The effects of the density extremum and boundary conditions on the stability of a horizontally confined water layer

Using a simple non-linear density relation, the effect of the density extremum on the onset of thermal instability in a horizontally confined layer of water heated from below (at t₁) and cooled from above (at t₂) has been studied both experimentally and analytically. Both analytical and experimental results show that the density extremum has the effect of stabilizing the fluid layer. The effects of boundary conditions were also investigated. The analysis shows that realistic boundary conditions (finite thermal capacity bounding surfaces) tend to destabilize both with and without density extremum effects included. However, the qualitative behavior of Ra_c with R = ( t_m - t₂) (t₁ - t₂) is relatively independent of the boundary conditions. The combined effect of both the density extremum and realistic boundary conditions is to destabilize (with respect to the Boussinesq limit of Ra_c = 1708) for large negative R; and to stabilize, by progressively larger amounts, as R increases. Different initial modes of instability for surface temperatures which spanned above and below 4°C were observed using a Schlieren system. The wavelengths of the observed distinct disturbance forms agree well with calculated wavelengths.