Illustrated Physics
physics, drawn
Concept

Wave breaking — where it appears

The collapse of a water wave when its crest moves faster than the wave itself and falls forward. In shallow water it occurs when the height reaches about three-quarters of the depth, and it turns the wave's ordered energy into turbulence and currents.

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

The orbits of an electron in a travelling wave. The possible motions of an electron in a plasma wave whose phase moves at γₚ = 10 and whose field is 0.2 of the cold wave-breaking field, drawn as its energy against its position in the wave over two wavelengths — the level curves of H = γ − βₚ u − ε cos ψ, which the electron's motion conserves. Inside the separatrix (thick) an electron is trapped: it slides back and forth through the wave, gaining energy while it outruns the wave and losing it while the wave outruns it. The separatrix reaches γ = 99 at its top, near 4γₚ²ε = 80, starting from electrons moving at the wave's own speed. Outside it, electrons that are too slow are overtaken by the wave and those that are fast enough outrun it; neither gains energy on average.

The wave an electron rides to a gigaelectronvolt

A laser pulse fired into a thin plasma pushes its electrons aside and leaves them oscillating behind it, a wave of charge travelling at nearly the speed of light. The field in that wave is a thousand times stronger than any metal accelerator can hold, and an electron caught in it at the right moment is carried along like a surfer, gaining a gigaelectronvolt in a few centimetres. Then it outruns the wave. The distance it can ride, and the energy it can gain, are both set by how nearly the wave keeps pace with it — which is to say, by relativity.

relativity · Relativistic dynamics Waves that turn to face the beach. The paths of crests' motion for a 10 s swell arriving at 50° on a plane beach of slope 1 in 50, seen from above, with depth contours dashed. Snell's law, sin α over speed is constant, holds along the ray because the depth changes only in the offshore direction, and the integrated paths were checked against it. The end of each ray is nearly normal to the shore: 5° from square-on by the point where it is about to break. In this sense all surf comes in nearly straight whatever direction the storm was in. The bend is complete because the speed falls almost to zero at the shore, whereas a prism's angles are bounded by its index. What remains of the angle drives the current along a beach.

The waves that always arrive square to the beach

A storm a thousand kilometres off sends out swell in whatever direction it pleases, and that swell arrives on the beach running almost straight in. It does so whichever way the coast faces. Waves slow down in shallow water, so the part of a crest nearest the shore lags and the whole line swings round, as light does in glass. It also explains why waves shrink before they grow, and why they gather on a headland and leave the bay alone.

waves · Wave motion

Named alongside it

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

Group velocityDispersion relationGreens lawLongshore currentParticle acceleratorPhase velocityPlasmaPlasma frequencyRelativistic dynamicsShoalingSnell's lawWakefield

All concepts