Penetrative convection in Nocturnal ABL: Numerical Simulations

After the sunset, under calm and clear sky conditions, aerosol laden surface air-layer, cools rapidly due to radiative cooling^{[1, 2, & 3]}.  Radiative cooling extends to several 100 meters from the surface and results in the development of a stable inversion layer. However, ground surface, owing to its high thermal inertia, lags in the cooling process and about a meter thick air layer just above the ground can be 2-6⁰ C cooler than the ground^[1,2]. Thus, at the surface about a meter thick unstable convective layer is present which capped by a stable inversion layer that extends up to about 300 meters. This configuration involving a convective mixed layer topped by a stably stratified inversion layer is a classic case of penetrative convection^{[4 & 5]}.  Here, we present a computational study of this penetrative convection in the nocturnal atmospheric boundary layer (see Fig 1) and show its relevance to fog-layer dynamics. Field and laboratory measurements of aerosol number density is used to model the strength of the cooling radiative flux term. Vertical profiles of horizontally averaged temperature, density and heat flux are presented. Dynamics of penetrative motion of the fluid from the mixed layer into the stable inversion layer across the interface, results in entrainment and growth of the mixed layer. Here we show, correct length scale to be used in the Richardson number correlation^[6], to estimate the entrainment rate and to model the mixed layer growth. Analysis of the mixed layer and the entrainment zone, shows a good agreement with the previously reported laboratory experiments on penetrative convection^[4]. We show how aerosol number density impacts the growth or decay of the mixed layer (see Fig 2).  Our study also indicates that occurrence of fog near the ground surface could induce a large-scale vertical mixing, which is observed in the field experiments.

References:

1. Mukund, V., et. al., (2014). Field and laboratory experiments on aerosol‐induced cooling in the nocturnal boundary layer. Quarterly Journal of the Royal Meteorological Society, 140(678), 151-169.

2. Mukund, V., et. al., (2010). Hyper-cooling in the nocturnal boundary layer: the Ramdas paradox. Physica Scripta, 2010(T142), 014041.

3. Ponnulakshmi, V. K., et. al., (2012). Hypercooling in the nocturnal boundary layer: Broadband emissivity schemes. Journal of the atmospheric sciences, 69(9), 2892-2905.

4. Deardorff, J. W.,  et. al., (1969). Laboratory investigation of non-steady penetrative convection. Journal of Fluid Mechanics, 35(1), 7-31.

5. Kumar, R. (1989). Laboratory studies of thermal convection in the interface under a stable layer. International journal of heat and mass transfer, 32(4), 735-749.

6. Sreenivas, K. R., et. al., (1995). Modeling the dynamics of the mixed layer in solar ponds. Solar energy, 54(3), 193-202.