The flow generated by a biorthogonally stretched membrane below a steadily rotating flow at infinity is examined. The flow's velocity field is shown to be an exact, self-similar solution of the fully three-dimensional Navier-Stokes equations with the solution governed by a set of four ordinary differential equations. It is demonstrated that dual solutions exist when the membrane is stretched in both directions (except in the radially symmetric case), as well as for a range of parameters where the membrane is stretched in one direction and allowed to shrink in the other. For stretching rates close to the radially stretched symmetric case, four solutions exist, including one which has a large wall-jet velocity profile close to the membrane. The linear stability of each solution is also examined, and it is found that only a single solution is stable (where one exists) for a given stretching and rotation rate.

中文翻译：

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均匀旋转流体下弹性膜的双正交拉伸

研究了由双正交拉伸膜在无限远的稳定旋转流下方产生的流。流的速度场显示为完全三维纳维-斯托克斯方程的精确自相似解，该解由一组四个常微分方程控制。结果表明，当膜在两个方向上拉伸时（径向对称情况除外），以及膜在一个方向上拉伸并允许在另一个方向上收缩的一系列参数，都存在双重解。对于接近径向拉伸对称情况的拉伸速率，存在四种解决方案，其中一种具有靠近膜的大壁射流速度分布。还检查了每个解的线性稳定性，