The character and stability of two- and three-dimensional thermocapillary
driven
convection are investigated by numerical simulations. In two dimensions,
Hopf bifurcation
neutral curves are delineated for fluids with Prandtl numbers (Pr)
10.0, 6.78,
4.4 and 1.0 in the Reynolds number (Re)–cavity aspect ratio
(Ax) plane corresponding to
Re[les ]1.3×104 and Ax[les ]7.0.
It is found that time-dependent motion is only
possible if Ax exceeds a critical value,
Axcr, which increases with decreasing Pr.
There
are two coexisting neutral curves for Pr[ges ]4.4. Streamline and
isotherm patterns are
presented at different Re and Ax
corresponding to stationary and oscillatory states.
Energy analyses of oscillatory flows are performed in the neighbourhood
of critical
points to determine the mechanisms leading to instability. Results are
provided
for flows near both critical points of the first unstable region with
Ax=3.0 and Pr=10.
In three dimensions, attention is focused on the influence of sidewalls,
located at
y=0 and y=Ay, and
spanwise motion on the transition. In general, sidewalls have
a damping effect on oscillations and hence increase the magnitude of the
first critical
Re. However, the existence of spanwise waves can reduce this critical
Re. At large
aspect ratios Ax=Ay=15,
our results with Pr=13.9 at the lower critical Reynolds
number of the first unstable region are in good agreement with those from
infinite
layer linear stability analysis.