On the evolution of a solitary wave in a gradually varying channel
On the evolution of a solitary wave in a gradually varying channel
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渐变通道中孤立波的演化
DOI：
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发表时间：
1979
影响因子：
3.7
通讯作者：
J. Miles
中科院分区：
文献类型：
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作者：
P. Chang;W. Melville;J. Miles
通过实验和广义Korteweg-de Vries(KdV)方程的数值解，验证了宽度b渐变、水深均匀的航道中孤立波的绝热近似。对线性发散航道的计算结果表明，无因次波幅α与预测的Protob^{-FRAC{2}{3}}$符合得很好。线性收敛通道的实验和数值解表明，波的增长可以用α∞b−ç来很好地近似。结果表明，发散通道和收敛通道之间的差异是由于在广义KdV方程中选择空间变量作为慢变量所引起的非线性效应。测量和计算的剖面分别显示了汇流航道和分流航道中的高度和凹陷的预测‘搁板’。
The adiabatic approximation for a solitary wave in a channel of gradually varying breadth b and uniform depth is tested by experiment and by numerical solution of the generalized Korteweg-de Vries (KdV) equation. The results for a linearly diverging channel show good agreement with the prediction α (dimensionless wave amplitude)$propto b^{-frac{2}{3}}$. The experiments and numerical solutions for the linearly converging channel show that the wave growth is well approximated by α ∞ b−½. The discrepancy between the diverging and converging channels is shown to be due to nonlinear effects associated with the choice of the spatial variable as the slow variable in the generalized KdV equation. The measured and computed profiles display the predicted ‘shelves’ of elevation and depression in the converging and diverging channels, respectively.