Department of Mathematics, Imperial College London, 180 Queen's Gate, London SW7 2AZ, UK
Philos Trans A Math Phys Eng Sci. 2014 Jul 28;372(2020). doi: 10.1098/rsta.2013.0347.
In this paper, the classical triple-deck formalism is employed to investigate two instability problems in which an acoustic feedback loop plays an essential role. The first concerns a subsonic boundary layer over a flat plate on which two well-separated roughness elements are present. A spatially amplifying Tollmien-Schlichting (T-S) wave between the roughness elements is scattered by the downstream roughness to emit a sound wave that propagates upstream and impinges on the upstream roughness to regenerate the T-S wave, thereby forming a closed feedback loop in the streamwise direction. Numerical calculations suggest that, at high Reynolds numbers and for moderate roughness heights, the long-range acoustic coupling may lead to absolute instability, which is characterized by self-sustained oscillations at discrete frequencies. The dominant peak frequency may jump from one value to another as the Reynolds number, or the distance between the roughness elements, is varied gradually. The second problem concerns the supersonic 'twin boundary layers' that develop along two well-separated parallel flat plates. The two boundary layers are in mutual interaction through the impinging and reflected acoustic waves. It is found that the interaction leads to a new instability that is absent in the unconfined boundary layer.
本文采用经典的三层形式理论研究了两个不稳定问题，其中声反馈回路起着至关重要的作用。第一个问题涉及到在平板上存在两个分离的粗糙元的亚声速边界层。在粗糙元之间的空间放大的 Tollmien-Schlichting（T-S）波被下游粗糙元散射，发出声波向前传播，并撞击上游粗糙元，重新生成 T-S 波，从而在流向方向上形成一个封闭的反馈回路。数值计算表明，在高雷诺数和中等粗糙元高度的情况下，远程声耦合可能导致绝对不稳定，其特征是在离散频率下产生自维持的振荡。随着雷诺数或粗糙元之间距离的逐渐变化，主要峰值频率可能从一个值跳跃到另一个值。第二个问题涉及沿着两个分离的平行平板发展的超音速“双边界层”。两个边界层通过冲击和反射声波相互作用。结果发现，这种相互作用导致了在无约束边界层中不存在的新的不稳定性。
