We demonstrate, via simulations of asymptotically reduced equations describing rotationally constrained Rayleigh-Bénard convection, that the efficiency of turbulent motion in the fluid bulk limits overall heat transport and determines the scaling of the nondimensional Nusselt number Nu with the Rayleigh number Ra, the Ekman number E, and the Prandtl number σ. For E << 1 inviscid scaling theory ...

We study the effects of severe non-Boussinesq conditions on thermal convection at the moderate Rayleigh numbers of Ra = 2× 108 and 2× 109 by resorting to direct numerical computations of the full governing equations. We illustrate the effects by considering low temperature gaseous helium. The properties of helium are allowed to depend on the temperature around the mean of 5.4K. The Nusselt numb...

We report the numerical simulations of the horizontal convection within a rectangle cavity tank at high Rayleigh numbers. The physical solution of horizontal convection depends on the spatial resolution of the meshes. The necessary mesh number N is proportion to Ra. The unstable numerical solutions are obtained asN < cRa. This power law also implies that the spatial resolution is dominated by v...

Linear instability and nonlinear energy stability analyses are developed for the problem of a fluid-saturated porous layer stratified by penetrative thermal convection and two salt concentrations. Unusual neutral curves are obtained, in particular non-perfect ‘heartshaped’ oscillatory curves that are disconnected from the stationary neutral curve. These curves show that three critical values of...

We investigate the influence of the thermal properties of the boundaries in turbulent Rayleigh-Bénard convection on analytical bounds on convective heat transport. Using the Doering-Constantin background flow method, we systematically formulate a bounding principle on the Nusselt-Rayleigh number relationship for general mixed thermal boundary conditions of constant Biot number η which continuou...

This computational study investigates the nonlinear dynamics of unstable convection in a 2D thermal convection loop (i.e., thermosyphon) with heat flux boundary conditions. The lower half of the thermosyphon is subjected to a positive heat flux into the system while the upper half is cooled by an equal-butopposite heat flux out of the system. Water is employed as the working fluid with fully te...

The results of a full numerical simulation of Rayleigh-Brnard convection in a cylindrical container of aspect ratio five are reported. Near onset, convection takes the form of five concentric rolls, which in fluids of moderate to large Prandtl number, are stable to nonaxisymmetric perturbations. As the Rayleigh number is increased, these ,,oils are succeeded by traveling waves when the sidewall...

We investigate the Rayleigh–Bénard convection problem within the context of a diffusion flame formed in a horizontal channel where the fuel and oxidizer concentrations are prescribed at the porous walls. This problem seems to have received no attention in the literature. When formulated in the low-Mach-number approximation the model depends on two main non-dimensional parameters, the Rayleigh n...