Numerical Simulations of Three-dimensional Quasi-geostrophic Convection in the Rotating Cylindrical Annulus

Abstract:

Efforts to understand the dynamics of the Earth's core are hampered by the intrinsic numerical stiffness of the governing equations. It is thought, however, that motions in the core are balanced in the sense that fluid acceleration is subdominant in comparison to the other forces present (Coriolis, pressure, Lorentz, etc.). By exploiting the idea of balanced motions, Busse (J. Fluid Mech., vol. 173, 1986, p. 545) developed a simplified analogue of the Earth's core by restricting the flow to lie within a radially narrow, axially-aligned cylindrical annulus, though the model is limited to motions that are invariant in the direction of the rotation axis and thus outer boundaries that are of small slope. Calkins, Julien and Marti (J. Fluid Mech., vol. 732, 2013, p. 214) extended the two-dimensional annulus model of Busse to three dimensions such that the more physically realistic case of steeply sloping endwalls can be studied. Numerical simulations of this new model show that it can reproduce phenomena that are thought to be present in the Earth's core and other natural systems, such as large-scale vortices and strong zonal jets. We find that the predominantly axially-aligned convective cells that form when the thermal forcing is weak quickly break down into strongly three-dimensional flows as the forcing is increased; the resulting Reynolds stresses lead to axially-aligned mean flows that dominate the kinetic energy spectrum (see figure). Furthermore, this new model has the advantage that it employs physically realistic parameters that are not currently accessible to simulations of the full governing equations.