Pattern Forming System in the Presence of Different Symmetry-Breaking Mechanisms

We report experiments on spatially forced inclined layer convection, where the combined effect of the intrinsic symmetry breaking due to a gravity-induced shear flow and spatially periodic 1D forcing is studied. We observed pattern selection processes resulting in stabilization of spatiotemporal chaos and the emergence of novel two-dimensional states. Phase diagrams depicting the different observed states for typical forcing scenarios are presented. Convection in the weakly nonlinear regime is compared with theory, and a good agreement is found.

Figure 1

(a) Schematic of forced inclined layer convection configuration. (b) Microscope image of fabricated SU-8 stripes on flat plate.

Figure 2

Parallel Forcing. (a) Phase diagram. The solid line is a guide to the eye indicating the interface between states. The broken line represents the theoretical curve of the instability to undulation chaos in the unforced case. (b) Selected patterns observed (square area shown has side length equal to $21d$). Upper side of inclined layer is at top part of images. From top left: Longitudinal rolls (LR), varicose pattern (VP), subharmonic resonances (SR), periodically spaced kink lines (KL), undulations (UN) and transverse bursts (TB). Movies depicting dynamics of UN and TB are presented in 22.

Figure 3

Orthogonal Forcing. (a) Phase diagram. (b) Selected patterns (size of area shown as in Fig. 2): transverse rolls (TR), rhombic pattern (RO), hexarolls (HR), bimodals (BM), scepter-shaped patterns (SP), and heart-shaped patterns (HP). Movies depicting dynamics of BM, SP, and HP are presented in 22.

Figure 4

(a) Bifurcation curve for parallel forcing at $\theta =20°$. The triangles and circles represent the unforced and forced experimental data, respectively. The broken line represents the fitted square-root law of the unforced cell, and the solid line depicts the theoretical imperfect bifurcation curve. Small frame shows dependency of constant term (scaled by theoretical value) on inclination angle.