Nonlinear convection in a rotating layer: Amplitude expansions and normal forms

摘要

Two-dimensional 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.