Hexagonal Patterns in a Model for Rotating convection
نویسندگان
چکیده
We study a model equation that mimics convection under rotation in a fluid with temperaturedependent properties (non-Boussinesq (NB)), high Prandtl number and idealized boundary conditions. It is based on a model equation proposed by Segel [1965] by adding rotation terms that lead to a Kiippers-Lortz instability [Kuppers & Lortz, 1969] and can develop into oscillating hexagons. We perform a weakly nonlinear analysis to find out explicitly the coefficients in the amplitude equation as functions of the rotation rate. These equations describe hexagons and oscillating hexagons quite well, and include the Busse-Heikes (BH) model [Busse & Heikes, 1980] as a particular case. The sideband instabilities as well as short wavelength instabilities of such hexagonal patterns are discussed and the threshold for oscillating hexagons is determined.
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عنوان ژورنال:
- I. J. Bifurcation and Chaos
دوره 14 شماره
صفحات -
تاریخ انتشار 2004