Ocean Dynamics

, Volume 57, Issue 3, pp 189–203 | Cite as

Lagrangian modelling of multi-dimensional advection-diffusion with space-varying diffusivities: theory and idealized test cases

  • Darya SpivakovskayaEmail author
  • Arnold W. Heemink
  • Eric Deleersnijder
Open Access
Original paper


To efficiently simulate the advection-diffusion processes along and across density surfaces, we need to deal with a diffusivity tensor containing off-diagonal elements (Redi, J Phys Oceanogr, 12:1154–1158, 1982). In the present paper, the Lagrangian model, in case of a space-varying diffusivity tensor, is developed. This random walk model is applied for two idealized test cases for which the analytical solutions are known. Results of the testing show that the Lagrangian approach provides accurate and effective solutions of advection-diffusion problems for general diffusivity tensor.


Space-varying diffusivity Lagrangian model Pycnocline 


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Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  • Darya Spivakovskaya
    • 1
    Email author
  • Arnold W. Heemink
    • 1
  • Eric Deleersnijder
    • 2
  1. 1.Department of Mathematical Physics, Delft Institute of Applied Mathematics (DIAM)Delft University of TechnologyDelftThe Netherlands
  2. 2.G. Lemaitre Institute of Astronomy and Geophysics (ASTR) & Centre for Systems Engineering and Applied Mechanics (CESAME)Université catholique de LouvainLouvain-la-NeuveBelgium

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