Illustrated Physics
physics, drawn
Concept

Water waves — where it appears

Waves on the surface of water, restored by gravity at long wavelengths and by surface tension at short ones. They are dispersive, with long waves outrunning short ones on deep water, and steep enough trains become nonlinear and modulationally unstable.

Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.

Speed against wavelength. Phase and group speed for waves on water 4 m deep. Short waves are dispersive — the speed rises as the square root of the wavelength and the group travels at half the phase speed — and long ones all travel at √(gh) = 6.26 m/s together, which is why a tsunami keeps its shape across an ocean while a wind sea spreads out into swell.

The speed that depends on the length

Long waves on water travel faster than short ones, which is why a distant storm arrives as a slow swell and a tsunami crosses an ocean without spreading. One relation covers both, and the two familiar rules taught separately are its two limits.

fluids · Wave packets A tiny ripple that grows, peaks, and gives the energy back. The highest point of a wave train's envelope against time, starting from an even train of amplitude 1 with a ripple of 1 per cent at the fastest-growing wavenumber, integrated from the nonlinear Schrödinger equation. For a while nothing happens that the eye could see; the ripple grows exponentially from a per cent. Then, near t = 5.6, the energy of a whole modulation period gathers into one crest 2.41 times the original amplitude — 1 + √2, the height of the Akhmediev breather this wavenumber produces. Then it spreads out again, and by t ≈ 11 the train is almost even once more, its highest point 1.01: the energy returns to where it came from, and the cycle repeats, the crest rising again near t = 17. The wave's total norm is conserved throughout to a part in a hundred million.

The even wave train that cannot stay even

In the mid-1960s a team at the National Physical Laboratory tried to make a long, perfectly regular train of waves in a towing tank, and could not: however carefully they set the paddle going, a few hundred metres down the tank the waves had bunched into groups. Their paddle was not at fault. A uniform train of steep waves on deep water is unstable — small modulations of its height grow, the energy of many waves gathers into a few, and then, astonishingly, gives itself back. Out of that instability comes a wave three times the height of the sea around it, with no history before and none after.

waves · Wave packets

Named alongside it

The objects these essays reach for when they reach for this one.

Wave packetDeep waterDispersionDispersion relationGroup velocityModulational instabilityNonlinear schrodinger equationNonlinear wavesPhase velocityRecurrenceRogue waveShallow water

All concepts