On the merging of double-diffusive convection cells at a vertical boundary

When a body of fluid with a vertical salinity gradient is subjected to an increase in temperature at a vertical wall instabilities may form. These instabilities take the form of almost horizontal convection cells with a height scale of approximately H=‖αΔT‖/(−βS̄z), where ΔT is the instantaneous perturbation wall temperature, S̄z the vertical salinity gradient, and α and β are the coefficient of thermal expansion and the equivalent coefficient for salt. As the wall temperature increases further, these cells merge. At later times, experimental observations show that the average cell height is approximately 2/3H. A simple model of cell merging is presented in which the interfaces between cells remain fixed except when adjacent cells merge to form combined cells of height H, and, as a result, the average cell height is found to be 0.6805H, in reasonable agreement with observations.