I am not an oceanographer, but meteorologist, but in the atmosphere using LES for 2D simulation is a non-sense. Even more so for a simplified model such as the shallow water equations.
LES to work properly must resolve a big part of the turbulence spectrum and therefore must be able to explicitly simulate the dynamics turbulent flow. In the limit of very large resolution and disabled subgrid model you need the code to approach DNS. You hardly can expect that from 2D shallow water model.
It is true that the Smagorinsky model originated in 2D simulations of atmosphere, but the true correct application proved to be elsewhere.