Spatio-temporal patterns in inclined layer convection

Abstract

This paper reports on a theoretical analysis of the rich variety of spatio-temporal patterns observed recently in inclined layer convection at medium Prandtl number when varying the inclination angle γ and the Rayleigh number R. The present numerical investigation of the inclined layer convection system is based on the standard Oberbeck-Boussinesq equations. The patterns are shown to originate from a complicated competition of buoyancy driven and shear-flow driven pattern forming mechanisms. The former are expressed as longitudinal convection rolls with their axes oriented parallel to the incline, the latter as perpendicular transverse rolls. Along with conventional methods to study roll patterns and their stability, we employ direct numerical simulations in large spatial domains, comparable with the experimental ones. As a result, we determine the phase diagram of the characteristic complex 3-D convection patterns above onset of convection in the γ -R plane, and find that it compares very well with the experiments. In particular we demonstrate that interactions of specific Fourier modes, characterized by a resonant interaction of their wavevectors in the layer plane, are key to understanding the pattern morphologies.

Time-dependent patterns in quasivertical cylindrical binary convection

“…Figure 8 shows the temperature and concentration contour plots at midplane for Ra = 1680 as well as the space-time diagram of temperature computed at two parallel lines along the direction of inclination of the cylinder. In pure fluid inclined convection and σ ≈ 1, the longitudinal roll configuration is observed for inclination angles below 78 • [26]. However, in the binary-fluid configuration under consideration, we have not obtained stable stationary longitudinal rolls in the range of Ra explored.…”

“…Very recent three-dimensional numerical works deal with the study of inclined layer convection in one-component fluids. Subramanian et al [26] analyze in extended layers the rich variety of spatiotemporal patterns that had been observed experimentally by Daniels et al [27,28] when varying the inclination angle. Torres et al [29] study the transition from the Rayleigh-Bénard convection to the heated-from-the-sides configuration in parallelepipedic cavities.…”

Inclined convection in a layer of liquid water with poorly conducting boundaries

“…4(b)], a result that differs significantly from the one found by us, due to the different boundary conditions adopted. However, it must be stressed here that both our results and those of Shadid and Goldstein have been obtained with poorly conducting boundaries, a configuration that differs significantly from the one where the boundaries conduct heat well, a condition that has been investigated extensively, both theoretically and experimentally for Pr = 1.07 [8,9,16,17]. Experiments and theoretical models performed with perfectly conducting 033481-4 boundaries and in the absence of inclination show that the convective planform is made by parallel rolls with wave number k = 3.117.…”

“…At larger inclination angles, a transition from longitudinal rolls to transverse rolls occurs [6,7]. Depending on the inclination angle, the Rayleigh number, and the Prandtl number, a complex scenario of convective patterns appears [8,9]. This scenario comprises dynamical configurations such as Busse oscillations, subharmonic oscillations, undulation chaos, longitudinal and transverse bursts [6,[10][11][12][13][14][15][16][17].…”

Effect of small inclination on binary convection in elongated rectangular cells

“…Bodenschatz et al reviewed the main numerical and experimental results obtained in the 80s and 90s on extended layers [13]. More recent experimental [14,15] and numerical [16] studies of extended layers show that a rich variety of spatio-temporal patterns may be realized when the inclination angle is varied. Other geometries have also been considered.…”