Estimation of turbulent diffusion coefficients from decomposition of Lagrangian trajectories

Abstract

A new technique is proposed for estimating turbulent diffusion coefficients (in the present paper turbulence is assumed to be homogeneous) which is based upon wavelet decomposition which separates the mean and oscillatory (random) parts of Lagrangian trajectories. A one-dimensional discrete Daubechies wavelet transform is applied to decompose Lagrangian trajectories into components, each of which corresponds to a specific time scale τ. Diagonal diffusion coefficients are calculated from equations obtained from a combination of classical mixing length theory and general ideas from a theory of turbulent diffusion. Non-diagonal diffusion coefficients are found using the classical theory of the first passage boundary. The technique is illustrated through the analysis of twelve trajectories of RAFOS floats along the California-Oregon coast, twenty surface drifters deployed in the California Current System, and forty-five surface drifters deployed in the Black Sea in 2000–2002. The approach is compared with the well-known Davis (1991) approach in applications to the Black Sea drifters and single float trajectories along the California-Oregon coast.