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Overshootings and spurious oscillations caused by biharmonic mixing
Delhez, E.J.M.; Deleersnijder, E. (2007). Overshootings and spurious oscillations caused by biharmonic mixing. Ocean Modelling 17(3): 183-198. dx.doi.org/10.1016/j.ocemod.2007.01.002
In: Ocean Modelling. Elsevier: Oxford. ISSN 1463-5003; e-ISSN 1463-5011, more
Peer reviewed article  

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Keywords
    Mixing processes
    Models > Mathematical models
    Marine/Coastal
Author keywords
    biharmonic mixing; numerical model; ocean dynamics; monotonicity; positiveness

Authors  Top 
  • Delhez, E.J.M., more
  • Deleersnijder, E., more

Abstract
    Biharmonic mixing is often used in large scale numerical models of the ocean because of its scale selectivity; it effectively damps small scale noise and leaves the large scale dynamics nearly unaffected. The biharmonic operator lacks however positiveness and monotonicity and can therefore produce unphysical results exhibiting spurious overshootings and oscillations. This problematic behaviour cannot be avoided by the addition of an ordinary Laplacian diffusion term. It appears in both continuous and discrete approaches/solutions in both unbounded and bounded domains. The overshootings and oscillations are induced by the strong damping of the smaller scale modes and are therefore comparable to the Gibbs’ phenomenon. With appropriate boundary conditions, the variance of the field decreases monotonically and the oscillations are expected to remain small. The lack of positiveness is however a severe drawback for (dynamic) tracer studies.

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