Importance of subgrid-scale parameterization in numerical simulations of lake circulation

Two subgrid-scale modeling techniques––Smagorinsky’s postulation for the horizontal eddy viscosity and the Mellor–Yamada level-2 model for the vertical eddy viscosity––are applied as turbulence closure conditions to numerical simulations of resolved-scale baroclinic lake circulations. The use of the total variation diminishing (TVD) technique in the numerical treatment of the advection terms in the governing equations depresses numerical diffusion to an acceptably low level and makes stable numerical performances possible with small eddy viscosities resulting from the turbulence closure parameterizations. The results show that, with regard to the effect of an external wind stress, the vertical turbulent mixing is mainly restricted to the topmost epilimnion with the order of magnitude for the vertical eddy viscosity of 10−3 m2 s−1, whilst the horizontal turbulent mixing may reach a somewhat deeper zone with an order of magnitude for the horizontal eddy viscosity of 0.1–1 m2 s−1. Their spatial and temporal variations and influences on numerical results are significant. A comparison with prescribed constant eddy viscosities clearly shows the importance of subgrid-scale closures on resolved-scale flows in the lake circulation simulation. A predetermination of the eddy viscosities is inappropriate and should be abandoned. Their values must be determined by suitable subgrid-scale closure techniques.