Effect of divergence,stretching and nonnormal distribution on apparent diffusion of surface drifters

Kawai (1976, 1979) derived two simple relations among the apparent diffusivity (based on the geometric-average variance for principal axes of spreading) for many surface drifters in a patch and horizontal divergence and isotropic turbulent diffusivity for ambient water. By a new term medley diffusivity is meant an average of the products of the position coordinates relative to the centroid of drifters and the residual velocity, that is, the velocity left by subtracting the mean velocity and the velocity due to the linear velocity gradient from the velocity of a drifter. Regarding the medley diffusivity as the isotropic turbulent diffusivity that is weighted anisotropically according to drifters spreading along each of the principal axes, this paper derives a new relation with a form intermediate between the above two relations. Using the relation, this paper defines the new critical period within which the effect of horizontal divergence on the apparent diffusion surpasses that of isotropic turbulent diffusion, and discusses the time-scales on which the space-scale dependence of the squared divergence (Kawai, 1985b) is based. Stretching of a patch of drifters and deviation of drifters' position from the bivariate normal distribution enhance the effect of isotropic turbulent diffusion on the apparent diffusion. This stretching effect is equivalent to the shear effect on a horizontal plane. Remarks on reducing errors in the estimation of isotropic turbulent diffusivity are made.