Transitions in time-dependent thermal convection in fluid-saturated porous media

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Abstract
Numerical simulations of single-cell, two-dimensional, time-dependent thermal convection in a square cross-section of fluid-saturated porous material heated uniformly from below reveal a series of transitions between distinct oscillatory dynamical regimes. With increasing Rayleigh number R, the flow first evolves from steady-state behaviour into periodic motion with a single frequency f which depends on R approximately according to . The two frequencies in the narrow transition regime may be locked to a rational ratio, in which case the flow is periodic, or they may be commensurate, in which case the flow is quasi-periodic. The spectral characteristics of numerical realizations of unsteady convection and the occurrences of transitions therein are highly dependent on truncation level in Galerkin schemes or resolution in finite-difference approaches.