Numerical Simulation of Turbulent Convection over Wavy Terrain

Abstract

Thermal convection of a Boussinesq fluid in a layer confined between two infinite horizontal walls is investigated by direct numerical simulation (DNS) and by large-eddy simulation (LES) for zero horizontal mean motion. The lower-surface height varies sinusoidally in one horizontal direction while remaining constant in the other. Several cases are considered with amplitude δ up to 0.15H and wavelength λ of H to 8H (inclination up to 43°), where H is the mean fluid-layer height. Constant heat flux is prescribed at the lower surface of the initially at rest and isothermal fluid layer. In the LES, the surface is treated as rough surface (z₀ = 10^-4H) using the Monin-Oboukhov relationships. At the flat top an adiabatic frictionless boundary condition is applied which approximates a strong capping inversion of an atmospheric convective boundary layer. In both horizontal directions, the model domain extends over the same length (either 4H or 8H) with periodic lateral boundary conditions. We compare DNS of moderate turbulence (Reynolds number based on H and on the convective velocity is 100, Prandtl number is 0.7) with LES of the fully developed turbulent state in terms of turbulence statistics and Characteristic large-scale-motion structures. The LES results for a flat surface generally agree well with the measurements of Adrian et al. (1986). The gross features of the flow statistics, such as profiles of turbulence variances and fluxes, are found to be not very sensitive to the variations of wavelength, amplitude, domain size and resolution and even the model type (DNS or LES), whereas details of the flow structure are changed considerably. The LES shows more turbulent structures and larger horizontal scales than the DNS. To a weak degree, the orography enforces rolls with axes both perpendicular and parallel to the wave crests and with horizontal wavelengths of about 2H to 4H. The orography has the largest effect for λ = 4H in the LES and for λ = 2H in the DNS. The results change little when the size of the computational domain is doubled in both horizontal directions. Most of the motion energy is contained in the large-scale structures and these structures are persistent in time over periods of several convective time units. The motion structure persists considerably longer over wavy terrain than over flat surfaces.