Tollmien-Shlichting和声波相互作用：一般描述和非线性共振
Tollmien-Shlichting and sound waves interaction: general description and nonlinear resonances
摘要：
将具有任意状态方程（泰勒级数近似）的2+1维流体热力学方程组分裂成本征模：Tollmienn-Schlichting（TS）波和两个声学波。模态定义是通过局部关系方程来实现的，该方程是从边界层流动上的一般系统的线性化中提取的。每个这样的连接定义子空间和对应的投影仪。因此，分区是在本地执行的，可以帮助初始（或边界）问题的制定。一般的非线性帐户确定的声学和涡边界层扰动场之间的相互作用的具体形式。在下一个投影到Orr-Sommerfeld方程的TS波的解的子空间和声学的相应程序之后，方程转到描述沿着基本流的演化的一维系统。提出了一种新的机制，非线性共振激发TS波的声音，并通过四波相互作用建模。主题类别：第35 Q30;关键词：流体力学，边界层，本征模投影，Tollmien-Schlichting波，声波，非线性共振，N波系统。
英文摘要：
The general hydro-thermodynamic system of equations in 2+1 dimensions with arbitrary equations of state (Taylor series approximation) is split to eigen modes: Tollmienn-Schlichting (TS) wave and two acoustic ones. A mode definition is realized via local relation equations, extracted from the linearization of the general system over boundary layer flow. Each such connection defines the subspace and the corresponding projector. So the division is performed locally and could help in initial (or boundary) problems formulation. The general nonlinearity account determines the specific form of interaction between acoustic and vortical boundary layer perturbation fields. After the next projecting to a subspace of Orr-Sommerfeld equation solution for the TS wave and the corresponding procedure for acoustics, the equations go to one-dimensional system that describes evolution along the basic stream. A new mechanism of nonlinear resonance excitation of the TS wave by sound is proposed and modelled via four-wave interaction. Subjectclass: Primary 35Q30 ; Secondary 76F70, 35Q72; Keywords: keywords fluid mechanics, boundary layer, projector to eigen modes, Tollmien-Schlichting waves, acoustic waves, nonlinear resonance, N-wave system.
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