On a Role of Viscosity in Phenomena of Mass Transfer Caused by Nonlinear Periodic Waves Propagating Over the Liquid Surface

Abstract

In the 1847 G. Stokes pointed out in his work [G.G. Stokes, 1847] that the propagation of periodic gravitational waves on the horizontal surface of a liquid induces the total drift of liquid particles at a velocity lower than the phase velocity of waves, which became known as the Stokes drift. Stokes considered the problem of calculation of the velocity field in an infinitely deep inviscid incompressible liquid with a gravitational wave propagating over its surface, the wave amplitude being much smaller than the wavelength. The solution of the problem in the second order approximation in the wave amplitude showed that the periodic wave perturbation of the free surface induces not only a periodic motion of liquid particles about a certain mean position in the bulk of the liquid, but also a horizontal motion of the mean position in the direction of wave propagation. Stokes derived the following expression for the absolute value of the velocity of this drift [G.G. Stokes, 1847, 1880]: ( ) 2 S 0 w = A k┱ exp -2kd . (1)