Direct Measurement of Turbulent Diffusion Induced by Waves in a Tank

Abstract

Turbulent diffusivity D is estimated in laboratory experiments in a wind-wave tank. The estimates make an initial verification of the available theoretical results on the dependence of D on different parameters possible. To estimate D by the Einstein formula, we use measurements of the spreading rate of an inkblot in a water layer under waves. A comparison between the estimates and a set of model parameterizations of D has shown the statistical advantage of parameterization $D \propto {{u}_{*}}{{a}_{0}}\delta$ in the presence of wind waves and parameterization $D \propto {{a_{0}^{3}{{f}_{p}}} \mathord{\left/ {\vphantom {{a_{0}^{3}{{f}_{p}}} z}} \right. \kern-0em} z}$ in the presence of mechanical waves (${{u}_{*}}$ is the friction velocity, ${{a}_{0}}$ is the wave amplitude on the surface, ${{f}_{p}}$ is the wave-spectrum peak frequency, $\delta$ is wave steepness, and z is the measuring depth). The measurement procedure and the technique for comparison between the theory and experiment are discussed.