Transition to Chaos of Natural Convection Flows in Differentially Heated Vertical Slots

Aim of the present study is the preliminary numerical analysis of the transition to turbulence of natural convection of air between two infinite vertical plates, with a focus on the effect of modeling and discretization choices on the predicted transitional patterns. In particular, the effect of the domain size, grid resolution and perturbation amplitude are explored. For the study of the problem, different Direct Numerical Simulations (DNS) have been performed. The governing equations of the problem are the continuity, momentum and temperature equations under the Boussinesq assumption. Such equations are tackled numerically by means of a pseudospectral method which discretizes space with Chebychev polynomials in the direction normal to the walls and with Fourier modes in the wall-parallel directions. For low Rayleigh number values, the predictions of the flow regimes are consistent with the results classical analytical results and linear stability analyses. In particular, the first bifurcation from the so-called conduction regime to steady convection is correctly captured. By increasing the Rayleigh number beyond a second critical value (Ra ≈ 10200), the predicted flow regime is observed to be extremely sensitive to all the above-mentioned numerical parameters, which lead to physically sound results only in some cases. In particular, the appearance of 3D structures is seen to be linked either to the adoption of a large enough domain or to the superimposition of finite-amplitude disturbances to the initial flow field.