A Simon-Weiss model for supergranule flows and their cross-correlations

Supergranule revolution rate and lifetime can be measured by cross-correlat ing pairs of Doppler-velocity maps that have been filtered (by Hathaway's m ethod) to remove other flows. As a conceptual framework for that analysis, this exploratory paper develops an idealized, phenomenological model of sup ergranule flows. Assumptions made about supergranule cells on the Sun's pho tosphere include: random location in space and time, and horizontal flows w ith circular symmetry and having a Simon-Weiss velocity function. Each supe rgranule is stable for a time, dies, and after a while, a daughter is born at a nearby position determined by a random walk. The effect on the crossco rrelations of changing projection onto the line-of-sight as the Sun rotates is analyzed. The total cross-correlation for strips of constant latitude d epends on two generic, slowly-varying projection functions. Effects of diff erential rotation and time-evolution are also considered. GONG observations of June 1994 show systematic variations in the width and shape of correlat ion peaks with latitude; our model suggests that projection effects alone c an account for these without invoking any intrinsic variations of the super granules.