藉由外力作用產生水面之波動，除了一般直接擾動水面外，尚有自由液面承受不均勻的壓力分佈或是水中物體運動等造波之情形。本文將以明渠流經水中固定物體擾動自由水面之造波現象，討論波流互制機制。若考慮一二維淺水渠道其靜水深為H，水流以瞬時(t>0)流速U通過一浸沒於水中(或水流)之圓柱體時，會使自由液面產生波動，當福祿數( ，g為重力加速度)小於1時，稱之為亞臨界流況，其波動將分向上下游傳遞。本文為簡化分析流況，將固定上游之水深與臨近流速，計算有限時間內無黏性自由液面之波動。求解波浪的問題時，一般多假設不可壓縮非旋性流且滿足Laplace之勢能函數來求解，本研究以流函數模式模擬波流場，使用有限解析法滿足完全的非線性液面條件，並引用複數與代數內插格網生成矩陣疊代計算時間精確解，探討圓柱體與自由液面互制之現象。此方法將作為後續考量黏性旋流之比較參考用。

關鍵字：複數與代數內插格網、波流互制、自由液面、福祿數

　　Water-Wave motion generated by external force can be often set up from direct disturbing the free surface, or applying the uneven pressure distribution on the free surface or the induced flow motion by moving sulmerged bodies near the free surface. In the present study, I attempt to investigate the flow-wave interaction an approaching flow passing through a fixed submerged body in the water channel. Consider in the undisturbed water depth of H a uniform stream of velocity U passing a submerged cincular cylindrical body of on the bottom or in the water to generate waves on the free surface. When the Froude number being(defined as for the gravitational constant g)of flow is less than 1, the waves tends to propagate in both upstream and downstream directions. To simplify formulation for the present problems, I fixed water depth and approaching flow speed at upstream to calculate the inviscid free-surface wave profiles at various Fr’s. As is different from the traditional way by means of a potential function solution under the incompressible and rotational, assumption faplcian formulation, we apply, instead, the stream function modeling which is easier for further extension to the more general viscous rotational flow problems. These are simulations the time-accurate wave-flow field by the Finite analytic discretization, complete satisfication of the nonlinean free-surface boundary conditions, complex function and algebraic interpolation grid and scheme in all with this study of ciscular cylinder and free-surface wave interaction calculation to include the viscous effects in the general motational flow by this method can be research performed as well in the continued.

Keyword: complex function and algebraic interpolation grid, flow-wave interaction, free-surface, Froude number

張志華(1997)，「孤立波與結構物在黏性流體中互制作用之研究」，博士論文，國立成功大學水利及海洋工程研究所，台南。

張志華(1992)，「孤立波與水工結構物互制的動態分析」，碩士論文，國立成功大學水利及海洋工程研究所，台南。

張志華、唐啟釗(1994)，「孤立波與近岸台階陸棚作用之數值分析」，中國土木水利工程學刊，第六卷，第三期，第309-319頁。

李自強(2005)，「孤立波造波之研究」，碩士論文，國立成功大學水利及海洋工程研究所，台南。

楊百皓(1997)，「潛沒平面射流與自由或固體界面初始互制分析」，碩士論文，國立成功大學水利及海洋工程研究所，台南。

Chang, J. H., and C. J. Tang(1995) “Numerical Analyses on the Damping of Solitary Wave” High-Performance Computing ASIA Electronic Proceedings, EN122, Taipei, Taiwan, R.O.C. .

Frederic, D., and Christodulides, P.(1991) “Ideal jets falling under gravity,” Physics of Fluids, Vol. 3, No.7, pp. 1711-1717.

Huang, N., E.(1970) “Mass Transport Induced by Wave Motion”, J. Marine Research, Vol.28, No.1, p.p.35-49.

Kim,Tae In(1984) “Mass Transport Induced by Water Wave Flumes”, P.H.D.

Longuet-Higgins, M. H.(1953) “Mass Transport in Water Waves”, Philosophical Transaction of the Royal Society of London, A245, p.p.535-581.

Mei,C.C.(1986)“Radiation of Solitions by Slender Bodies Advancing in a Shallow Channel” J. Fluid Mech, Vol. 162, pp. 53-67.

Seabra-Santos,F. J., D. P. Renouard, and A. M. Temperville(1987) “Numerical and Experimental Study of the Transformation of a Solitary Wave over a Shelf or Isolated Obstacle” J. Fluid Mech., Vol. 118, pp. 285-304.

Timman, R., A. J. Hermans, and G. C. Hsiao(1985) Water Wave and Ship Hydrodynamics Martinus Nijhoff Publishers(page 5).

Vanden-Broeck, J.-M., and Keller, J. B. (1982) “Jets rising and falling under gravity,” Journal of Mechanics, Vol. 124, pp. 335-345.

Wehausen, J. V., and E. V. Laitone(1960) “Surface wave. In Handbuch der Physik
(Ellgüe, S., ed.)”,Vol.9, Strömungsmeehannik III. Berlin: Springer.