Characterization of linear and oscillatory behaviours of radiation-induced natural convection boundary layer in response to constant and time-varying thermal forcing

This paper considers linear and oscillatory behaviours of the natural convection boundary layer induced by the absorption of incoming radiation in response to constant and time-varying (ramp) thermal forcing. The considered configuration is relevant to the flow in littoral regions of lakes and reservoirs in response to the daytime thermal forcing due to solar radiation. The absorption of the incoming solar radiation is depth-dependent, following Beer's law, whilst the residual radiation at the bottom bathymetry is absorbed and released back to the water body as a boundary flux. Therefore, a potentially unstable thermal boundary layer forms adjacent to the bottom bathymetry and the associated thermoconvective instability induces vertical mixing in the form of rising plumes (i.e. intermittent convection). The linear theory is applied to investigate the incipient evolution of the instability, and direct comparisons of linear and direct stability analyses are performed. The fastest growing mode and the corresponding temporal growth rate obtained via a quasi-static linear stability analysis are shown to be in excellent agreement with the results of the direct stability analysis based on numerical simulations of the flow. Further, the time and frequency scales of the unstable bottom thermal boundary layer are derived via a local Rayleigh number analysis. It is then demonstrated that the boundary layer response to the time-varying thermal forcing is in equilibrium with the forcing intensity at each instant of time.