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• SECONDARY INSTABILITIES OF A DEVELOPING THERMAL FRONT IN A POROUS MEDIUM  download article

Asma Selim
Department of Mechanical Engineering, University of Bath, Bath BA2 7AY, UK

Andrew Rees
University of Bath

ABSTRACT

In this paper we study the instability of the developing thermal boundary layer which is induced by suddenly raising the temperature of the lower horizontal boundary of a uniformly cold semi-infinite region of saturated porous medium. The basic state consists of no flow, but the evolving temperature field may be described by the complementary error function. Recent papers by Selim and Rees (2006a, b) have sought to determine when this evolving thermal boundary layer becomes unstable and to follow its subsequent evolution well into the nonlinear regime. In this paper we investigate the secondary instability of the nonlinear cells by introducing subharmonic disturbances into the evolving flow. In general we find that the subharmonic, which has twice the wavelength of the primary vortex, tends to decay at first as the primary cells grow, but soon after the primary cells begin to decay, the subharmonic experiences an extremely rapid growth and it quickly establishes itself as the dominant flow pattern. If we take the magnitudes of the surface rate of heat transfer of the subharmonic and the primary cell as measures of the strength of each of these modes, then we may define equality of these values as corresponding to the time of subharmonic transition. This transition time is found to vary with the wavenumber of the primary cell and with the amplitudes of both the primary cell and the subharmonic disturbance.

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