Is the Smagorinsky coefficient sensitive to uncertainty in the form of the energy spectrum

We investigate the influence of uncertainties in the shape of the energy spectrum over the Smagorinsky [“General circulation experiments with the primitive equations. I: The basic experiment,” Mon. Weather Rev. 91(3), 99 (1963)] subgrid scale model constant CS: the analysis is carried out by a stochastic approach based on generalized polynomial chaos. The free parameters in the considered energy spectrum functional forms are modeled as random variables over bounded supports: two models of the energy spectrum are investigated, namely, the functional form proposed by Pope [Turbulent Flows (Cambridge University Press, Cambridge, 2000)] and by Meyers and Meneveau [“A functional form for the energy spectrum parametrizing bottleneck and intermittency effects,” Phys. Fluids 20(6), 065109 (2008)]. The Smagorinsky model coefficient, computed from the algebraic relation presented in a recent work by Meyers and Sagaut [“On the model coefficients for the standard and the variational multi-scale Smagorinsky model,” J....