- Top of page
- 1. Introduction
- 2. Ordinary Double-Diffusive Convection: A Summary
- 3. Formulation of Fluid Instability in the Presence of Crystallization
- 4. Results and Discussion
- 5. Conclusions
- Appendix A.: Details of Mathematical Analysis
 Buoyancy forces derived from either thermal or compositional origins, or both, are the main driving mechanisms for dynamic instabilities within natural fluid systems. Crystallization can contribute to the compositional buoyancy due to density differences between the original bulk fluid and the residual fluid of crystallization. Depending on the density contrast, the compositionally induced buoyancy force may enhance or decrease the thermal buoyancy force established by the prevailing temperature gradient of the environment. The purpose of this paper is to examine the complex interactions between the compositional and the thermal buoyancy forces within a thermal chemical system incorporating the effects of crystallization. Like a thermal chemical system without crystallization (also known as an ordinary double-diffusive system), our results identify a dynamic and an oscillatory instability boundary in a traditional stability diagram. A dynamic instability boundary separates the stability diagram into two regimes. On one side of the boundary, fluid dynamic perturbations will grow indefinitely, leading to rigorous convection eventually. On the other side, perturbations decay in time, and the system will ultimately return to a static condition. In the absence of crystallization the oscillatory instability boundary defines a regime where perturbations lead to oscillatory motions. In the presence of crystallization, however, other investigators have observed the formation of convective layering. Despite these similarities, our results show significant differences in flow characteristic when crystallization is present. When crystallization is taken into consideration, the slope of a dynamic instability boundary is no longer governed by the diffusion coefficient ratio between heat and composition alone. The release of latent heat and the location of crystallization also play some roles. In addition, convective layering (i.e., the oscillatory instability regime) is no longer confined within a domain where fluid composition is stably stratified. It can extend into the compositionally unstable domain as well. Applications of our results to the solidification of magmatic bodies, the formation of columnar joints, and the cooling of the outer liquid core are examined. The existence of oscillatory instability within the compositionally unstable domain is significant because it suggests that the possible existence of convective layering within a cooling tholeiitic magma body cannot be ruled out, in contrast to a conclusion derived from double-diffusion studies in the absence of crystallization. Our analysis also suggests a possible criterion to test if columnar jointing has a double-diffusive origin. If columnar joints were thermal cracks formed along a preexisting double-diffusive fingering pattern as speculated, they should occur only in calc–alkaline basaltic lava, and they are not expected to appear in tholeiitic basalts. Iron–nickel precipitation above the inner–outer core boundary operates in a compositionally unstable domain because the residual liquid is expected to be less dense. Since the condition is unstable both thermally and compositionally at this boundary, solidification should lead to rigorous convection above the inner core. However, the existence of convective layering remains a possibility if the latent heat release is sufficient to cause the solidification process to operate within the newly determined oscillatory instability regime. Although the averaged temperature beneath the core–mantle boundary is believed to exceed the melting temperature of iron and nickel, local solidification is possible, resulting in the production of stabilizing convective layering that can inhibit large-scale convection near the top of the liquid outer core.