Rotating Boussinesq convection in a plane layer is governed by two dimensionless
groups in addition to the Rayleigh number R: the Prandtl number σ and the Taylor
number Ta. Scaled equations for fully nonlinear rotating convection in the limit of
rapid rotation and small Prandtl number, where the onset of convection is oscillatory,
are derived by considering distinguished limits where σnTa1/2 ∼ 1
but σ → 0 and Ta → ∞, for different n > 1.
In the resulting asymptotic expansion in powers of Ta−1/2
and the amplitude of convection. Three distinct asymptotic regimes
are identified, distinguished by the relative importance of the subdominant buoyancy
and inertial terms. For the most interesting case, n = 4, the stability of different
planforms near onset is investigated using a double expansion in powers of Ta−1/8 and the amplitude of convection ε. The lack of a buoyancy term at leading order
demands that the perturbation expansion be continued through six orders to derive
amplitude equations determining the dynamics. The case n = 1 is also analysed. The
relevance of this theory to experimental results is briefly discussed.
Comprehensive Search for New Phases and Compounds in Binary Alloy Systems Based on Platinum-Group Metals, Using a Computational First-Principles Approach