Geophysical Waves: planetary scale wave motion

The waves in the last chapter broke on beaches. The waves in this one can stretch across an entire ocean basin and take months to cross it. To understand them, Serena Illig introduces the two great pillars of ocean dynamics: the rotation of the Earth, and the stratification of the sea.

The lecture builds up one wave at a time, and each answers a question the one before it raises.

What rotation does to a wave

Start with a simple wave on a shallow layer, with no rotation: all wavelengths travel at the same speed, set only by the depth. Now switch on the Earth’s rotation, and the wave becomes dispersive – different wavelengths travel at different speeds. These are inertia-gravity waves.

For short waves, rotation barely matters. But for large waves something striking happens: the wave stops going anywhere. Its energy no longer travels – water parcels simply circle in place, tracing inertial oscillations.

Which raises the puzzle: if rotation kills off large-scale waves, can large geophysical waves exist at all on a rotating planet?

Kelvin waves: waves that hug the coast

Yes – but they need something the open ocean lacks: a wall. A coastline imposes a strict condition, since water cannot flow through it. From that single constraint emerges the coastal Kelvin wave, with three remarkable properties:

• Non-dispersive – it keeps its shape as it travels, at a speed set by the depth
• Trapped against the coast – largest at the shore, fading offshore
• One-way only – travelling with the coast on its right in the northern hemisphere, its left in the southern

Kelvin waves are the ocean’s coastal express service. But they raise the next question: can large waves also travel in the open ocean, with no coast to hug?

Rossby waves: the westward drift

Again yes – and here the restoring force is something new: not gravity, and not even the Coriolis force itself, but the fact that the Coriolis force varies with latitude.

Picture a parcel of water nudged north, where the Coriolis effect is stronger. To conserve its total spin, its own relative spin must fall – it picks up a clockwise rotation, which swings it back south. Inertia carries it too far, and the opposite happens. The parcel oscillates – and that, propagating, is a Rossby wave.

Their signature: relative to the background flow, Rossby waves always travel westward, never east, and they move faster nearer the equator. They are the ocean’s long memory, crossing whole basins over months to years – which is why they matter so much for seasonal prediction.

Internal waves: waves inside the ocean

Every wave so far has rippled the sea surface. But the ocean is layered, and waves can travel on the boundary between layers, deep inside the sea. Here the restoring force is buoyancy: push a parcel up into lighter water and it sinks back; inertia carries it too deep, and buoyancy pushes it up again.

Two things make internal waves extraordinary. Because the density contrast between two water layers is tiny compared with air and water, they can reach enormous amplitudes, making them a major stirrer of the deep ocean. And their energy travels at right angles to their crests – the pattern going one way, the energy another – which gives them their characteristic slanting beams.

Why they matter

Each of these waves has its own restoring force – gravity, the latitude-varying Coriolis effect, or buoyancy – and together they span scales from ripples to planetary motions. They are the ocean’s long-distance messengers, carrying signals across entire basins, and they are represented across the full range of ocean models.

Most exist in the atmosphere too, where rotation and stratification produce similar dynamics. The one real exception is the coastal Kelvin wave – it needs a boundary, so it belongs to the ocean.

As always, focus on the physical pictures rather than the mathematics.