Dynamics and scaling of moist, internally cooled convection

Idealised models of convection such as Rayleigh-Bénard convection, horizontal convection etc. have been widely used to study the behaviour of natural fluid systems including but not limited to the atmosphere, the oceans and the flow of lava in the earth's core in a simplified setting ^1,2. While such idealised models include only a small subset of the physical processes occurring in nature, their simplified dynamics allows for easier interpretation and study of the interactions of individual physical processes. 

In this numerical study, we consider the case of an idealised moist convecting thermal system, with various Dirichlet and Neumann boundary conditions for the temperature and water vapour mixing ratio. The model includes a vertical temperature lapse-rate, the release of latent heat due to the condensation of water vapour and a constant bulk-cooling term to simulate moist convection accompanied by radiative cooling in the earth's atmosphere. This study follows previous studies which have used similar idealised scenarios to understand dry ³ as well as as moist ⁴ atmospheric convection. 

The model is studied for its dynamical response and scaling for varying boundary conditions and input parameters such as the strength of the radiative cooling, the steepness of the lapse rate and the latent heat of condensation to better understand the interaction between moist convection and radiative cooling in the atmosphere. We also compare the convective organisation in our simplified model with more complex cloud-resolving atmospheric simulations ⁵. 

References:

1. G. Ahlers, S. Grossmann, and D. Lohse, “Heat transfer and large scale dynamics in turbulent Rayleigh-Bénard convection,” Reviews of modern physics, vol. 81, no. 2, p. 503, 2009.

2. G. O. Hughes and R. W. Griffiths, “Horizontal convection,” Annu. Rev. Fluid Mech., vol. 40, pp. 185–208, 2008.

3. M. Berlengiero, K. Emanuel, J. Von Hardenberg, A. Provenzale, and E. Spiegel, “Internally cooled convection: a fillip for philip,” Communications in Nonlinear Science and Numerical Simulation, vol. 17, no. 5, pp. 1998–2007, 2012

4. G. K. Vallis, D. J. Parker, and S. M. Tobias, “A simple system for moist convection: the rainy–bénard model,” Journal of Fluid Mechanics, vol. 862, pp. 162–199, 2019

5. C. J. Muller and I. M. Held, “Detailed investigation of the self-aggregation of convection in cloud-resolving simulations,” Journal of the Atmospheric Sciences, vol. 69, no. 8, pp. 2551– 2565, 2012.

Acknowledgement - This project has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 101034413.