On the stability of turbulence closure schemes for stratified flows
Deleersnijder, E.; Burchard, H.; Dijkstra, H.A. (2003). On the stability of turbulence closure schemes for stratified flows, in: 6th National Congress on Theoretical and Applied Mechanics, Ghent, May 26-27, 2003. pp. 1-5
In: (2003). 6th National Congress on Theoretical and Applied Mechanics, Ghent, May 26-27, 2003. Nationaal Comité voor Theoretische en Toegepaste Mechanica: Gent. 1 cd pp., meer
The cause is sought of the spurious oscillations arising in some numerical models of stratified flows including a sophisticated turbulence closure scheme. A generic system of diffusion equations is considered, in which the diffusivities depend on the solutions and their gradients. The stability of the solutions is investigated, showing that small-scale space perturbations can be unstable. The associated stability criterion is established, indicating that instabilities, if any, are due to the diffusivities depending in an inappropriate way on the gradient of the solutions. Numerical simulations of Kato-Phillips flows are performed, which may be regarded as a highly idealised representation of the upper layers of the ocean. Several versions of the Munk-Anderson and Mellor-Yamada turbulence closure schemes are implemented. The stable or unstable nature of their behaviour is seen to be in good agreement with the predictions of the theoretical stability analysis.
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