Interface depth used in a two-layer model of nonlinear internal waves

Abstract

A two-layer model includes three parameters: interface depth h ₁, upper layer density $\rho_{1}$, and lower layer density $\rho_{2}$. Many theoretical and laboratorial studies of internal waves, as well as most numerical models, are based on the two-layer assumption. However, these three parameters cannot be directly measured because a pycnocline in the real ocean has finite thickness, and the densities in both the mixed layer and the deep ocean are not constant. In the present study, seven different methods are used to determine the interface depth of the two-layer model and compared with the depth of maximum vertical displacement: the depth of maximum buoyancy frequency (Ν _max), the depth where the first mode eigenfunction has its maximum (Φ_max), the depth where the lowest mode temperature empirical orthogonal function has its maximum, the depth where either the two-layer Korteweg–de Vries (KdV) or Benjamin–Ono equation has closest coefficients with their continuously stratified counterparts, and the same KdV approach with stratification replaced by two idealized distributions. The multi-ship measurement conducted near the Luzon Strait is used for deep ocean comparison, and two measurements conducted in the east of Dongsha Atoll are used for shallow water comparison. The results show that in the deep ocean, the KdV approach with idealized type I stratification gives the interface closest to the depth of maximum vertical displacement. In shallow waters, the KdV approach agrees with the measurement best.