Abstract: We introduce a novel method for describing and controlling a 3D smoke simulation. Using harmonic analysis and principal component analysis, we define an underlying description of the fluid flow that is compact and meaningful to non-expert users. The motion of the smoke can be modified with high level tools, such as animated current curves, attractors and tornadoes. Our simulation is controllable, interactive and stable for arbitrarily long periods of time. The simulation's computational cost increases linearly in the number of motion samples and smoke particles. Our adaptive smoke particle representation conveniently incorporates the surface-like characteristics of real smoke.