On the energy–consistent plume model in the convective boundary layer

Generalized eddy-diffusivity mass-flux (GEM) formulation for the parameterization of atmospheric convection and turbulence

“…Wang and Law, 2002;Kaminski et al, 2005;Ezzamel et al, 2015;van Reeuwijk and Craske, 2015;van Reeuwijk et al, 2016;Kewalramani et al, 2022;Milton-McGurk et al, 2023). Therefore, as also suggested by Savre and Herzog (2019), Vraciu (2022) or Yano (2023), we believe that the energy-consistent plume model can also be a better choice for modeling the atmospheric subgrid-scale convection than the entraining plume model that is currently used in the mass-flux formulations. Although the energy-consistent plume model requires closure for the radial profiles of the convective plume, switching the closure problem from entrainment to radial profiles, it has the advantage of providing a physical-based entrainment and of allowing to consider more realistic radial profiles for the plume model.…”

“…On the other hand, Pergaud et al (2009) consider as in Gregory (2001) that ϵ ∝ B ′ c /w ′2 based on scaling arguments. Vraciu (2022) showed that by following the Priestley and Ball (1955) formalism one may obtain the system of Equations 8 and 10 with a fractional entrainment rate that scales as ϵ ∝ z −1 in which the plume radius is not assumed constant but follows a linear growth with the height, giving thus a theoretical explanation for the entrainment parameterization closures assumed by de Roode et al (2000), Siebesma and Teixeira (2000), Soares et al (2004) and Siebesma et al (2007).…”

Generalized eddy‐diffusivity mass‐flux formulation for the parametrization of atmospheric convection and turbulence

“…The energy-consistent plume model has been proven by both numerical simulations and experimental studies to predict with a high accuracy the convective flow of plumes in idealized set-ups (e.g., Ezzamel et al, 2015;Kaminski et al, 2005;Kewalramani et al, 2022;Milton-McGurk et al, 2023;van Reeuwijk et al, 2016;van Reeuwijk & Craske, 2015;Wang & Law, 2002). Therefore, as also suggested by Savre and Herzog (2019), Vraciu (2022), or Yano (2023), we believe that the energy-consistent plume model can also be a better choice for modeling the atmospheric subgrid-scale convection than the entraining plume model that is currently used in the mass-flux formulations. Although the energy-consistent plume model requires closure for the radial profiles of the convective plume, switching the closure problem from entrainment to radial profiles, it has the advantage of providing a physical-based entrainment and of allowing consideration of more realistic radial profiles for the plume model.…”

“…On the other hand, Pergaud et al (2009) consider as in Gregory (2001) that $$$ \epsilon \propto {B}_{\mathrm{c}}^{\prime }/{w}^{\prime 2} $$$ based on scaling arguments. Vraciu (2022) showed that by following the Priestley and Ball (1955) formalism one may obtain the system of Equations and with a fractional entrainment rate that scales as $$$ \epsilon \propto {z}^{-1} $$$ in which the plume radius is not assumed constant but follows a linear growth with the height, thus giving a theoretical explanation for the entrainment parametrization closures assumed by de Roode et al (2000), Siebesma and Teixeira (2000), Soares et al (2004), and Siebesma et al (2007).…”