Using the linear approximation for predicting velocities under periodic water waves, relationships are established between the velocity spectrum and the surface elevation spectrum for three-dimensional waves. The two dimensional forms of these relationships are used for comparison with velocity and elevation spectra measured in a laboratory wave tank. The predicted distortion of the spectrum shape can be observed in the experimental results. Velocity measurements were recorded using a laser

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... cimeter employing a rotating diffraction grating for shifting the optical frequencies. This allows measurement without sign ambiguity. The random waves were generated using a servo-driven paddle with a filtered white noise input.