Influence of Large Scale Vertical Field on Convective Patterns: a Speculation from Swift-Hohenberg Model

The influence of a large scale vertical field or a temperature gradient field on convection patterns is investigated using the Swift-Hohenberg (SH) model, which is a weakly nonlinear convection model describing evolution of convection patterns in a two-dimensional plane. The external field is introduced in the model as an additional forcing term. It is shown that the convection pattern changes from roll type to hexagonal cells, and eventually to a uniform flow as the external field strength is increased. This can be explained by dynamics of the reduced system derived from the SH model by truncation of number of wave modes. Further, when an appropriate gradient field is applied, there appear three types of convection patterns, which are:(a) hexagonal open cells with a down-flow in the middle and up-flow at the cell boundaries, (b) rolls with the longitudinal axis parallel to the direction of the temperature gradient, and (c) hexagonal closed cells with opposite flow directions to (a). The patterns (a) and (c) appear in regions with predominantly up-flow, and down-flow, respectively, and the pattern (b) in the region between them. The appearance of the hexagonal cells are well explained by the above amplitude equation. The obtained results in our numerical model bear some similarities to satellite cloud images which display a sequence of patterns, rolls first, then the open cells, and finally uniform clouds, as one traverses from the continental seacoast to the ocean.