Scale dependence of divergence and vorticity of near-surface flows in the sea

Abstract

To area-average the horizontal divergence and the vertical component of vorticity, three methods are proposed and examined. The polygon method is based on deformations of a polygon made by connecting drifters. They are deployed at widely different scales of 1 cm− 1,000 km and tracked using various procedures. The loop method is adopted when a drifter completes at least two loops of trajectory in a tidal vortex, a ring or a gyre. Even if data for a drifter completing only one loop is available, the vorticity can be calculated. The crossing method is applied to the GEK data on the circumference of a Kuroshio ring. The data which will be used to calculate them in Part 2 are summarized in tables. Offset dispositions of positive and negative divergences or vorticities on a horizontal plane and in a water column are shown. Probably, the vertical offset of vorticities does not occur in general. The area-turnover of a polygon of drifters are discussed. Sampling time-intervals, appropriate to the scale of the area, for the polygon and loop methods are examined. A first impression of Rhines' (1979) sketch has produced a misunderstanding that the polygon method would be useless because a limited number of drifters cannot follow such a complicated deformation of the material line over a long period. It is shown that adopting a short time-scale appropriate to the length scale furnishes a practical solution to the problem.