In this work, we investigate the stability of stably stratified flow in a nearly semicircular pool with an upper free surface where fluid can be fed in, and with porous lower boundaries where fluid can escape. This generic geometry is representative of numerous problems were solid materials are melted [1]. We solve the equations governing stably stratified flow under Boussinesq approximation in a curved geometry using the spectral element method. The linear stability analysis shows that the two-dimensional steady base flow [2] becomes unstable to oscillatory or non-oscillatory three-dimensional (3D) modes depending on the inlet net mass flux. Further, the analysis of the nonlinear evolution of the system using 3D direct numerical simulation and the Stuart—Landau equation [3] exhibit both supercritical as well as subcritical transition for different parameters.

References

[1] Flood and Davidson, Mat. Sci. Tech., (1994).
[2] Barkley et al., J. Fluid Mech., (2002).
[3] Sheard et al., J. Fluid Mech., (2004).