The Coriolis effect and travelling waves in porous media convection subject to rotation.
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Date
2000
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Abstract
This study intends to recover and expand the analytical work of Vadasz (1998) for linear
and weak non-linear stability of a rotating porous media heated form below and subject to
gravity and Conolis forces. It is shown that the viscosity has a destabilising effect at high
rotation rate. It has been established that the critical wave number in a plane containing
the streamlines is dependent on rotation. Finite amplitude calculations provide a set of
differential equations for the amplitude and phase, corresponding to the stationary and
over-stable convection, identifying the post-transient conditions that a fluid is subject to,
i.e. a pitchfork bifurcation for the stationary case, or a Hopf bifurcation in the case of
over-stable convection. The previous model (Vadasz [1998]) was extended with an
additional time scale in order to represent amplitude fluctuations and a short space scale
to include horizontal modes of oscillations. When the complete solution for the stream
function or temperature is analysed, where left and right travelling waves are considered,
we obtain a set of differential equations for the amplitude and phase. The solutions are
discussed in this context.
Description
Thesis (Ph.D.)-University of Durban-Westville, 2000.
Keywords
Coriolis force., Porous materials., Transport theory., Theses-- Electrical engineering.