The DoNUT Kinematic Model for Convective Circulation and the Divergence-Free, Non-Traditional Coriolis Force

Abstract:

Using careful analysis of the equations of motion, we show that the often neglected, non-traditional Coriolis force terms have as important an effect of tilting convective flows westward at the equator as the traditional Coriolis force has in generating vorticity in convective inflow and outflow. The Mach number of most atmospheric convection is significantly less than one, so flows respond like an incompressible (or anelastic) fluid. Therefore, the net forces on the atmosphere are divergence-free. The Coriolis force being one such force, we will show how the Coriolis force can be uniquely projected onto divergence-free vector fields. We can apply these fields to a recently introduced poloidal model of convection, the Dynamic of Non-rotating Updraft Torri (DoNUT) model, in which updraft air ascends inside a narrow radius from the center of the toroid and air descends over a wide ring of radii beyond. With the DoNUT, we show that the vertical component of the net Coriolis force vanishes. This allows us to compute the Coriolis pressure from a simple vertical integral of the zonal velocity. Having these tools in hand, we will then show the exact net Coriolis force arising in the DoNUT model. We split the force into two components. The first is the traditional Coriolis force which is proportional to the sine of the latitude and is well known to impart cyclonic circulation on axially converging flows. The second is the non-traditional Coriolis force which is strongly westward in the core of a convective cell and diffluent at the top of a convective cell. We conclude that these often-neglected non-traditional Coriolis force terms, acting on convective elements in the deep tropics, drive systematic westward tilts which can affect large scale circulation.