Arch Appl Mech (2011) 81: 513–530 DOI 10.1007/s00419-010-0425-8 ORIGINAL I. S. Shivakumara · S. Sureshkumar · N. Devaraju Coriolis effect on thermal convection in a couple-stress fluid-saturated rotating rigid porous layer Received: 16 July 2009 / Accepted: 19 March 2010 / Published online: 7 April 2010 © Springer-Verlag 2010 Abstract Both linear and weakly nonlinear stability analyses are performed to study thermal convection in a rotating couple-stress fluid-saturated rigid porous layer. In the case of linear stability analysis, conditions for the occurrence of possible bifurcations are obtained. It is shown that Hopf bifurcation is possible due to Coriolis force, and it occurs at a lower value of the Rayleigh number at which the simple bifurcation occurs. In contrast to the nonrotating case, it is found that the couple-stress parameter plays a dual role in deciding the stability characteristics of the system, depending on the strength of rotation. Nonlinear stability analysis is carried out by constructing a set of coupled nonlinear ordinary differential equations using truncated rep- resentation of Fourier series. Sub-critical finite amplitude steady motions occur depending on the choice of physical parameters but at higher rotation rates oscillatory convection is found to be the preferred mode of instability. Besides, the stability of steady bifurcating equilibrium solution is discussed using modified pertur- bation theory. Heat transfer is calculated in terms of Nusselt number. Also, the transient behavior of the Nusselt number is investigated by solving the nonlinear differential equations numerically using the Runge–Kutta–Gill method. It is noted that increase in the value of Taylor number and the couple-stress parameter is to dampen the oscillations of Nusselt number and thereby to decrease the heat transfer. Keywords Couple-stress fluid · Porous medium · Rotation · Hopf bifurcation · Nonlinear stability 1 Introduction Thermal convection in fluid-saturated porous media has generated an increasing interest during recent years because of its relevance in a wide range of applications such as water movement in geothermal reservoirs, thermal insulation, solid-matrix compact heat exchangers, energy storage units, ceramic processing and packed bed chemical reactors among others. As a consequence, several studies have been undertaken to investigate the effects of different phenomena connected with such media, and majority of these studies are concerned with Newtonian fluid saturating porous media [1–6]. In the aforementioned applications, the effect of rotation expressed as a Coriolis force plays a vital role. The effect of rotation on the onset of thermal convection in a horizontal fluid layer is well known for ordinary viscous fluids ([7–9], references therein). Its counterpart in a porous layer has also received considerable atten- tion. Friedrich and Rudraiah [10] have studied large amplitude convection in a rotating fluid-saturated porous layer using the Darcy model. Palm and Tyvand [11] have used the same model to study the linear stability I. S. Shivakumara (B ) · N. Devaraju UGC-Centre for Advanced studies in Fluid Mechanics, Department of Mathematics, Bangalore University, Bangalore 560001, India E-mail: shivakumarais@gmail.com S. Sureshkumar Department of Mathematics, Siddaganga Institute of Technology, Tumkur 572103, India