對二度空間裡，前進於平緩坡度α底床上之週期性規則表面重力波，產生連續時空變形至碎波時，探討其碎波波高、碎波水深與底床坡度之相關性。在聯合代表波浪本質的波浪尖銳度ε，作為兩攝動參數展開下，本文引用已被印証之所得至的εα^2階的Eulerian系統之流速勢函數的解析解與被轉換至對應的Lagrangian系統的流場解析解，然後由波峯處水粒子之水平速度分量恰等於波速之碎波條件的引入，來描述波動由深至淺至碎波的時空連續演化，進而理論解析推導出碎波的特性並與前人之試驗結果比較印證，顯示出本文對碎波特性之闡述已提出一可行之後續研究途徑。

Because of shoaling, refraction, friction, and other effects, a surface-wave propagating on a gently sloping bottom of slope α will eventually break. In this paper, the analytical solution for velocity potential function is derived to perturbation's εα^2 order for the gentle sloping bottom and wave steepness in the Eulerian system. Then, the wave profile and the breaking wave characteristics are found by transforming the flow field into a Lagrangian system. By using the kinematic stability parameter, new theoretical breaking wave characteristics are derived. Thus, the linear theories of other scholars are extended to breaking waves. Furthermore, the relation between the breaker height, breaker depth and bottom slope is discussed and verified with the experimental study or empirical formula that other scholars show reasonable agreement. It demonstrates that there has been an approach of the follow-up study proposed for the depiction of breaking wave characteristics.