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Mass conservation takes care of itself by acting through the pressure. Large granules require a large pressure perturbation to drive their horizontal flows. If there is insufficient pressure to push enough mass out horizontally, the density builds up over the granule until the pressure is raised sufficiently to expel it. The excess pressure also decelerates the upflow and thus reduces the energy transport to the surface, in particular near the granule center, which then cools (Massaguer and Zahn, 1980). Hence, as granules grow, the upflow velocity near their center decreases and they develop an edge brightened appearance.
The horizontal flow, driven by the excess pressure in the interiors of the granules, must be halted when it reaches an intergranular lane, by which time it has cooled, become denser and is being pulled down by gravity. This requires an excess pressure also in the intergranular lanes (Hurlburt et al., 1984).
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