1 On nonlinear convection in mushy layers. Part 2. Mixed oscillatory and stationary modes of convection

This paper presents part 2 of the problem of nonlinear convection in horizontal mushy layers during the solidification of binary alloys. Part 1 of the problem dealt with only the oscillatory modes of convection, which was investigated very recently (Riahi2002). In the present paper we consider particular range of the parameter values where the critical values of the scaled Rayleigh number R for the onset of oscillatory and stationary convection are sufficiently close, and we develop and analyze a nonlinear theory in such parameter regime which takes into account both stationary and oscillatory modes of convection. Under a near-eutectic approximation and the limit of large far-field temperature, we determine the weakly nonlinear solutions due to mixed oscillatory and stationary modes. Twelve new classes of these solutions, which are referred to hereafter as mixed solutions, are detected. The oscillatory component of any mixed solution depends on a parameter b, which lies in the range |b|≤0.5. The standing wave component corresponds to b=0.0, the simple travelling components correspond to |b|=0.5, and the general travelling components correspond to 0.0<|b|<0.5. The preferred mixed solutions