(6)Dynamic modeling of the horizontal eddy viscosity coefficient for quasigeostrophic ocean circulation problems
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Romit Maulik, Omer San ∗
School of Mechanical and Aerospace Engineering, Oklahoma State University, Stillwater, OK 74078, USA
Received 4 January 2016; received in revised form 15 July 2016; accepted 9 August 2016
Available online 22 September 2016
Abstract
This paper puts forth a simplified dynamic modeling strategy for the eddy viscosity coefficient parameterized in space and time. The eddy viscosity coefficient is dynamically adjusted to the local structure of the flow using two different nonlinear eddy viscosity functional forms to capture anisotropic dissipation mechanism, namely, (i) the Smagorinsky model using the local strain rate field, and (ii) the Leith model using the gradient of the vorticity field. The proposed models are applied to the one-layer and two-layer wind-driven quasigeostrophic ocean circulation problems, which are standard prototypes of more realistic ocean dynamics. Results show that both models capture the quasi-stationary ocean dynamics and provide the physical level of eddy viscosity distribution without using any a priori estimation. However, it is found that slightly less dissipative results can be obtained by using the dynamic Leith model. Two-layer numerical experiments also reveal that the proposed dynamic models automatically parameterize the subgrid-scale stress terms in each active layer. Furthermore, the proposed scale-aware models dynamically provide higher values of the eddy viscosity for smaller resolutions taking into account the local resolved flow information, and addressing the intimate relationship between the eddy viscosity coefficients and the numerical resolution employed by the quasigeostrophic models.
© 2016 Shanghai Jiaotong University. Published by Elsevier B.V.
This is an open access article under the CC BY-NC-ND license ( http://creativecommons.org/licenses/by-nc-nd/4.0/ ).
Keywords: Eddy viscosity; Dynamic Smagorinsky model; Dynamic Leith model; Anisotropic dissipation; One-layer problem; Two-layer problem.