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

Abstract

The theoretical modeling of turbulent plumes in stratified environment is key for understanding the physics of convective systems of further complexity such as the atmospheric and oceanic convection. In this work we consider the round buoyancy plumes in stratified environments governed by the conservation of momentum, kinetic energy, and buoyancy, also referred to as energy-consistent plumes. Analytical solutions for the convective plumes for a particular case when the plume radius follows a linear grows with the height are presented. It is also shown that for this particular case the energy-consistent plume model gives the same type of equations as the well known one-dimensional Lagrangian model that is currently used to model the convection in the atmospheric boundary layer. Since in the atmospheric convection the assumption that the plume has a constant radius is a very common closure, the physical conditions that allow one to consider such an assumption are also discussed. In addition, a possible implementation of the energy-consistent plume model in the eddy-diffusivity mass-flux formulation is also presented in the last part of this work.