Cellular flow patterns and their evolutionary scenarios in three-dimensional Rayleigh-Bénard convection

Abstract

The evolution of three-dimensional, cellular convective flows in a plane horizontal layer of a Boussinesq fluid heated from below is studied numerically. Slow motion in the form of a spatially periodic pattern of hexagonal cells is introduced initially. In a further development, the flow can undergo a sequence of transitions between various cell types. The features of the flow evolution agree with the idea of the flow seeking an optimal scale. In particular, two-vortex polygonal cells may form at some evolution stages, with an annular planform of the upflow region and downflows localized in both central and peripheral regions of the cells. If short-wave hexagons are stable, they exhibit a specific, stellate fine structure.

When organisations and ecosystems interact: toward a law of requisite fractality in firms

“…Assuming a substantive increase in resource flow driven by opportunity tension by an entrepreneurial leader, the theory then makes a very strong hypothesis: at a minimum threshold of bifurcation, new order will emerge as rapidly as possible in the system, i.e., as soon as enough resources are available (Swenson 1989(Swenson , 1992(Swenson , 1997. That is, in the absence of other constraints, new order will self-organise instantaneously (Getling and Brausch, 2003) in order to dissipate new energy potentials at the maximal rate (Swenson, 1992(Swenson, , 1997Lichtenstein, 2000;McKelvey, 2004). Since the most efficient way to dissipate these tensions is through endogenous order production (i.e., order creation), that's what will happen.…”

The helicity of the velocity field for cellular convection in a rotating layer

“…5). Let us note that the velocity field in the cells exhibits a fairly rapid change to a "two-vortex" structure [16] during its early evolution, viz., a downflow develops in the central part of the cell (as at its periphery), being surrounded by an annular upflow region; the flow thus forms two vortices in a meridional cross section of the cell (which was the basis for denoting this a two-vortex structure). Precisely this structure is demonstrated by the cells during the period of their quasi-stationary behavior.…”

Front Propagation in Stirred Media

“…The two-dimensional flow (24) generates cellular pattern. For a general discussion on cellular pattern in three dimensional Rayleigh-Bénard convection see [34]. The oscillatory instability is accounted for by the term B sin ωt, representing the lateral oscillation of the rolls [33].…”

“…We have neglected the y-dependence, replacing it with a constant β which takes into account the average effect of the vertical component of the velocity field along the path followed by (x M , y M ). By solving (34) in the interval x M ∈ (0, 2π) one obtains the time, T , needed for x M to reach the end of the cell. The front speed, as the speed of the edge particle, is then given by…”