Nonlinear convection in a rotating layer  Amplitude expansions and normal forms
Abstract
Twodimensional convection in a horizontal layer of Boussinesq fluid rotating about a vertical axis is studied. For certain choices of the parameters the dispersion relation describing the stability of the conductive solution has two zero eigenvalues. For nearby parameter values nonlinear solutions are accessible analytically, using either the method of normal forms or an amplitude expansion. The results provide a complete description of the transitions between oscillatory and steady convection as functions of the Rayleigh and Taylor numbers near their critical values.
 Publication:

Geophysical and Astrophysical Fluid Dynamics
 Pub Date:
 1983
 DOI:
 10.1080/03091928308209045
 Bibcode:
 1983GApFD..23..247G
 Keywords:

 Computational Fluid Dynamics;
 Convective Flow;
 Free Convection;
 Rotating Fluids;
 Two Dimensional Flow;
 Angular Velocity;
 Boussinesq Approximation;
 Eigenvalues;
 Oscillating Flow;
 Rayleigh Number;
 Steady Flow;
 Fluid Mechanics and Heat Transfer;
 CONVECTION;
 THEORY;
 ROTATION