Linear and nonlinear study of thermal instability in a fluid layer with general hydrodynamic boundaries under gravity variations

This study investigates the impact of changing gravity on the onset of thermal instability in a horizontal liquid layer heated from below and trapped between thermally conducting, general hydrodynamic boundaries (permeable). Both linear and nonlinear analysis are employed to examine the instability and stability of the system. The numerical results from both linear and nonlinear techniques are compared to determine the subcritical region. Chandrasekhar’s method is utilized to examine the impact of different physical parameters on the system’s stability. The principle of exchange of stabilities (PES) is verified for general hydrodynamic boundaries and is numerically shown to be violated as gravity decreases upward. A comprehensive parametric analysis reveals that as the gravity and permeability parameters increase, the critical Rayleigh number initially rises, indicating a stabilizing effect. Also, Stability curves depicting the interplay between gravity and permeability are presented graphically. However, for sufficiently large gravity values, gravity reversal alters the stability conditions, leading to the emergence of an alternative instability mechanism. This transition marks a fundamental shift in system behavior and underscores the limitations of traditional stability analysis under extreme gravity variations. These findings offer novel insights into convection dynamics and contribute to the broader understanding of stability in variable-gravity environments.