Despite the importance of flow for transporting and organizing populations, few laboratory systems exist to systematically investigate the impact of advection on their spatial evolutionary dynamics. To address this problem, we study the morphology and genetic spatial structure of microbial colonies growing on the surface of a nutrient-laden fluid 104 to 105 times more viscous than water in Petri dishes; the extreme but finite viscosity inhibits undesired thermal convection and allows populations to effectively live at the air-liquid interface due to capillary forces. We discover that S. cerevisiae (baker's yeast) growing on a viscous liquid behave like “active matter": they metabolically generate fluid flows many times larger than their unperturbed colony expansion speed, and that flow, in turn, can dramatically impact their colony morphology and spatial population genetics. We show that yeast cells generate fluid flows by consuming surrounding nutrients and decreasing the local substrate density, leading to misaligned fluid pressure and density contours which ultimately generates vorticity via a thresholdless baroclinic instability. Numerical simulations with experimentally measured parameters demonstrate that an intense vortex ring is produced below the colony's edge. As the viscosity of the substrate is lowered and the self-induced flow intensifies, we observe three distinct morphologies: at the highest viscosity, cell proliferation and movement produces compact circular colonies with, however, a stretched regime of exponential expansion; intermediate viscosities give rise to compact colonies with “fingers" that are usually monoclonal and then break into smaller cell clusters; and at the lowest viscosity, the expanding colony fractures into many genetically-diverse, mutually repelling, island-like fragments that can colonize an entire 94 mm-diameter Petri dish within 36 hours. We propose a simple phenomenological model that predicts the early colony dynamics. Our results provide rich opportunities to study the interplay between fluid flow and spatial population genetics for future investigations.