A Model to Determine Open or Closed Cellular Convection

Abstract

A simple mechanism is proposed to help explain the observed presence in the atmosphere of open or closed cellular convection. If convection is produced by cooling concentrated near the top of the cloud layer, as in radiative cooling of stratus clouds, it develops strong descending currents which are compensated by weak ascent over most of the horizontal area, and closed cells result. Conversely, heating concentrated near the bottom of a layer, as when an air mass is heated by warm water, results in strong ascending currents compensated by weak descent over most of the area, or open cells. This mechanism, unlike that of Hubert (1966), does not invoke vertical variations of the eddy diffusion coefficients, and is similar to the one suggested by Stommel (1962) to explain the smallness of the oceans? sinking regions. This mechanism is studied numerically by means of a two-dimensional, nonlinear Boussinesq model. For this purpose we define open (closed) convection as a convective circulation pattern in which the majority of the fluid has a descending (ascending) motion. An internal heat source-sink destabilizes a layer of fluid adding no net heating. A steady state is attained. The resulting circulation is closed, as expected, when the cooling is concentrated near the upper surface, and the heating is spread throughout the lower region. The mean lapse rate is unstable in the upper half of the fluid and stable in its lower half. Conversely, the circulation is open when heating is concentrated near the bottom. In this case, the lower half of the fluid has an unstable mean lapse rate, and the upper half of the fluid is stable. The numerical results indicate that the width of the plume produced by the cooling in the upper part of the layer or by the heating in the lower part of the layer is largely independent of the degree of vertical asymmetry of the internal heating profile. On the other hand, the compensating motion occupies a region which becomes broader as the heating profile becomes more asymmetric. In other words, if cooling is very concentrated near the top of the layer with heating spread throughout the rest of the region or if heating is very concentrated near the bottom with cooling spread throughout, the generated closed or open cells have an aspect ratio much larger than 1. These results may help explain the large aspect ratios observed in atmospheric convection.