| The focus of this thesis is the study of rotationally constrained convection. This problem is studied in the frame work of the tall rotating differentially heated annulus, where the thermal forcing is aligned perpendicular to gravity and rotation. This geometric configuration acts as a canonical model for large scale atmospheric circulation and related geophysical systems. Experimentation, asymptotic reduction, derivation of steady states, linear stability analysis and computational modeling are combined to provide a rich study of the nature of the fluid dynamics. The asymptotic model derived from the Navier Stokes equations extends previous work to the cylindrical domain, and accurately reproduces steady state solutions and stability features observed in laboratory experiments.; Developed in parallel to this work is a new technique for solving discretized partial differential equations with Chebyshev spectral methods. This technique is shown to be very efficient and adaptable in Cartesian, cylindrical and spherical geometries. This new methodology has additional applications including eigenvalue analysis, where the method is used to validate a long held assumption about Rayleigh Benard convection. |
