Note on the velocity and related fields of steady irrotational two-dimensional surface gravity waves

Abstract

The velocity and other fields of steady two-dimensional surface gravity waves in irrotational motion are investigated numerically. Only symmetric waves with one crest per wavelength are considered, i.e. Stokes waves of finite amplitude, but not the highest waves, nor subharmonic and superharmonic bifurcations of Stokes waves. The numerical results are analysed, and several conjectures are made about the velocity and acceleration fields.

Experimental Study of the Velocity Field in Solitary Water Waves

“…For the vertical velocity distribution, it is not the non-monotonicity. The experimental horizontal velocity distribution presented is in close agreement with the theoretical findings [7,9,12,13]. The experimental evidences of vertical velocity distribution can be used to validate the numerical and theoretical theories.…”

“…The horizontal velocity under solitary wave is already rigorously demonstrated; however, the structure of the vertical one is lacking. Clamond [7] developed a numerical method to show the structure of the velocity and related field.…”

A Hamiltonian approach to wave-current interactions in two-layer fluids

“…12 Another particular case is obtained in the absence of stratification but with an underlying current of constant vorticity. 13 In the setting of travelling waves propagating in irrotational flow with no stratification, the Hamiltonian structure was essential in uncovering the flow pattern beneath the surface waves: theoretical studies 14,15 were confirmed numerically 16 and experimentally. 17 In this special context, the presence of an underlying current -that can only be uniform in these circumstances -increases considerably the dynamical complexity.…”

Extrema of the dynamic pressure in an irrotational regular wave train

“…For example, laboratory measurements 24,25 and numerical simulations 2,21 indicate that the maximal values of the dynamic pressure are encountered in the region below the a) Electronic mail: adrian.constantin@univie.ac.at…”