Measurements of the concentration field in nonlinear travelling-wave convection

Abstract

We present observations of travelling-wave convection in ethanol/water mixtures in a rectangular container using shadowgraphic flow visualization along the axes of the convective rolls. The entrainment of solute into the centre of the fluid layer from the boundary layers at the top and bottom of the cell is clearly observed in the shadowgraph images as sharp features at the roll boundaries. The shadowgraph images are integrated to yield a map of the two-dimensional refractive-index field. The contributions to this field from the convective temperature and the concentration fields have sufficiently different spatial character to be reliably separated using image-processing techniques. This has allowed us to produce a map of these two flow fields that is in good quantitative agreement with numerical integrations of the full Navier–Stokes equations in the Boussinesq approximation. We also present qualitative visualizations of transients caused by abruptly triggering and quenching travelling-wave convection. These experiments illustrate the formation of concentration boundary layers and reveal the existence of large-scale currents which are an inherent part of travelling-wave convection.

Bistability of Slow and Fast Traveling Waves in Fluid Mixtures

“…The structural changes that occur with growing χ can be observed experimentally in topview and even better in sideview shadowgraph intensity distributions [20,10,12]. The sideviews in Fig.…”

“…The convective amplitude of the fast (slow) TW is small (large) while the amplitude of its concentration contrast is large (small). The fast stable TWs have so far remained unnoticed in experiments [4][5][6][7][8][9][10][11][12][13] and numerical simulations [14,15]. They develop with increasing Soret coupling via a saddle node bifurcation out of a dent in the subcritically bifurcating unstable TW branch.…”

“…1 at ψ = −0.25. The significance of such a dent on the lower unstable branch of solutions being unaccessible to experiments [4][5][6][7][8][9][10][11][12][13] as well as to earlier numerical simulations [14,15] has not been appreciated appropriately although it can be seen in the paper of Bensimon et al [21] in the limit of small Soret coupling and σ → ∞. With our new finite difference method and our many mode Galerkin scheme we can now trace out the complete solution branch and determine how its bifurcation topology changes with ψ. Sideview shadowgraph intensity distributions obtained as described in [10,15] from the numerically determined TW states that are marked by the respective triangles in Fig.…”

Localized structures in convective experiments

“…Out of these states emerge stable stationary spatially localized structures embedded in a background of small amplitude standing waves (see fig-3). In 1990 P. Kolodner [36,9,[37][38][39], presented evidence for the reflection of traveling waves in a localized structure. The relation of these states to the time-independent spatially localized states that characterize the so called pinning region is investigated by exploring the stability properties of the later, and the associated instabilities.…”

Traveling wave fronts and localized traveling wave convection in binary fluid mixtures

“…TW and LTW convection has been studied experimentally and theoretically for some time [1,4,5,6,7,8,9,10,11,12,13,14]. The transient oscillatory growth of convection was investigated by numerical simulations [15].…”