Three-dimensional numerical simulation of convection in giant planets: Effects of solid core size

Abstract

By solving the compressible hydrodynamic equations, the effects of solid core size on planetary winds are studied with a three-dimensional spherical spectral method. Four cases with solid core sizes χ (core radius ratio)=0, 0.1, 0.35 and 0.75 are discussed. A prograde equatorial jet and two adjacent retrograde jets are prominently produced in each model. The surface speed of the prograde equatorial jet increases as the solid core size increases from χ=0 to 0.35, then drops as χ further increases to 0.75. Alternating zonal wind bands in the mid latitudes are produced only in the case where the convection zone is most shallow. The velocity fields are significantly controlled by the Taylor–Proudman theorem (in the sense that the mean zonal velocities do not change much along the angular velocity direction). Three-dimensional effects are essential for the dynamics, as both the meridional-zonal and radial-zonal components of the Reynolds stress play key roles in driving the equatorial jet. The solid core affects the flows through changing the spatial geometry inside the tangent cylinder. As a result, the tangent cylinder controls the width of the prograde equatorial jet when the core becomes sufficiently large.