The onset of natural convection in lakes and reservoirs due to night time cooling

摘要

A theoretical model, based on linear stability analysis, is proposed to predict the onset of natural convection in lakes and reservoirs due to night time cooling. To such purpose, the system was modelled as a initially quiescent deep Boussinesq fluid reservoir, whose upper boundary temperature changes sinusoidally. From scaling analysis, it is found that critical onset times for convection are proportional to R −2/7, where R is a Rayleigh number including fluid properties and forcing frequency. The proportionality constant was found, from the solution of an eigenvalue problem, as a function of the Prandtl number. The onset time for convection was easily observed from experiments and quantitatively detected as a rapid increase of the RMS of the computed velocity field obtained using PIV. In this controlled conditions, differences close to 10% between predicted and observed times for the start of the convective flow was found. It is apparent from the present set of results that predictions are reasonable.