A prognostic turbulence scheme for the nonhydrostatic plume model ATHAM

The presented turbulence scheme was developed for the Active Tracer High-Resolution Atmospheric Model (ATHAM) to parameterize the effect of subgrid-scale turbulence. In contrast to the commonly used assumption of local isotropy in high-resolution atmospheric modeling, this scheme differentiates between horizontal and vertical turbulent exchange to represent the strong influence of buoyancy forces and vertical transports. Its computational efficiency is similar to classical turbulent kinetic energy approaches while preserving one of the main feature of higher-order schemes. The present extensions to include anisotropic effects in a turbulent kinetic energy approach do not need any ad hoc assumptions and are equivalent to the classical formulation in the isotropic limit. The presence of high tracer concentrations in a particle-laden plume is taken into account, as well as supersonic effects at low Mach numbers. The turbulent exchange coefficients used in the equations of motion are derived from a set of three coupled differential equations for the horizontal and vertical turbulent energy and the turbulent length scale. No turbulent equilibrium is assumed. All turbulent quantities are treated prognostically. Numerical simulations of convective plumes of a typical Plinian volcanic eruption with the nonhydrostatic plume model ATHAM reveal that a complex treatment of turbulent quantities is necessary in order to capture the bulk characteristics of the plume, such as the plume height, the horizontal extent, and plume development in time. Anisotropic effects of turbulence have a significant impact on the stability and internal structure of the plume. For the first time, results from a fully three-dimensional simulation of a volcanic plume are presented. Because of its general formulation the presented turbulence scheme is suitable for a wide range of atmospheric applications.