Turbulent diffusion in a shearing oscillatory flow

The diffusion in a shearing oscillatory flow from an instantaneous surface point source is considered. An analytical solution is obtained by Fourier transform. The results show that, for three dimensional diffusion in an oscillatory flow with constant shear, the distribution of the contaminant follows the multivariate Gaussian distribution rule. When the frequency is very high, or the time very short, the shear does not influence the diffusion. For moderate values of time, there are fluctuations with longitudinal variance. For large values of time the longitudinal variance increases as t, and the peak concentration decreases as t^−1.5, which are faster than those in a flow without shear, but much slower than those in a steady flow, where the longitudinal variance increases as t³ and the peak concentration decreases as t^−2.5. The contaminant patch is elongated in the longitudinal direction of the shear flow and moves back and forth with the water motion. Contribution No. 1306 from the Institute of Oceanology, Academia Sinica. Received July 12, 1985