Optimal wave packets in a boundary layer and initial phases of a turbulent spot
Optimal wave packets in a boundary layer and initial phases of a turbulent spot
复制标题
边界层中的最佳波包和湍流点的初始阶段
DOI：
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发表时间：
2010
影响因子：
3.7
通讯作者：
P. D. Palma
中科院分区：
文献类型：
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作者：
S. Cherubini;J. Robinet;A. Bottaro;P. D. Palma
本文用伴随优化方法研究了平板边界层三维整体最优动力学问题。本地化的最佳初始扰动的特点是由一对流向调制的反向旋转涡，倾斜的上游，在最佳时间产生交替符号的细长条纹在流向方向。这表明非零流向波数的扰动在边界层的瞬态动力学中起作用。提供了一个标度律，描述的最佳初始扰动相对于流向域长度和雷诺数的流向调制的变化。对于展向扩展域，在优化过程中提取了接近最优的三维扰动;它也在展向方向上被定位，导致在展向和流向方向上调制的细长扰动的波包。通过直接数值模拟研究了最优和近优扰动的非线性演化。发现这两种扰动都比局部最优和次优扰动在较低的初始能量水平上诱导跃迁。此外，据观察，过渡发生在对流波包的一个明确定义的区域，靠近其中心，通过一种机制，包括在同一时间的准弯曲和准静脉曲张性质的条纹振荡。在转捩之前观察到发夹涡;它们在条纹的破裂中起着积极的作用，并导致在边界层中扩散的湍流点。
The three-dimensional global optimal dynamics of a flat-plate boundary layer is studied by means of an adjoint-based optimization in a spatial domain of long – but finite – streamwise dimension. The localized optimal initial perturbation is characterized by a pair of streamwise-modulated counter-rotating vortices, tilted upstream, yielding at the optimal time elongated streaks of alternating sign in the streamwise direction. This indicates that perturbations with non-zero streamwise wavenumber have a role in the transient dynamics of a boundary layer. A scaling law is provided, describing the variation of the streamwise modulation of the optimal initial perturbation with respect to the streamwise domain length and to the Reynolds number. For spanwise-extended domains, a near-optimal three-dimensional perturbation is extracted during the optimization process; it is localized also in the spanwise direction, resulting in a wave packet of elongated disturbances modulated in the spanwise and streamwise directions. The nonlinear evolution of the optimal and near-optimal perturbations is investigated by means of direct numerical simulations. Both perturbations are found to induce transition at lower levels of the initial energy than local optimal and suboptimal perturbations. Moreover, it is observed that transition occurs in a well-defined region of the convected wave packet, close to its centre, via a mechanism including at the same time oscillations of the streaks of both quasi-sinuous and quasi-varicose nature. Hairpin vortices are observed before transition; they have an active role in the breakdown of the streaks and result in a turbulent spot which spreads out in the boundary layer.