This paper considers the linear stability of confined planar impinging jet flow of a non-Newtonian inelastic fluid. The rheology is shear rate dependent with asymptotic Newtonian behavior in the zero shear limit, and the analysis examines both shear thinning and shear thickening behavior. The planar configuration is such that the width of the inlet nozzle is smaller than the distance from the jet exit to the impinging surface, giving an aspect ratio e = 8 for which two-dimensional time dependent flow is readily manifest. For values of the power-law index n in the range 0.4≤n≤1.1, the bi-global linear stability of the laminar flow is analyzed for Newtonian Reynolds numbers Re ≲200. The calculations show that for certain values of n, including the Newtonian value n = 1, the steady flow exhibits multiplicity leading to hysteresis in the primary separation vortex reattachment point and a consequent jump in stability behavior. Even in the absence of hysteresis, relatively small changes in viscosity significant...

中文翻译：

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平面非牛顿约束层流冲击射流：滞后、线性稳定性和周期性流动

本文考虑了非牛顿非弹性流体受限平面撞击射流的线性稳定性。流变学与剪切速率相关，在零剪切极限下具有渐近牛顿行为，并且分析检查了剪切变稀和剪切增稠行为。平面配置是这样的，入口喷嘴的宽度小于从射流出口到撞击表面的距离，给出纵横比 e = 8，二维时间相关流动很容易表现出来。对于幂律指数 n 在 0.4≤n≤1.1 范围内的值，层流的双全局线性稳定性被分析为牛顿雷诺数 Re ≲200。计算表明，对于某些 n 值，包括牛顿值 n = 1，稳定流表现出多重性，导致初级分离涡流重新附着点的滞后和随之而来的稳定性行为的跳跃。即使没有滞后现象，相对较小的粘度变化也会显着...