Steady and oscillatory instabilities of buoyancy convection in a laterally heated cube with perfectly thermally insulated horizontal boundaries and perfectly thermally conducting spanwise boundaries is studied. The problem is treated by Newton and Arnoldi methods based on Krylov subspace iteration. The finite volume grid is gradually refined from ${100}^3$ to ${256}^3$ finite volumes. It is revealed that en route to unsteadiness the flow undergoes a steady symmetry-breaking pitchfork bifurcation, which breaks its reflection and two-dimensional rotational symmetries. With a further increase of the Grashof number, the nonsymmetric flow bifurcates into an oscillatory state via a Hopf bifurcation. It is argued that the steady symmetry-breaking bifurcation takes place owing to the instability of counter-rotating vortical motions. The oscillatory instability develops as a result of the interaction between the unstable boundary layer flow and the stabilizing effect of the stable temperature stratification.

中文翻译：

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侧向加热的立方体中的空气自然对流的不稳定性，该立方体具有完美绝缘的水平边界和完美传导的展向边界

研究了侧向加热的立方体的浮力对流的稳态和振荡不稳定性，该立方体具有完全绝热的水平边界和完全导热的翼展方向边界。该问题由基于Krylov子空间迭代的Newton和Arnoldi方法处理。有限体积网格从${100}^3$ 至 ${256}^3$有限的体积。结果表明，在流向不稳定的过程中，流体经历了一个稳定的，破坏对称性的干草叉分叉，破坏了它的反射和二维旋转对称性。随着Grashof数的进一步增加，非对称流通过Hopf分叉而分叉成振荡状态。有人认为，由于反向旋转的涡旋运动的不稳定性，所以会发生稳定的对称破坏分叉。由于不稳定的边界层流动与稳定的温度分层的稳定作用之间的相互作用而导致振荡不稳定。