Multiple states and heat transfer in two-dimensional tilted convection with large aspect ratios

The coexistence of multiple turbulent states was reported in several recent studies in different flows. We present in this work that multiple turbulent states also exist for thermal convection in two-dimensional tilted cells with large aspect ratios (Gamma = width/height) through direct numerical simulations for the Rayleigh number Ra = 10(7) and the Prandtl number Pr = 0.71. The considered Gamma ranges from 1 to 16. The tilt angle beta varies from 0 degrees to 180 degrees. Multiple states are identified for small beta with Gamma >= 2, where the different flow states are reflected in different numbers of convection rolls. The corresponding Nu is generally higher for the flow state with more convection rolls. Moreover, flow mode transitions between different roll states are observed for large Gamma >= 8 when beta is larger than a critical value. The effect of cell tilting on Nu and Re is also investigated. It is found that for Gamma <= 4, Nu first increases with increasing beta and then declines after reaching its local maximum. However, Nu generally decreases monotonically with increasing beta for Gamma = 8, 12, and 16. This indicates that the idea to enhance heat transfer by tilting the cell can be realized only for relatively small Gamma for the present system. It is also found that the previous finding that Re decreases monotonically with increasing beta for large beta with Gamma = 1 does not hold for large-Gamma cases.