Universidad Nacional Aut\'onoma de M\'exico
Coyoac\'an, Mexico
The importance the free surface deformation of a convecting fluid layer has on the stability has been demonstrated in recent papers by Izakson and Yudovich [1], in the stationary case, and by Benguria and Depassier [2] in the non stationary case. It has also been shown by D\'{a}valos-O. and Lopez-M. [3] in a great variety of cases that surface deformation has an important influence on the thermoconvective instability of a rotating fluid layer.
Here, results of the linear natural convection instability of a viscoelastic fluid layer heated from below and with a deformable free surface will be presented. The lower surface of the layer is also considered free but flat. The selected viscoelastic model is the Oldroyds' one with relaxation and retardation times. As a particular case, results for the Maxwell model will be presented when the retardation time is zero. The results will be given for three different values of the Galileo number.
Besides, the results will be compared with those of the viscoelastic fluid with an upper flat surface (also calculated here for the sake of comparison) and those of the Newtonian fluid calculated by Benguria and Depassier [2].
References:
[1] Izakson, V. Kh. and Yudovich V. I., ''Convection development in a liquid with a free boundary'' Izv. An SSSR. Mekh. Zhid. i Gaza {\bf 3}, 23 (1968).
[2] Benguria, R. D. and Depassier, M. C., ''Oscillatory instabilities in the Rayleigh-B\'{e}nard problem with a free surface'' Phys. Fluids {\bf 30}, 1678 (1987).
[3] L. A. Davalos-O. and P. G. Lopez-M., ''Natural convection in a rotating fluid layer with deformable free surface'', Geophys. Astrophys. Fluid Dyn. {\bf 80}, 75 (1995).