Mixing by chaotic convection in an infinite Prandtl number fluid and implications for mantle convection

Two‐dimensional flow in an infinite Prandtl number constant viscosity fluid is chaotic in high‐resolution numerical experiments; however, it is unknown how many modes are appropriate to describe the convection in the Earth’s mantle. It is known, for instance, that nonhomogeneous mechanical and thermal boundary conditions, such as those found in the Earth’s mantle, limit the suite of modes present and that low‐order modes dominate thermal convection in the Earth’s mantle, yet the mixing consequences of limiting the spatial spectrum of thermal convection at infinite Prandtl number are unknown. Therefore the mixing which results from the nonlinear interaction of a single convection roll with a single spatial subharmonic is examined. To study mixing in this flow, the deformation history of infinitesimal strain markers and the dispersion of clusters of passive markers in the fluid are calculated. Observing the rapid scattering of clusters of markers provides a useful visualization of the mixing process. The de...