Wave reflection from a gently sloping beach
Wave reflection from a gently sloping beach
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DOI：
10.1017/s0022112090000040
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发表时间：
1990-05
影响因子：
3.7
通讯作者：
J. Miles
中科院分区：
文献类型：
--
作者：
J. Miles
频率为 ω 的斜入射重力波从海岸线坡度为 σ 且特征长度为 l 的缓坡海滩的线性反射由 σ [Lt ] 1 [Lt ] ω2l/g 确定。在浅水域中一致有效的渐近 (σ↓0)、无粘近似与 Keller (1958) 对于非浅水的几何光学近似相匹配。在浅水域中获得了剖面 h = σl[1−exp (−x/l)] 的精确解，并用于测试渐近近似。没有粘度意味着完美的反射。结合了小粘度和小毛细管现象的模型预测了固定的接触线和反射系数 |R| = exp [−πσ−2g−1(2νω3)½]，其中 ν 是运动粘度。这些预测与 Mahony 和 Pritchard (1980) 的实验结果定性一致。
The linear reflection of an obliquely incident gravity wave of frequency ω from a gently sloping beach of shoreline slope σ and characteristic length l is determined for σ [Lt ] 1 [Lt ] ω2l/g. An asymptotic (σ↓0), inviscid approximation that is uniformly valid in the shallow-water domain is matched to Keller's (1958) geometrical-optics approximation for non-shallow water. An exact solution is obtained for the profile h = σl[1−exp (−x/l)] in the shallow-water domain and used to test the asymptotic approximation. The absence of viscosity implies perfect reflection. A model that incorporates both small viscosity and small capillarity predicts a fixed contact line and the reflection coefficient |R| = exp [−πσ−2g−1(2νω3)½], where ν is the kinematic viscosity. These predictions are in qualitative agreement with the experimental results of Mahony & Pritchard (1980).