本文發展數值模式求解二維時變的Navier-Stokes方程及完整的邊界條件，利用曲線座標系統模擬沙漣底床並探討波浪通過沙漣底床邊界層流之運動特性。數值模式與Marin (2004)的實驗結果比較相當一致。在確認模式的正確性後，本文以定性與定量的角度探討不同波浪條件與不同粗糙度下，沙漣底床附近流場特性，渦流的生成與消散，邊界層內水平速度運動特性。在相同沙漣底床下，隨波浪 數增加，渦流強度變化越急遽，波峰造成的順時針渦流強度大於波谷形成的逆時針渦流強度，而渦流中心移動軌跡也更趨於沙漣中心位置，顯示渦流影響範圍的擴大。在邊界層內水平速度部份，在相同沙漣底床下，回流隨波浪 數增加而影響變大，造成漣峯位置超射現象減弱，漣谷位置速度方向與邊界層外緣速度方向相反，此外在相同波浪條件下，沙漣尖銳度越大，底床速度受到回流抵銷的效果也越明顯。

A numerical scheme was developed to solve the unsteady, two-dimensional Navier-Stokes equations and complete boundary conditions for simulating the propagation of water waves over rigid rippled beds. A boundary-fitted coordinate system was used in this model. The accuracy of the numerical model was verified by comparing with the measurements of Marin (2004). Five numerical tests were carried out and discussed in qualitative and quantitative aspects, such as the velocity and vorticity fields, vortex shedding and characteristic of the horizontal velocity within the boundary layer. As the Ursell number increases under the same ripple geometry, the circulation changes rapidly and the negative vortex produced under the wave crest is stronger than the positive vortex formed under the wave trough. The horizontal velocity within boundary layer is counteracted by the reverse flow, and therefore the variation of velocity overshooting above the ripple crest is not obvious.

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