Effect of subgrid-scale mixing on the evolution of submesoscale instabilities (PREPRINT, click below to download)
We study the effect of subgrid-scale (SGS) mixing on the evolution of a zonal, frontal jet initially in thermal-wind balance with a meridional density gradient and forced by downfront surface winds. The horizontal size of the model domain (O (100 km)) is large enough to contain mesoscale eddies while the horizontal grid resolution (\(500\)m) is fine enough to resolve submesoscale eddies. We compare the performance of two subgrid-scale (SGS) models: (i) constant lateral SGS viscosities (1 m^2/s and 5 m^2/s) and an analytically prescribed vertical SGS viscosity; and (ii) an existing variant of the original Smagorinsky SGS model developed for anisotropic grids with large aspect ratios. Our simulations show the subgrid model can influence adversely the dynamics at scales of motion far removed from the grid cutoff scale. In particular, we find the following are insufficiently robust to changes in the subgrid model or the model constant for a given subgrid model: (i) the strength of the inverse and forward cascades; (ii) the efficiency of conversion of available potential energy (APE) to eddy kinetic energy (EKE); and (iii) the zonally-averaged resolved-scale EKE budgets. Among the different simulations, those using a constant lateral SGS viscosity of 5 m^2/s exhibit the weakest inverse and forward cascades, and the most inefficient conversion of APE to EKE. Differences in the zonally-averaged resolved-scale EKE budgets obtained using the two SGS models are minimal within a near-surface layer similar to the traditional Monin-Obukhov (MO) layer. Below this MO-like layer, however, the differences are significant as simulations with a constant lateral SGS viscosity and a background SGS vertical viscosity fail to reproduce a realistic balance between the various terms in the EKE budget. A lateral viscosity of 1 m^2/s predicts the production of EKE is balanced solely by pressure transport with negligible SGS destruction, whereas recent experimental studies show enhanced destruction near fronts. For a constant lateral viscosity of 5 m^2/s the magnitude of the dominant production term is an order of magnitude smaller than scaling estimates in the literature due to the poor conversion of APE to EKE. The EKE budgets obtained using the anisotropic Smagorinsky model (ASM) show production of EKE is balanced by a combination of pressure transport and SGS destruction. The magnitude of the dominant production term is consistent with existing scaling estimates in the literature.