The onset of thermal convection in a rapidly rotating sphere

• DOI: 10.1017/s0022112099007235
• Publication Date: 2002-07-27T09:23:06Z
• Authors: CHRIS A. JONES; ANDREW M. SOWARD; ALI I. MUSSA
• Keywords: 01 natural sciences; 0105 earth and related environmental sciences

The linear stability of convection in a rapidly rotating sphere studied here builds on well established relationships between local and global theories appropriate to the small Ekman number limit. Soward (1977) showed that disturbance marginal theory necessarily decays with time due process phase mixing (where spatial gradient frequency is non-zero). By implication, critical Rayleigh smaller than true value by an O (1) amount. complementary view mode cannot be embedded consistent WKBJ solution was expressed Yano (1992). He explained criterion for onset instability found extending onto complex s -plane, where distance from rotation axis, locating double turning point at which occurs. implemented related two-parameter family models, includes spherical problem particular values his parameters. Since he used one them as basis small-parameter expansion, results are approximate our problem. Here asymptotic developed along lines parallel hinges construction dispersion relation. Whereas Yano's relation algebraic consequence approximations, ours given second-order ODE, axial coordinate z independent variable. Our main goal determination leading-order together its first-order correction various Prandtl number. Numerical solutions relevant PDEs have also been found, down 10 −6 ; these good agreement theory. compared those Yano, surprisingly their nature.