Gerstner waves: each water particle traces a circle as the wave passes
A trochoidal wave (Gerstner wave, 1802) is the only exact nonlinear solution to the Euler equations for water waves. Each particle follows a perfect circle: surface particles have radius equal to wave amplitude A, and deeper particles have radius Ae^(kz) where k=2π/λ is the wavenumber. The wave is irrotational everywhere except at the crests.