Scaling Laws Behind Penetrative Turbulence: History and Perspectives

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.