中文摘要：

在采用线性化的浅水方程组并假设地形坡度沿山脉走向不变的情况下，本文对具有底面地形坡度的沿岸山地俘获波作了研究，结果表明，当底面地形缓变时，可用摄动法得到沿岸山地俘获波的结构，此时零级近似为经典Kelvin波解，一级近似体现了Rossby变形半径内的底面地形对经典Kelvin波解的修正；直至一级近似，沿岸山地俘获波仍是非频散的。在沿岸处当底面地形坡度平缓时，沿岸山地俘获波表现为Kelvin波结构，此时扰动位势高度最大值出现在沿岸；而当底面地形坡度陡峭时，其表现为修正Kelvin波结构，此时扰动位势高度最大值偏离沿岸，在沿岸则扰动位势高度相对为低值，而在沿岸外侧则有位势高度的高值。在沿岸底面地形高度越高，地形坡度越大，扰动位势高度廓线的变化就越剧烈。

英文摘要：

Using the linear shallow water wave equations and supposing that the orographic slope was invariable along the mountain range orientation but was variable across it, the coastally trapped waves was researched in the presence of the bottom topographical gradient. The results show that. When the variation of bottom topography is not significant, the structure of eoastally trapped wave can be achieved by the perturbation method and the zeroth order approximation leads to classical Kelvin solution, the first order correction is due to the variations within the Rossby deformation radius. It is noted that the first order approximation to the coastally trapped wave is also non-dispersive. When the gradient of the bottom topography is gentle and the height of topography is not big, the coastally trapped waves show the feature of Kelvin wave, the maximum height of perturbed geopotential is found along the coastal barrier; when the gradient of the bottom topography is so steep and the height of topography is big, it shows the feature of modified Kelvin wave, the maximum height is found a little away from the coastal barrier, along the shore is the low value of perturbed geopotential, beyond the shore is the high value of perturbed geopotential. The higher of the bottom topography and the bigger of the bottom topographical gradient, the fiercer of the disturbance profile.