Localised thermal convection in rotating spheres that undergo weak precession

Abstract

We report a new nonlinear phenomenon discovered in the classical problem of thermal convection in a rapidly rotating, self-gravitating, internally heated fluid sphere that also undergoes weak precession. When the Prandtl number of fluids is sufficiently large, convection-driven columnar rolls – which are nearly geostrophic and marked by small azimuthal scale – cannot have substantial nonlinear interaction with precession-driven flow that is in the form of an equatorially antisymmetric, large-scale inertial wave in the mantle frame of reference. When the Prandtl number of fluids is sufficiently small, convection-driven flow, because of predominant inertial effects in its dynamics, is non-geostrophic and in the form of an equatorially symmetric, large-scale inertial wave, and, hence, is able to interact destructively with the precession-driven large-scale inertial wave via nonlinear effects. We reveal that the destructive interaction between the convection-driven wave and the precession-driven wave leads to a localised convective wave that is nearly equatorially symmetric, progradely travelling in the azimuthal direction, and largely confined within a quarter of the sphere.