# Single SCA-plume dynamics

## Yano, Jun-Ichi ; Baizig, Hichem

A fully prognostic prototype of bulk mass–flux convection parameterization is presented. The bulk mass–flux parameterization is formulated by assuming a subgrid-scale system consisting only of a convective plume and environment. Both subcomponents (segments) are assumed to be homogeneous horizontally. This assumption is called the segmentally constant approximation (SCA). The present study introduces this purely geometrical constraint (SCA) into the full nonhydrostatic anelastic system. A continuous-space description of the full system is, thus, replaced by a discretization consisting only of two segments (plume and environment) in the horizontal direction. The resulting discretized system is mathematically equivalent to a 0th order finite volume formulation with the only two finite volumes. The model is presented under a two-dimensional configuration. Interfaces between the plume and the environment segments may either be fixed in time or Lagrangianly advected as two limiting cases. Under this framework, the single-plume dynamics is systematically investigated in a wide phase space of Richardson number, the aspect ratio, and a displacement rate of the plume interfaces relative to the Lagrangian displacement. Advantage of the present model is in evaluating the lateral mixing processes of the plume without invoking an entrainment–detrainment hypothesis. The fractional entrainment–detrainment rate diagnosed from the present model simulations highly varies both over space and time, suggesting a limitation of applying an entrainment–detrainment hypothesis to unsteady plumes, as in the present case, in which circulations of the plume scale dominates over the turbulent mixing process. Furthermore, when the entrainment–plume hypothesis of Morton et al. is adopted for defining the plume–interface displacement rate, the plume continuously expands with time without reaching equilibrium.

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