The problem of penetrative convection in a fluid saturated porous medium heated internally is analysed. The linear instability theory and nonlinear energy theory are derived and then tested using three dimensions simu...The problem of penetrative convection in a fluid saturated porous medium heated internally is analysed. The linear instability theory and nonlinear energy theory are derived and then tested using three dimensions simulation.Critical Rayleigh numbers are obtained numerically for the case of a uniform heat source in a layer with two fixed surfaces. The validity of both the linear instability and global nonlinear energy stability thresholds are tested using a three dimensional simulation. Our results show that the linear threshold accurately predicts the onset of instability in the basic steady state. However, the required time to arrive at the basic steady state increases significantly as the Rayleigh number tends to the linear threshold.展开更多
An unstably stratified flow entering into a stably stratified flow is referred to as penetrative convection,which is crucial to many physical processes and has been thought of as a key factor for extreme weather condi...An unstably stratified flow entering into a stably stratified flow is referred to as penetrative convection,which is crucial to many physical processes and has been thought of as a key factor for extreme weather conditions.Past theoretical,numerical,and experimental studies on penetrative convection are reviewed,along with field studies providing insights into turbulence modeling.The physical factors that initiate penetrative convection,including internal heat sources,nonlinear constitutive relationships,centrifugal forces and other complicated factors are summarized.Cutting-edge methods for understanding transport mechanisms and statistical properties of penetrative turbulence are also documented,e.g.,the variational approach and quasilinear approach,which derive scaling laws embedded in penetrative turbulence.Exploring these scaling laws in penetrative convection can improve our understanding of large-scale geophysical and astrophysical motions.To better the model of penetrative turbulence towards a practical situation,new directions,e.g.,penetrative convection in spheres,and radiation-forced convection,are proposed.展开更多
基金supported by the Iraqi ministry of higher education and scientific research
文摘The problem of penetrative convection in a fluid saturated porous medium heated internally is analysed. The linear instability theory and nonlinear energy theory are derived and then tested using three dimensions simulation.Critical Rayleigh numbers are obtained numerically for the case of a uniform heat source in a layer with two fixed surfaces. The validity of both the linear instability and global nonlinear energy stability thresholds are tested using a three dimensional simulation. Our results show that the linear threshold accurately predicts the onset of instability in the basic steady state. However, the required time to arrive at the basic steady state increases significantly as the Rayleigh number tends to the linear threshold.
基金supported by the Heilongjiang Touyan Innovative Program Teammade possible through the generous support of the NSFC (Grant No. 52176065)the Fundamental Research Funds for the Central Universities(Grant No. 2022FRFK060022)
文摘An unstably stratified flow entering into a stably stratified flow is referred to as penetrative convection,which is crucial to many physical processes and has been thought of as a key factor for extreme weather conditions.Past theoretical,numerical,and experimental studies on penetrative convection are reviewed,along with field studies providing insights into turbulence modeling.The physical factors that initiate penetrative convection,including internal heat sources,nonlinear constitutive relationships,centrifugal forces and other complicated factors are summarized.Cutting-edge methods for understanding transport mechanisms and statistical properties of penetrative turbulence are also documented,e.g.,the variational approach and quasilinear approach,which derive scaling laws embedded in penetrative turbulence.Exploring these scaling laws in penetrative convection can improve our understanding of large-scale geophysical and astrophysical motions.To better the model of penetrative turbulence towards a practical situation,new directions,e.g.,penetrative convection in spheres,and radiation-forced convection,are proposed.
