A comparison of Eulerian and Lagrangian current measurements

Abstract

During three periods in 1981 and 1982, each lasting 3 to 4 days, Eulerian and Lagrangian currents were simultaneously observed at a moderate number of positions in the southern North Sea. These currents were divided into the ensemble averaged current, first order deformation terms and a turbulent part. The Eulerian and Lagrangian ensemble averaged current fields, except for the low-frequency part, compare well. Stokes' velocity estimates do not significantly improve on the mismatch of the residuals as the Eulerian shear is under sampled. The Eulerian shear matrix terms show a strong semi-diurnal spectral peak, whereas the Lagrangian spectrum is more or less fiat as the drifters sample kinematically induced small-scale spatial velocity differences and therefore smear out this tidal peak. The turbulent fields yield estimates of the effective dispersion rates, which show that shear dispersion due to the tidal current is irrelevant at the time scales concerned. In agreement with the growth of a dye patch, released during one of the experiments, the drifter area grew very slowly or even decreased in time, indicative of anomalous dispersion. It is suggested that this may be due to the regularity of the bottom topography, as the generally highly nonlinear kinematic equations, describing the positions of particles in an idealized, tidally-varying Eulerian velocity field, then become (near-) integrable. In this view the (high) normal values of dispersion rates represent a coarse-grained parameterization of the chaotic processes, that arise from the nonlinearly coupled kinematic equations for a random bottom.