Plumes and waves in two-dimensional turbulent thermal convection

We have conducted a high-resolution, two-dimensional direct numerical simulation of Rayleigh-Bénard convection with stress-free and periodic boundary conditions at a Rayleigh (Ra) number of [Formula Presented] and Prandtl (Pr) number of unity. An aspect-ratio three box has been considered. A single cell has been used as the initial condition. First, the flow develops into time-dependent convection with a strong asymmetry and highly convoluted thermal plumes delineating a large-scale circulation. Smaller thermal plumes detach from the boundary layer and extend over the entire cell, creating a local inversion of the temperature gradient adjacent to the boundary layers. Then the conditions leading to the formation of internal waves are fulfilled, as the local Richardson number decreases sufficiently small to cross the linear threshold of [Formula Presented] Together with the strong shear, convective rolls with a Kelvin-Helmholtz wavelike character are produced. The secondary boundary layer itself becomes unstable and produces smaller plumes. At later times, the large-scale circulation is destroyed and the internal waves disappear. A Reynolds number, based on the global scale, of [Formula Presented] is attained at this stage. Only isolated thermal plumes and vortices are present. Thus, internal waves can be generated at finite Prandtl number fluids for sufficiently high Ra in the presence of a large-scale circulation. Spectral analysis reveals that the kinetic energy decays with a logarithmic slope of -3, while the logarithmic slope of the thermal variance has a value of around -[Formula Presented]