Do we observe Gerstner waves in wave tank experiments?

An exact solution for equatorially trapped waves

“…For a homogeneous fluid (the constant density ρ being set equal to 1), starting from the assumption of a circular motion of the fluid particles with a radius diminishing with the distance from the surface where x and z are the horizontal and vertical coordinates at time t of the particle labeled by the real parameter a and the parameter b ≤ b 0 with b 0 < 0, these authors constructed a beautiful explicit solution representing a trochoidal periodic wave with wavelength 2 π / k propagating to the right with celerity , in a flow with negative vorticity (in this two‐dimensional setting one identifies the vorticity vector with its middle component — the first and third components vanish). While the flow pattern predicted by this solution is not completely met in reality (we refer to Craik [2004] and Darrigol [2005] for a discussion of classical experiments and to Weber [2011]for recently performed wave tank measurements), the theoretical importance of Gerstner's wave was re‐confirmed in recent decades. This peculiar wave pattern opened up the possibility of the existence of exact (even though not explicit) traveling wave solutions to the governing equations for gravity water waves propagating at the surface of a flow with vorticity (and thus modeling wave‐current interactions); see the discussion in Constantin and Strauss [2004] and in Strauss [2010].…”

Ocean Wave Model and Wave Drift Caused by the Asymmetry of Crest and Trough

“…This indicates the wave drift still exists for Gerstner model from the viewpoint of Taylor expansion. In [1] the net drift observed in wave tank experiments had ever doubted, after all, the particles's trajectories of a Gerstner wave should be circles.…”

“…where 1 A and 2 A are the amplitudes of horizontal motion relative to the crest and trough parts separately which satisfy…”

“…Thus the doubt "Do we observe Gerstner waves in wave tank experiments?" in [1] can be well answered. This question stimulates us to reconsider the wave mechanism.…”

Mean Flow Velocities and Mass Transport for Equatorially-Trapped Water Waves with an Underlying Current

“…It was observed that key features of the mean fluid drift velocity, or so-called Stokes' drift velocity, could be characterised in terms of the mean Eulerian flow velocity and the mean Lagrangian flow velocity, whereby: Lagrange = Euler + Stokes. In spite of recent progress, determining the mean fluid flow velocities remains a highly complex and intricate issue from both a theoretical, and experimental [37,41], viewpoint.…”