Some Considerations on the Laminar Stability of Time-Dependent Basic Flows
Some Considerations on the Laminar Stability of Time-Dependent Basic Flows
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关于时变基本流层流稳定性的一些思考
DOI：
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发表时间：
1961
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通讯作者：
S. Shen
中科院分区：
文献类型：
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作者：
S. Shen
作为不可压缩、平行但随时间变化的基流中无穷小扰动的稳定性判据，建议引入“瞬时稳定性”的概念，如果扰动的动能作为基流动能的一部分趋于减小，则瞬时稳定性将占上风。这样一个标准的意义进行了简要讨论。对于特殊的与时间有关的基本流，在任何时候都用相似的速度分布（除了振幅的变化）来描述，在无粘性极限下，只需要改变时间尺度，就可以把解基本上减少到定常情况下的解。扰动可以是横波型，也可以是涡旋型。结果表明，减速度的失稳影响很大，在正常情况下，这可能会掩盖速度剖面的影响。Fales（关于平板上的流动）和Coles（关于旋转圆柱体之间的流动）的观察结果被认为主要是由于减速。在有限的雷诺数，通常的程序计算的基础上的瞬时轮廓的稳定性解决方案进一步证明是有效的，只有非常缓慢的加速或减速。即使当解是可接受的，中性稳定性的条件a = 0也不能毫无保留地使用。为了正确计算瞬时稳定性，还描述了一个缓慢变化但更一般的轮廓的程序。
As a stability criterion for infinitesimal disturbances in an incompressible, parallel but time-dependent basic flow, it is proposed to introduce the concept of "momentary stability," which is said to prevail at the instant if the kinetic energy of the disturbances, as a fraction of the kinetic energy of the basic flow, tends to decrease. The significance of such a criterion is briefly discussed. For special time-dependent basic flows which are described by similar velocity profiles at all times (except for changes in amplitude), in the inviscid limit only a change of the time scale is needed to reduce the solution essentially to that for the steady case. The disturbances may be of either the transverse-wave or the longitudinal-vortices type. The result indicates a very strong destabilizing influence of deceleration, which is likely to overshadow tha t of the velocity profile under normal circumstances. The observations of Fales (on flow over the flat plate) and Coles (on flow between rotating cylinders) are believed to be largely due to the deceleration. At finite Reynolds numbers, the usual procedure of calculating the stability solution on the basis of the instantaneous profile is further shown to be valid only for extremely slow acceleration or deceleration. Even when the solution is acceptable, the condition a = 0 for neutral stability may not be used without reservation. To calculate momentary stability properly, a procedure for a slowly varying but more general profile is also described.