Self-similar gravity currents with variable inflow revisited: plane currents
Self-similar gravity currents with variable inflow revisited: plane currents
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重温可变流入的自相似重力流：平面流
DOI：
10.1017/s0022112094003241
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发表时间：
1994
影响因子：
3.7
通讯作者：
C. Vigo
中科院分区：
文献类型：
--
作者：
J. Gratton;C. Vigo
我们使用浅水理论来研究自相似的重力流，描述了一个较轻的环境流体下面的重流体的入侵。我们详细地考虑了平面对称流的情况，这种流是由具有可变流入量的源产生的，使得侵入流体的体积根据tα型幂律随时间变化。通过von Kármán类型的边界条件来考虑周围流体的阻力，该边界条件取决于作为流体密度比的函数的参数β。流动的特征是β、α和靠近源的弗劳德数[Fscr ]0。我们发现四种自相似的解决方案：亚临界连续解决方案（I型），连续解决方案与超临界-亚临界过渡（II型），不连续的解决方案（III型），有一个水力跳跃，和不连续的解决方案，有水力跳跃和亚临界-超临界过渡（IV型）。电流在靠近前沿的地方总是亚临界的，但在靠近源的地方，I型电流是亚临界的（[Fscr ]0 < 1），II、III和IV型电流是超临界的（[Fscr ]0 > 1）。其他作者已经发现了I型解，但II、III和IV型电流是新的。我们发现这些解决方案存在的参数的区间，并讨论其性质。对于定容流，当β > 2时，在原点附近有一个“干”区，得到任意β的I型解。对于稳定入流，如果[Fscr ]0足够大，则发现O < β < ∞时的I型电流和β时的II型和III型电流。
We use shallow-water theory to study the self-similar gravity currents that describe the intrusion of a heavy fluid below a lighter ambient fluid. We consider in detail the case of currents with planar symmetry produced by a source with variable inflow, such that the volume of the intruding fluid varies in time according to a power law of the type tα. The resistance of the ambient fluid is taken into account by a boundary condition of the von Kármán type, that depends on a parameter β that is a function of the density ratio of the fluids. The flow is characterized by β, α, and the Froude number [Fscr ]0 near the source. We find four kinds of self-similar solutions: subcritical continuous solutions (Type I), continuous solutions with a supercritical-subcritical transition (Type II), discontinuous solutions (Type III) that have a hydraulic jump, and discontinuous solutions having hydraulic jumps and a subcritical-supercritical transition (Type IV). The current is always subcritical near the front, but near the source it is subcritical ([Fscr ]0 < 1) for Type I currents, and supercritical ([Fscr ]0 > 1) for Types II, III, and IV. Type I solutions have already been found by other authors, but Type II, III, and IV currents are novel. We find the intervals of parameters for which these solutions exist, and discuss their properties. For constant-volume currents one obtains Type I solutions for any β that, when β > 2, have a ‘dry’ region near the origin. For steady inflow one finds Type I currents for O < β < ∞ and Type II and III Currents for and β, if [Fscr ]0 is sufficiently large.