Natural convection and heat transfer in a valley shaped cavity filled with initially stratified water

Fog is omnipresent in the natural environment, namely valleys and mountains. A strong comprehension of the fluid flow dynamics pertaining to fog formation is of crucial importance. In the present study, the two-dimensional numerical method is used to investigate the transient natural convection in a valley-shaped triangular cavity initially filled with stratified water. A wide range of Rayleigh numbers (2.26 × 105-2.26 × 109) and aspect ratios (0.1-1.0) are considered. The numerical results are verified against experimental results. The development of natural convection flows in the cavity from the start up to the steady state is classified into two stages: an early stage and a transitional stage. Transient natural convection flows in the cavity are described. Spectral analysis is performed for different governing parameters. A simple scaling analysis is performed for the thermal boundary layer and the time scale of the stratification breakup describing the disappearance of fog in the valley is obtained and validated by numerical results. Additionally, mass and heat transfer in the cavity is measured and the scaling relation between the Nusselt number and the Rayleigh number for different aspect ratios are presented.