连续分层流体中垂直薄板的水动力特性  

HYDRODYNAMIC CHARACTERISTICS OF A VERTICAL THIN BARRIER IN A CONTINUOUSLY STRATIFIED FLUID

作　　者：尤云祥[1] 徐杰[2] 魏岗[1] 卢东强[2] 

机构地区：[1]上海交通大学船舶海洋与建筑工程学院,上海200030 [2]上海大学上海市应用数学与力学研究所,上海200072

出　　处：《力学学报》2007年第3期297-310,共14页Chinese Journal of Theoretical and Applied Mechanics

基　　金：国家自然科学基金(10572092;50323004);高等学校博士点基金资助项目

摘　　要：研究了在线性连续分层流体中水波与半潜式刚性垂直薄板相互作用的问题．在Boussinesq近似下,基于分离变量法,导出了具有自由面的平面前进波的色散关系,建立了半潜式刚性垂直薄板的反射与透射能量、水平波浪力的计算方法．对给定的频率,当它大于浮力频率时,流场中只有一种模态的平面前进波,当它小于浮力频率时,流场中有无数多个模态的平面前进波,并证明了对每一种模态的入射波,其它每个模态水波的反射与透射能量是相等的．对水面漂浮和座底半潜式薄板的反射与透射能量,以及作用在薄板上的水平波浪力进行了数值计算分析,表明了流体的线性连续分层效应对这些水动力的影响是不可忽视的．特别地,在入射波频率小于浮力频率时,与第1模态入射波的能量转化量及其对薄板产生的水平波浪力相比,其它模态入射波的能量转化量及其对薄板产生的水平波浪力都要大得多．This paper discusses the interaction of water waves with a vertical thin barrier in a continuously stratified fluid. Under the Boussinesq approximation, the dispersion relations are obtained for plane monochromatic waves in a continuously stratified fluid, and the theoretical solutions are obtained by the eigenfunction expansion for the reflection and transmission energies, as well as the exciting forces on the barrier due to incident waves. For a fixed frequency ω, when ω 〉 N （N being the buoyancy frequency）, there is only a monochromatic wave pattern with one mode. When ω 〈 N, there are monochromatic wave patterns with infinite modes, and it is shown that for the incident wave of each mode, the energies of the reflection and transmission waves of any other mode are equal. The reflection and transmission energies, as well as the exciting forces on the barrier due to incident waves are computed for two types of structures： a surface-piercing barrier and a bottom-touched one, respectively. The results indicate that the density stratification can have a significant effect on the hydrodynamic characteristics of the barrier over a wide range of frequencies. In particular, when ω 〈 N, the transferred energies and the exciting forces on the barrier due to incident waves of the first mode are much less than those due to incident waves of other modes.

关 键 词：连续分层流体 表面波模态 内波模态 刚性薄板 反射能量 透射能量 

分 类 号：O352.2[理学—流体力学]