Deducing an upper bound to the horizontal eddy diffusivity using a stochastic Lagrangian model

Daniel F. Carlson, Erick Fredj, Hezi Gildor*, Vered Rom-Kedar

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


We present a method for estimating the upper bound of the horizontal eddy diffusivity using a non-stationary Lagrangian stochastic model. First, we identify a mixing barrier using a priori evidence (e.g.,aerial photographs or satellite imagery) and using a Lagrangian diagnostic calculated from observed ormodeled spatially non-trivial, time-dependent velocities [for instance, the relative dispersion (RD) or finite time Lyapunov exponent (FDLE)]. Second, we add a stochastic component to the observed (or modeled) velocity field. The stochastic component represents sub-grid stochastic diffusion and its mean magnitude is related to the eddy diffusivity. The RD of Lagrangian trajectories is computed for increasing values of the eddy diffusivity until the mixing barrier is no longer present. The value at which the mixing barrier disappears provides a dynamical estimate of the upper bound of the eddy diffusivity. The erosion of the mixing barrier is visually observed in numerical simulations, and is quantified by computing the kurtosis of the RD at each value of the eddy diffusivity. We demonstrate our method using the double gyre circulation model and apply it to high frequency (HF) radar observations of surface currents in the Gulf of Eilat.

Original languageAmerican English
Pages (from-to)499-520
Number of pages22
JournalEnvironmental Fluid Mechanics
Issue number5
StatePublished - 2010

Bibliographical note

Funding Information:
Acknowledgements This research was supported by NATO SfP982220 and by The Israel Science Foundation (grant No. 1344/09). HG is the Incumbent of the Rowland and Sylvia Schaefer Career Development Chair and is supported by a research grant from the Estate of Sanford Kaplan. VRK is the Estrin Family Professor of Computer Science and Applied Mathematics and acknowledges support by the Minerva foundation. The Port in Eilat allowed us to install one of the HF radar sites on its property. Airspan provides the wireless communication between the radar sites. We thank the management and the staff of the Inter-University Institute for Marine Sciences of Eilat (IUI) for their cooperation and help. We thank two anonymous reviewers for greatly improving our manuscript.


  • Eddy diffusivity
  • High Frequency radar
  • Mixing barrier
  • Ocean mixing
  • Parameterization
  • Stirring
  • Turbulence


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