Beschreibung:
<jats:p>The convective flow in a thin liquid layer with a free
surface heated from below is
studied using a combination of accurate experiments with
silicone oil (<jats:italic>v</jats:italic>=0.1 cm<jats:sup>2</jats:sup> s<jats:sup>−1</jats:sup>)
and high-resolution direct numerical simulations of the
time-dependent governing equations. It is demonstrated that above
a certain value ε<jats:sub><jats:italic>s</jats:italic></jats:sub> of the threshold of
primary instability, ε=0, square convection cells
rather than the seemingly all-embracing
hexagons are the persistent dominant features of
Bénard convection. The transition
from hexagonal to square cells sets in via a subcritical
bifurcation and is accompanied
by a sudden rapid increase of the Nusselt number. This
implies that square cells are the
more efficient mode of heat transport. Their wavenumber
exceeds that of hexagonal
cells by about 8%. The transition depends on the Prandtl
number and it is shifted
towards higher ε<jats:sub><jats:italic>s</jats:italic></jats:sub> if the Prandtl
number is increased. The replacement of hexagonal
by square cells is mediated by pentagonal cells. In the
transitional regime from
hexagonal to square cells, characterized by the presence of
all three planforms, the
system exhibits complex irregular dynamics on large spatial
and temporal scales. The
time dependence becomes more vivid with decreasing Prandtl
number until finally
non-stationary square cells appear. The simulations agree
with the experimental
observations in the phenomenology of the transition, and
in the prediction of both
the higher Nusselt number of square Bénard cells and
the subcritical nature of
the transition. Quantitative differences occur with
respect to the values of ε<jats:sub><jats:italic>s</jats:italic></jats:sub> and
the Prandtl number beyond which the time dependence vanishes.
These differences are the result of a considerably weaker
mean flow in the simulation and of residual
inhomogeneities in the lateral boundary conditions of the
experiment which are below the threshold of control.</jats:p>