Trochoidal wave
![](/Images/godic/202502/17/Trochoidal_wave.svg3047.png")
![Animation (5 MB) of swell waves using multi-directional and multi-component Gerstner waves for the simulation of the ocean surface and POV-Ray for the 3D rendering. (The animation is periodic in time; it can be set to loop after right-clicking on it while it is playing).](/Images/godic/202502/17/-Gerstner_waves_10deg_rendering.ogv3047.jpg")
In fluid dynamics, a trochoidal wave or Gerstner wave is an exact solution of the Euler equations for periodic surface gravity waves. It describes a progressive wave of permanent form on the surface of an incompressible fluid of infinite depth. The free surface of this wave solution is an inverted (upside-down) trochoid – with sharper crests and flat troughs. This wave solution was discovered by Gerstner in 1802, and rediscovered independently by Rankine in 1863.