李景远，张庆河，陈同庆
AuthorsHTML:李景远，张庆河，陈同庆
AuthorsListE:Li Jingyuan，Zhang Qinghe，Chen Tongqing
AuthorsHTMLE:Li Jingyuan，Zhang Qinghe，Chen Tongqing
Unit:天津大学水利工程仿真与安全国家重点实验室，天津 300072
Unit_EngLish:State Key Laboratory of Hydraulic Engineering Simulation and Safety，Tianjin University，Tianjin 300072，China
Abstract_Chinese:针对内孤立波数值模拟研究，绝大多数****采用忽略密度跃层厚度的两层流体模型进行分析研究．从海洋实际物理环境来看，内孤立波形成的两大因素为海水稳定层化和存在扰动，且密度层化是内孤立波存在的必要条件，显然这种两层流体模型不能完全表征实际海洋环境下内孤立波的真实特性．为了还原真实海洋环境下的内孤立波，亟待开发一套考虑密度连续变化的内孤立波数值模型．基于雷诺时均Navier-Stokes方程，引入密度输运方程，将内孤立波理论解作为初始场，建立了密度连续变化内孤立波数值模型，并对其合理性进行了验证．结果表明，所建模型在不同上下层水深比和不同波高条件下，均能造出符合理论解与传播演变规律的内孤立波．通过引入有效势能概念，将有效势能为99.8%总势能所对应的波长作为有效波长，讨论了网格尺寸与有效波长的关系，推荐内孤立波模拟的水平向空间步长取有效波长的1/80，垂向空间步长取波高的1/15．基于所开发的模型，展开了密度连续变化模型与两层流体模型的对比研究，结果表明：两层流体模型忽略了实际海洋环境中密度跃层的厚度，会导致其高估实际海洋环境下内孤立波的传播速度、能量耗散及波高衰减．密度连续变化水体内孤立波模型能更好地反映实际海洋环境下内孤立波的各项特性．
Abstract_English:For the numerical simulation of internal solitary waves(ISWs)，most scholars use a two-layer fluid model that ignores the pycnocline thickness for analysis and research. From the actual physical environment of the ocean，the stable stratification of seawater and the existence of disturbance are two decisive factors for the formation of ISWs，and density stratification is a necessary condition for the existence of ISW. A two-layer fluid model cannot fully characterize the true characteristics of ISWs in the actual marine environment. To restore the ISWs in the real marine environment，it is urgent to develop a numerical model of ISWs that considers the continuous changes in density. A numerical model of ISW in continuously stratified fluid is developed. The governing equations are the Reynolds-averaged Navier-Stokes(RANS)equation and the density transport equation，and the numerical solution is initialized with an analytical solution of ISW. The verification of the model shows that the numerical model can generate ISWs consistent with an analytical solution and propagation characteristics for conditions of different water depth ratios between the upper and lower layers and different wave heights. By introducing the concept of the available potential energy，the effective wavelength is determined as the wavelength corresponding to the available potential energy of 99.8% of the total potential energy. The grid size relative to the effective wavelength is analyzed，and the horizontal grid is recommended to take one-eightieth of the effective length，while the vertical grid takes one-fifteenth of the ISW amplitude. The simulation results from the continuously stratified and two-layer fluid model are compared，and it is found that the latter may overestimate the propagation speed，energy dissipation，and wave height attenuation of the ISW because the pycnocline thickness is ignored. The ISW model in continuously stratified fluids can better reflect the characteristics of ISW in the actual ocean environment.
Keyword_Chinese:密度连续变化模型；内孤立波数值水池；网格敏感性分析；eKdV理论；两层流体模型
Keywords_English:continuously stratified model；internal solitary wave tank；grid independence；the eKdV equation；two-layer fluid model

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