Mixing induced by nonbreaking surface waves was investigated in a wave tank by measuring the thermal destratification rate of the water column. One experiment without waves and four experiments with waves of amplitudes ranging from 1.0 to 1.5 cm and wavelength from 30 to 75 cm were conducted. Water temperature variations at depths from 4 to 12 cm below the surface were measured. In the layer from 4 to 7 cm, the originally dense isothermal lines disperse soon after the waves are generated, whereas the vertical gradient from 9 to 12 cm is maintained for a relatively long time. The time span, during which the water temperature becomes well mixed, changes from about 20 h for the case with no waves to tens of minutes for the case with waves, and it decreases with increasing wave amplitude and wavelength. A one-dimensional diffusion numerical model with wave-induced mixing parameterization shows consistent results with the measurement. The study demonstrates that the mixing induced by nonbreaking waves may add an important contribution to the vertical mixing process in the upper ocean and suggests a way to parameterize wave-induced mixing in numerical ocean models.

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A complete second-order solution is presented for the two-dimensional wave motion forced by a generic planar wavemaker. The wavemaker is doubly articulated and includes both piston and hinged wavemakers of variable draught. It is shown that the first-order evanescent eigenseries cannot be neglected when computing the amplitude of the second-order free wave. A previously neglected, time-independent solution that is required to satisfy an inhomogeneous kinematic boundary condition on the wavemaker as well as an mhomogeneous Neumann boundary condition on the free surface is examined in detail for the first time. This time-independent solution is found to accurately estimate the mean return flow in a closed wave flume computed by the Eulerian method. This mean return current due to Stokes drift is usually estimated using the principle of kinematic conservation of mass flux. Even though the first-order eigenseries will converge for any geometry of a generic planar wavemaker, the second-order solutions obtained from Stokes perturbation expansions will not converge for all planar wavemaker geometries.