Over continental shelves (h ≈ 200 m), the speed drops to about 45 m/s (160 km/h). In water 10 metres deep near shore, it’s about 10 m/s (36 km/h).

The wave slows down as the water gets shallower. And here’s where things get dangerous.

Shoaling: Why the Wave Gets Tall

When a tsunami approaches a coast and the water depth decreases, the wave slows down. But the energy flux — the rate at which energy passes through a cross-section of water — must remain roughly constant (in the absence of major dissipation). If the wave slows but the energy flux stays the same, something has to give. What gives is the wave height.

The wave compresses. Its wavelength shortens (the back of the wave is still in deep water, moving fast, while the front has slowed in shallow water — the wave bunches up). Its height increases. A wave that was 50 cm tall in 4,000 m of water can become 10 metres tall in 10 m of water. In extreme cases — narrow bays, V-shaped inlets, resonant harbour geometries — the amplification can produce waves of 30 metres or more.

This is shoaling, and it follows directly from conservation of energy flux. The physics is:

H₂ ≈ H₁ × (h₁/h₂)^(1/4)

where H is wave height and h is depth. Going from 4,000 m to 10 m depth gives an amplification factor of about (4000/10)^(1/4) ≈ 4.5. A 50 cm deep-water wave becomes roughly 2.2 metres. Bathymetric focusing, harbour resonance, and wave refraction can amplify this further, sometimes dramatically.

The 2011 Tōhoku tsunami reached heights of over 40 metres in some locations along the Sanriku coast, where the underwater topography funnelled and focused the incoming wave energy into narrow inlets. The physics predicted this — the geometry of the coastline was known to be dangerous. But the seawall defences had been designed for smaller events.

It’s Not One Wave

A common misconception: a tsunami is a single wave. In reality, it’s a wave train — a series of waves, often with the largest not being the first. The 2004 tsunami hit the Thai coast in a series of waves over roughly two hours, with the third wave being the most destructive in many locations.

The wave period — the time between successive crests — is typically 10 to 60 minutes. This is enormously long compared to wind-generated waves (5–15 seconds). It means that the “wave” arriving at the coast is not a curling breaker that crashes and retreats in seconds. It’s more like the sea rising by several metres over a period of 5–10 minutes, flooding far inland, and then withdrawing over the next 5–10 minutes — followed by the next wave.

This sustained inflow is what makes tsunamis so destructive. A normal storm wave breaks and retreats. A tsunami is a mass of moving water, kilometres deep, pushing inland at walking speed or faster for minutes at a time. The force is not the dramatic impact of a breaking wave but the relentless hydraulic pressure of a wall of water that just keeps coming.

Survivors of the 2011 Tōhoku tsunami describe the water not as a crashing wave but as a rapidly rising flood — the sea coming up like a bathtub filling, but filling with a current of debris-laden water flowing at 5–10 m/s. The destructive power comes from the current, not the initial impact.

Early Warning: The Physics of Detection

Tsunami warning systems exploit the physics in a straightforward way. Seismographs detect the earthquake within seconds. If the earthquake meets certain criteria — magnitude above 7.0, shallow depth, location near a subduction zone — a tsunami warning is issued.

But the earthquake alone doesn’t confirm a tsunami was generated. For that, you need to detect the wave itself. Deep-ocean pressure sensors (DART buoys) sit on the seafloor at depths of 4,000–6,000 m. A tsunami wave passing overhead changes the water pressure at the sensor by a tiny amount — a few centimetres of water column at those depths. Modern sensors can detect these changes with millimetre precision.

Once the wave is detected, its travel time to any coastline can be calculated from the depth map of the ocean and the speed formula v = √(gh). These calculations are remarkably accurate — predicted arrival times are typically correct to within a few minutes over journeys of thousands of kilometres. The physics is simple; the bathymetric data is the hard part.

For nearby coastlines — within 100 km of the earthquake — there’s effectively no warning time. The wave arrives in minutes. This was the case for many communities hit by the 2011 Tōhoku tsunami: the earthquake struck offshore, and the first wave arrived in 15–30 minutes. Seawalls bought some time. But for many coastal towns, the only effective warning was the earthquake shaking itself — and the knowledge, passed down through generations and carved on stone markers on Japanese hillsides, that when the ground shakes near the sea, go to high ground immediately.

What We Still Get Wrong

Despite everything we know about tsunami physics, we keep underestimating them. The Fukushima Daiichi nuclear power plant was designed to withstand a 5.7-metre tsunami. The 2011 wave was over 14 metres. The city of Banda Aceh in Indonesia had no tsunami warning system at all when the 2004 wave struck.

The physics is not the problem. The wave speed equation, shoaling theory, and numerical wave propagation models are well understood and well validated. The problem is probabilistic: how big can the earthquake be, and therefore how big can the tsunami be? Historical records are short. The geological record is hard to read. And humans are not good at planning for events with return periods of centuries.

The Cascadia subduction zone off the Pacific Northwest coast of North America last ruptured in 1700, producing a tsunami that was recorded in Japan. The average return period is about 240 years. The physics of the next Cascadia tsunami is predictable — the wave speeds, shoaling behaviour, and affected coastlines can all be modelled. What we don’t know is when. The physics of plate tectonics tells us it will happen. It doesn’t tell us the date.