Abstract
In Stokes’ wave theory, wave numbers are corrected in the third order solution. A change in wave number is also associated with a change in current velocity. Here, it will be argued that the current is the reason for the wave number correction, and that wave-generated current at the mean free surface in infinite depth equals half the Stokes drift. To demonstrate the validity of this second-order formulation, comparisons to computational fluid dynamics (CFD) results are shown; to indicate its effect on wave loads on structures, model tests and analyses are compared.
Highlights
IntroductionWaves do not create a current, and the widely used wave kinematics by Stokes [1] can be applied
Within potential theory, waves do not create a current, and the widely used wave kinematics by Stokes [1] can be applied
In Stokes’ wave theory, wave numbers are corrected in the third order solution
Summary
Waves do not create a current, and the widely used wave kinematics by Stokes [1] can be applied. Some examples from model tests and analyses are given that may support the suggestion in [3]; that waves in infinite water depth may create a shear current, which at the mean free surface, equals half the Stokes drift. Grue and Kolaas [6] did perform measurements of the drift with modern equipment, but their very steep waves and shallow water mean that the present theory needs to be extended in order to be fit for comparison. If wave-generated current exists, it influences the wave kinematics and the loads on offshore structures
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