瞬态流体动力扰动的新观测。频率跳跃、中期和现货形成
New observations in transient hydrodynamic perturbations. Frequency jumps, intermediate term and spot formation
摘要：
剪切不可压缩流通常被认为是非色散介质。因此，瞬态中的频率演化比波能量密度或增长因子受到的关注少得多。通过对平面通道和尾流中纵向、斜向和正交扰动进行大量的长期瞬态模拟，我们可以观察到频率的复杂时间演化。复杂性主要与瞬变过程中出现的相当远的跳跃有关。我们将这些跳跃解释为早期瞬态和中间项开始之间的过渡，中间项的出现时间足够长，以至于初始条件的细节影响消失。中间项导致渐近指数状态，并且具有比早期项长一个数量级的持续时间，这表明存在中间渐近性。由于在中间项扰动消失或爆破之后，中间项可以被认为是扰动生命中最可能的状态。长的结构瞬变可能与亚临界过渡壁流中通常观察到的点型有关。通过考虑一个大组的3D波在一个狭窄的波数范围内，我们叠加在一个有限的时间窗口，斜波和纵波随机延迟相对于一个正交波，这是应该维持其激烈的瞬态增长的斑点形成。我们表明，以这种方式，它是可以恢复的线性初始演变的模式，其特征在于存在纵向条纹。我们还确定了通道和尾流的渐近频率和相速波数谱。观察到的轻微色散可以部分解释光斑的向后和向前波前的不同传播速度。
英文摘要：
Sheared incompressible flows are usually considered non-dispersive media. As a consequence, the frequency evolution in transients has received much less attention than the wave energy density or growth factor. By carrying out a large number of long term transient simulations for longitudinal, oblique and orthogonal perturbations in the plane channel and wake flows, we could observe a complex time evolution of the frequency. The complexity is mainly associated to jumps which appear quite far along within the transients. We interpret these jumps as the transition between the early transient and the beginning of an intermediate term that reveals itself for times large enough for the influence of the fine details of the initial condition to disappear. The intermediate term leads to the asymptotic exponential state and has a duration one order of magnitude longer than the early term, which indicates the existence of an intermediate asymptotics. Since after the intermediate term perturbations die out or blowup, the mid-term can be considered as the most probable state in the perturbation life. Long structured transients can be related to the spot patterns commonly observed in subcritical transitional wall flows. By considering a large group of 3D waves in a narrow range of wavenumbers, we superposed them in a finite temporal window with oblique and longitudinal waves randomly delayed with respect to an orthogonal wave which is supposed to sustain the spot formation with its intense transient growth. We show that in this way it is possible to recover the linear initial evolution of the pattern characterized by the presence of longitudinal streaks. We also determined the asymptotic frequency and phase speed wavenumber spectra for the channel and wake flows. The mild dispersion observed can in part explain the different propagation speeds of the backward and forward fronts of the spot.
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