  We show that buoyancy driven flows can be steered in an arbitrary time
towards any state by applying as control only an external temperature profile
in a subset of small measure. More specifically, we prove that the 2D
incompressible Boussinesq system on the torus is globally approximately
controllable via physically localized heating or cooling. In addition, our
controls have an explicitly prescribed structure; even without such structural
requirements, large data controllability results for Boussinesq flows driven
merely by a physically localized temperature profile were so far unknown. The
presented method exploits various connections between the model's underlying
transport-, coupling-, and scaling mechanisms.
