The same isocontours obtained with the DSM are shown in Fig.22. First, as previously noted for the analysis of plane-averaged values, noticeably less SGS energy transfer (both forward and backward) occurs with the DSM than with the DTM. Moreover, it is clear that the zones of non-negligible backward and forward scatter correspond to the peaks (negative and positive) of the model parameter, observed in Fig.19a. In particular, most of the forward transfer corresponds to the stagnation streamline in the right lower part (see Fig.3), where vt/v assumes the highest positive peak. Only a region of very low backscatter is observed in the right upper part of the domain, where an upwelling occurs. Thus, even if the dynamic procedure of determination of the model parameter seems to be effective in someway, since high peaks of C correspond to regions where physical phenomena (downdraft or upwelling) actually occur, the DSM seems to be generally inadequate to account for the energy transfer between unresolved and resolved scales at the free surface.
The large eddy simulation of free-surface decaying turbulence with the dynamic two-parameter model compares very favorably with the direct numerical simulation. In particular, the reverse cascade of energy from small scales to large scales at the free surface, which is a feature of freely decaying two-dimensional turbulence, is properly taken into account by the DTM. Moreover, as in the DNS, the two-dimensional region thickens during the decay. A slight delay in the decay process is observed in the large eddy simulation, with respect to the DNS, but it is reduced by increasing the grid resolution near the free surfaces. Nevertheless, the basic mechanisms of the decay process are not affected by grid resolution.
Using the dynamic subgrid model (DSM), a large eddy simulation was carried out for the same flow geometry and boundary and initial conditions as for the DTM. Significant discrepancies were observed between the DSM and the DNS simulations during the decay process at the free surface.
The analysis of the SGS energy transfer shows that the DTM, and, in particular, the part related to the modified Leonard tensor, captures the basic mechanisms of interscale energy transfer, observed at the free surface by filtering the DNS data. Conversely, the DSM seems to be generally inadequate to account for the energy transfer between resolved and unresolved scales at the free surface: in particular, very low backscatter is observed there during the whole simulation.
As expected, the magnitude of the dynamically computed eddy viscosity in the DTM is significantly reduced compared with that in the DSM; the contribution of the Smagorinsky part to SGS energy transfer in the DTM becomes negligible with increasing decay time. Moreover, the large isolated peaks observed in local values of the eddy viscosity in the DSM almost disappear for the DTM.
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