The approach to self-similarity of the solutions of the shallow-water equations representing gravity-current releases
The approach to self-similarity of the solutions of the shallow-water equations representing gravity-current releases
复制标题
代表重力流释放的浅水方程解的自相似性方法
DOI：
10.1017/s0022112085001975
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发表时间：
1985
影响因子：
3.7
通讯作者：
J. Rottman
中科院分区：
文献类型：
--
作者：
R. E. Grundy;J. Rottman
从平面几何和轴对称几何两个方面研究了描述等体积重力流运动的浅水方程的已知相似解。结果表明，这些解对相应的对称小扰动是线性稳定的，它们构成了初值问题解的大时间极限。此外，分析表明，相似解是以振荡方式逼近的。用有限差分法数值求解了两个初值问题，并将每种情况下的相似解方法与解析预测进行了比较。
Known similarity solutions of the shallow-water equations representing the motion of constant-volume gravity currents are studied in both plane and axisymmetric geometries. It is found that these solutions are linearly stable to small correspondingly symmetric perturbations and that they constitute the large-time limits of the solutions of the initial-value problem. Furthermore, the analysis reveals that the similarity solution is approached in an oscillatory manner. Two initial-value problems are solved numerically using finite differences and in each case the approach to the similarity solution is compared with the analytic predictions.