Nonmodal analysis typically uses square-integrated quantities to characterize amplification of disturbances. However, such measures may be misleading in viscoelastic fluids, where polymer stresses can be strongly amplified over a small region. Here, we show that when using a localized measure of disturbance amplification, spanwise-constant polymer-stress fluctuations can be more amplified than streamwise-constant polymer-stress fluctuations, which is the opposite of what is observed when a square-integrated measure of disturbance amplification is used. To demonstrate this, we consider a model problem involving two-dimensional pressure-driven inertialess channel flow of an Oldroyd-B fluid subject to a localized time-periodic body force. Nonmodal analysis of the linearized governing equations is performed using recently developed well-conditioned spectral methods that are suitable for resolving sharp stress gradients. It is found that polymer-stress fluctuations can be amplified by an order of magnitude while there is only negligible amplification of velocity fluctuations. The large stress amplification arises from the continuous spectrum of the linearized problem, and may put the flow into a regime where nonlinear terms are no longer negligible, thereby triggering a transition to elastic turbulence. The results suggest an alternate mechanism that may be useful for understanding recent experimental observations of elastic turbulence in microchannel flows of viscoelastic fluids.

非模态分析通常使用平方积分的量来表征干扰的放大。但是，这样的措施在粘弹性流体中可能会产生误导，在这种情况下，聚合物应力会在很小的区域内强烈放大。在这里，我们表明，当使用干扰放大的局部度量时，跨度恒定的聚合物应力波动要比沿流恒定的聚合物应力波动更大，这与对干扰进行平方积分度量时所观察到的相反使用扩增。为了证明这一点，我们考虑一个模型问题，该问题涉及受局部时间周期体力作用的Oldroyd-B流体的二维压力驱动无惯性通道流。线性化控制方程的非模态分析是使用最近开发的条件良好的光谱方法进行的，该方法适合解决尖锐的应力梯度。发现聚合物应力波动可以放大一个数量级，而速度波动的放大可以忽略不计。较大的应力放大来自线性化问题的连续频谱，并且可能使流量进入一种非线性项不再可忽略的状态，从而触发了向弹性湍流的过渡。结果提示了另一种机制，可能有助于理解粘弹性流体微通道流动中弹性湍流的最新实验观察。发现聚合物应力波动可以放大一个数量级，而速度波动的放大可以忽略不计。较大的应力放大来自线性化问题的连续频谱，并且可能使流量进入一个非线性项不再可忽略的状态，从而触发了向弹性湍流的过渡。结果提示了另一种机制，可能有助于理解粘弹性流体微通道流动中弹性湍流的最新实验观察。发现聚合物应力波动可以放大一个数量级，而速度波动的放大可以忽略不计。较大的应力放大来自线性化问题的连续频谱，并且可能使流量进入一个非线性项不再可忽略的状态，从而触发了向弹性湍流的过渡。结果提示了另一种机制，可能有助于理解粘弹性流体微通道流动中弹性湍流的最新实验观察。并可能使流量进入一个非线性项不再可忽略的状态，从而触发向弹性湍流的过渡。结果提示了另一种机制，可能有助于理解粘弹性流体微通道流动中弹性湍流的最新实验观察。并可能使流量进入一个非线性项不再可忽略的状态，从而触发向弹性湍流的过渡。结果提示了另一种机制，可能有助于理解粘弹性流体微通道流动中弹性湍流的最新实验观察。