Numerical Simulation of Internal Solitary Wave in Continuously Stratified Fluid

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. © 2021, Editorial Board of Journal of Tianjin University(Science and Technology). All right reserved.