Surface wrinkling of a channelized flow
Surface wrinkling of a channelized flow
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通道化流的表面起皱
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
J. C. Miller
中科院分区：
文献类型：
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作者：
A. Slim;N. Balmforth;R. Craster;J. C. Miller
本文考虑一个倾斜的等截面矩形管道输送粘性流体，管道外覆盖一个弹性板。流体由Stokes方程描述，板由Föppl-von Kármán方程描述。该方程允许一个平衡解，其中板是平的，流体由于重力在下面流动。这种底部流动在板上引起变化的牵引力，由于相关的面内剪切，这可能导致面外屈曲。线性稳定性分析表明，屈曲发生足够薄的板在陡坡和深槽。最不稳定的模式采取对称或反对称的下坡方向的人字形图案的形式，以基流的平均速度的一小部分向下游行进。一个类似的分析表明，如果弹性板被一个非常粘滞的流体薄蒙皮代替，也会发生类似的屈曲。我们的描述提供了一个简单的模型，形成绳状pahoehoe熔岩。
We consider an inclined rectangular duct of constant cross-section conveying viscous fluid and covered by an elastic plate. The fluid is described by the Stokes equations and the plate by the Föppl–von Kármán equations. The equations admit an equilibrium solution in which the plate is flat and fluid flows underneath due to gravity. This base flow induces a varying traction across the plate, which can lead to out-of-plane buckling due to the associated in-plane shear. Linear stability analysis demonstrates that buckling occurs for sufficiently thin plates on steep slopes and deep channels. The most unstable modes take the form of either symmetric or antisymmetric downslope-directed chevron patterns that travel downstream at a fraction of the average speed of the base flow. An analogous analysis shows that similar buckling also occurs if the elastic plate is replaced by a thin skin of very viscous fluid. Our description provides a simple model for the formation of ropy pahoehoe lava.