Abstract
The life cycle of three-dimensional cumulus convection is numerically simulated by a large eddy simulation method using a one-equation model. The basic equations contain nine prognostic equations : the Navier-Stokes equations, pressure and thermodynamic equations, three moisture and water equations, and a model equation. The model equation is a transport equation for subgrid scale kinetic energy ; buoyancy and shear produce subgrid scale kinetic energy. A terrain-following coordinate transformation is employed in order to map a simulation domain with an irregular lower boundary onto a rectangular domain. A finite difference scheme solves the transformed equations, conserving heat, moisture, water substances, and subgrid scale motion. The life cycle of an isolated cell of cumulus convection is simulated over a bell-shaped mountain for a simplified atmospheric condition. The result is in good qualitative agreement with observed characteristics. A simulation is also made over a flat surface to investigate the effects of the mountain. For comparison, the mountain case is simulated using Smagorinsky's model. The overall level of subgrid scale kinetic energy within the cloud is less than that computed from the one-equation model. However, subgrid scale kinetic energy diffuses outwards the cloud.
