A note on the difference in the speed of gravity waves in a physical and numerical wave tank

Abstract

Precise measurements of gravity waves with very small wave slope in a physical wave tank are compared with an explicit linear inviscid wave maker theory. The main purpose is to measure the speed of the physical waves relative to those computed. We find that the wave speed in the physical wave tank is slightly less than in the computations. The small difference in the wave speed leads to a relative phase difference between the real waves and the inviscid computations of about 0.01±0.006 rad per wavelength (0.16±0.1%), which is comparable to an estimated phase delay due to the boundary layer at the tank walls. In this result, the estimated effects of weak non-linearity and surface tension in the experiments are subtracted. This relative phase difference is significantly smaller than what previous investigations in wave tanks of similar size have indicated. This means that physical wave tank simulations can effectively be applied as reference for numerical simulations of steep (non-linear) waves.