Ocean Dynamics

, Volume 58, Issue 3–4, pp 237–246 | Cite as

On the mathematical stability of stratified flow models with local turbulence closure schemes

  • Eric Deleersnijder
  • Emmanuel HanertEmail author
  • Hans Burchard
  • Henk A. Dijkstra


Occasionally, numerical simulations using local turbulence closure schemes to estimate vertical turbulent fluxes exhibit small-scale oscillations in space, causing the eddy coefficients to vary over several orders of magnitude on short distances. Theoretical developments suggest that these spurious oscillations are essentially due to the way the eddy coefficients depend on the vertical gradient of the model’s variables. An instability criterion is derived based on the assumptions that the artefacts under study are due to the development of small-amplitude, small time- and space-scale perturbations of a smooth solution. The relevance of this criterion is demonstrated by applying it to a series a closure schemes, ranging from the Pacanowski–Philander formulas to the Mellor–Yamada level 2.5 model.


Marine modelling Vertical mixing Turbulence closure Stability 


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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Eric Deleersnijder
    • 1
  • Emmanuel Hanert
    • 2
    Email author
  • Hans Burchard
    • 3
  • Henk A. Dijkstra
    • 4
  1. 1.Centre for Systems Engineering and Applied Mechanics, Louvain School of EngineeringUniversité catholique de LouvainLouvain-la-NeuveBelgium
  2. 2.Department of MeteorologyUniversity of ReadingReadingUK
  3. 3.Leibniz Institute for Baltic Sea Research WarnemündeWarnemündeGermany
  4. 4.Institute for Marine and Atmospheric research UtrechtUtrecht UniversityUtrechtThe Netherlands

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