Comparison of the Characteristics of Internal Wave Propagation under Two Surface-Boundary Conditions in Continuously Density-Stratified Oceans

Zhang, H.-s.; He, L.; Zhang, Z.-h., and Zhang, Y., 2023. Comparison of the characteristics of internal wave propagation under two surface boundary-conditions in continuously density-stratified oceans. Journal of Coastal Research, 39(2), 303–316. Charlotte (North Carolina), ISSN 0749-0208. Complete theoretical solutions were developed for the propagation of internal waves (IWs) with small amplitudes in a continuously density-stratified ocean under the free surface-boundary condition and rigid lid assumption. Additionally, a numerical model was established for the propagation of IWs under the free surface-boundary condition. In the proposed model, the Euler equations are employed as the governing equations and are discretized with an improved SIMPLE algorithm. In waters with a constant depth, a comparison between the numerical and theoretical results proved the reasonability and accuracy of the proposed method. Additionally, the numerical results under the free surface-boundary condition were compared with those under the rigid lid assumption to analyse the differences between the calculated velocities and density fields. Herein, the influences of characteristic parameters, including the period and amplitude of the incident waves and the coefficient of density and the mode number on the velocity fields under the two surface-boundary conditions, are discussed thoroughly. In the waters with nonuniform varied depths, numerical simulations on the IWs propagation were performed under the two surface-boundary conditions. Differences between the calculated physical fields of IWs in front of and behind the submerged dike are discussed. The detailed analyses showed that differences exist between the calculation results under the two surface-boundary conditions. In particular, they were obvious for the cases with high mode number and variable topography. The results are significant considering the propagation mechanism of IWs under different surface-boundary conditions in a continuously density-stratified ocean.