For a family of oscillatory Stokes layers, the spatio-temporal evolution of impulsively excited disturbances is investigated, using direct numerical simulations of the linearised Navier-Stokes equations. The semi-infinite planar Stokes layer is modified to incorporate a low-amplitude, high-frequency harmonic, which provides a simplified model of the external noise found in physical experiments. For the unmodified Stokes layer, impulsively excited disturbances are known to form family-tree-like structures, composed of multiple wavepackets. The long-term behaviour that is encompassed within these structures is studied, together with the effects upon them of the alterations to the base flow. In the absence of any base-flow modification, the disturbances are discovered to exhibit a subharmonic pattern of temporal growth, with a periodicity that is twice that of the basic state. It is also shown that when linear instability first arises, it takes an absolute rather than a convective form. Inclusion of a high-frequency harmonic into the basic state is found to have a strong and destabilising impact upon the impulse response. The development of the family-tree like disturbance structure can be disrupted, changing the character of the absolute instability and promoting its appearance at much reduced Reynolds numbers.

中文翻译：

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斯托克斯层线性扰动时空发展的数值模拟：绝对不稳定性和高频谐波的影响

对于一类振荡斯托克斯层，使用线性化的Navier-Stokes方程的直接数值模拟研究了脉冲激励扰动的时空演化。对半无限平面斯托克斯层进行了修改，以合并低振幅，高频谐波，从而提供了物理实验中发现的外部噪声的简化模型。对于未经修改的斯托克斯层，已知脉冲激发干扰会形成由多个波包组成的类树状结构。研究了这些结构中包含的长期行为，以及基流变化对它们的影响。在没有任何基流修改的情况下，发现扰动表现出时间增长的次谐波模式，周期是基本状态的两倍。还表明，当线性不稳定性首次出现时，它采取绝对形式而不是对流形式。已经发现，将高频谐波包含在基本状态中会对脉冲响应产生强大且不稳定的影响。像家庭树一样的干扰结构的发展可能会被破坏，从而改变绝对不稳定的特征，并以大大减少的雷诺数促进其出现。