A stable and scale-aware dynamic modeling framework for subgrid-scale parameterizations of two-dimensional turbulence

The physical mechanism of two-dimensional turbulence poses challenges for modeling subgrid-scale physics in large-scale geophysical flows. To this end, we put forth a modular dynamic modeling approach for subgrid-scale parameterizations of two-dimensional turbulence. For developing a unifying dynamic modeling approach, a set of coupled subgrid-scale models are proposed by minimizing the error between the functional and structural models. This approach is fundamentally different to the test-filtering based dynamical approach, which is also included in our analysis. Our efforts include two different functional nonlinear eddy viscosity kernels: (i) Smagorinsky's strain-rate and (ii) Leith's vorticity-gradient based formulations. The mixing length scales associated with these eddy viscosity kernels are dynamically computed from the local flow physics by incorporating the structural models based upon the scale similarity and approximate deconvolution approaches. A set of decaying turbulence experiments up to Re = 128,000 are compared against direct numerical simulations (DNSs) obtained by a resolution of 20482. First, it is shown that less dissipative results are generally obtained using Leith's eddy viscosity kernel due to its more scale-selective behavior. Among the proposed hybrid models, it is seen that the dynamic Bardina approach yields the least dissipative results, followed by the dynamic Layton, and the dynamic AD models. Due to its more dissipative character, the dynamic AD model seems to be an efficient approach for very large eddy simulations on coarse grid descriptions. To elucidate the effects of numerics on the subgrid-scale physics, two different high-order discretization schemes are considered, namely the fourth-order Padé and Arakawa schemes. Based on numerical assessments we conclude that the choice of underlying numerical discretization plays a more important role than that of the subgrid modeling in obtaining an energy spectrum that closely approximates the DNS data.