Chaotic and periodic natural convection for moderate and high Prandtl numbers in a porous layer subject to vibrations

摘要

The analysis of natural convection for moderate and high Prandtl numbers in afluid-saturated porous layer heated from below and subject to vibrations is presented with atwofold objective. First, it aims at investigating the significance of including a time derivativeterm in Darcy’s equation when wave phenomena are being considered. Second, it isdedicated to reporting results related to the route to chaos formoderate and high Prandtl numberconvection. The results present conclusive evidence indicating that the time derivativeterm in Darcy’s equation cannot be neglected when wave phenomena are being consideredeven when the coefficient to this term is extremely small. The results also show occasionalchaotic “bursts” at specific values (or small range of values) of the scaled Rayleigh number,R, exceeding some threshold. This behavior is quite distinct from the case without forcedvibrations, when the chaotic solution occupies a wide range of R values, interrupted only byperiodic “bursts.” Periodic and chaotic solution alternate as the value of the scaled Rayleighnumber varies.