Scaling and direct stability analyses of natural convection induced by absorption of solar radiation in a parallelepiped cavity

• Obtained scaling relations for the bottom and surface layers and for the onset of instability.
• Demonstrated the existence of the most unstable range of the normalised water depth.
• Studied the dependence of the stability properties on the controlling parameters.
• Showed the increased stability with reducing the box dimension.

The present study considers the early stage of the flow development in a water-filled, three-dimensional parallelepiped cavity subject to solar radiation. The thermal structure consists of an upper stable stratification due to internal heating, provided by the direct absorption of radiation, and a bottom potentially unstable boundary layer due to the absorption and re-emission of the residual radiation by the bottom boundary. The growth of the competing thermal layers and the stability properties of the bottom thermal boundary layer are investigated by means of a scaling analysis and a direct stability analysis based on three-dimensional numerical simulation. The scaling relations are benchmarked against the numerical simulation, and the effects of the normalised water depth, the Rayleigh number and the box aspect ratio on the thermal instability are studied.