We propose a simple method for the intuitive authoring and efficient animation of virtual tornadoes. Users control the tornado kinematics by sketching two types of curves to specify the initial geometry of the tornado's core and the profile of the surrounding swirling air, known as the funnel. The first input, a 3D curve, initializes the core as a vortex filament. This filament induces a \emph{swirl} flow and advects according to its initial curvature, resulting in progressive bending and twisting. The second input consists of one or multiple 2D profile curves that parameterize the Stokes stream function, governing the radial and axial motion of the air around the core and thereby dictate the funnel shape over time. The core and funnel profile are coupled in local frames through closed-form velocities, which together describe the rotation, sliding and uplift within the tornado's air volume. As shown in our case studies, our method provides a controllable and efficient way to animate visually plausible tornadoes capable of tearing off infrastructure and transporting debris, as well as interacting with uneven terrain.