摘要
本文给出了一种计算二维弱非线波的方法,此方法将渐近匹配方法和差分求解络合起来,从而可以较快地求解弱非线性波的运动。利用这个方法求解了带槽岸壁的孤立波反射。
Because of the complexity and pecularity, the 2-Dimensional weak nonlinear wave-has been an interesting problem. Solitary wave, as a special kind of weak nonlinear wave has-been attracting many scholars. And many papers concerning the solitary wave are published (See Ref. [1] ). Sugimoto, N & Kakutani, T proposed the so-called edge-layer method (in fact, it is a kind of matched-asymptotic method). By this method they obtained the solution of solitary wave near the irregular costline, but the out solution did not appear.In this paper, the reflection of solitary wave at a costline with slot is consided. To solve this problem, the whole flow field in divided into two subfields: the out field ∑3 (far from the costline); the inner field .∑1 + ∑2 (near the costline). The inner fieldis is also divided into two subfields: edge-layer ∑2 and the slot ∑1.Due to the weak nonlinearity of problem under consideration, the govening equation in the out field is Boussinesq's equation. By using the matched-asymptotic method, the relation of out field and inne field is obtained. Introducing the function ψ, similar to Sugimoto, N & Kalu-tani, T's, then the eigenfunction expansion of ψ is got. And the eigenfunction expansion of velocity potential ψ in slot is also obtained. Because the pressure and velocity along the interface of ∑1 and ∑2 should be continuous, so the equations for the eigenfunction expansion coefficients of ψ and ψ are set up. The Boussinesq's equation is solved numerically by finite-difference approximation. An iterative process is adopted to match the inner and out field. As an example of computation, the reflection of a solitary wave is calculated. The wave elevation in out field and inner field, the pressure distribution on the costline at different time are plotted. The results show that the reflecting wave is almost the same as the incident wave. The only difference between them is thet there are tail waves behind the reflecting wave.
出处
《力学学报》
EI
CSCD
北大核心
1989年第2期161-167,共7页
Chinese Journal of Theoretical and Applied Mechanics
关键词
孤立波
反射
弱非线性波
岸壁
Weak nonlinear wave, matched-asymptotic method, Solitary wave.
