Linear and nonlinear analyses on the onset of gravitational instabilities in a fluid saturated within a vertical Hele-Shaw cell

In relation with the carbon dioxide sequestration into a saline aquifer, the onset of buoyancy-driven convection in a Hele-Shaw cell is analyzed theoretically and numerically. Under the linear stability theory and the Brinkman equation, new stability equations are derived in the global domain and transformed into a similar domain. By expanding the disturbance quantities using orthonormal functions, linear stability equations are solved analytically. The present prediction suggested that the onset of convection in a Hele-Shaw cell is governed by the Hele-Shaw modified Rayleigh number and the Brinkman number (or Hele-Shaw number) rather than by the Hele-Shaw modified Rayleigh number only. Using the linear stability analysis result as an initial condition for the nonlinear analysis, direct numerical simulations are also conducted. The present linear stability analysis and the numerical DNS calculation support each other.