To investigate the effect of wave-induced mixing on the upper ocean structure, especially under typhoon conditions, an ocean-wave coupled model is used in this study. Two physical processes, wave-induced turbulence mixing and wave transport flux residue, are introduced. We select tropical cyclone (TC) Nepartak in the Northwest Pacific ocean as a TC example. The results show that during the TC period, the wave-induced turbulence mixing effectively increases the cooling area and cooling amplitude of the sea surface temperature (SST). The wave transport flux residue plays a positive role in reproducing the distribution of the SST cooling area. From the intercomparisons among experiments, it is also found that the wave-induced turbulence mixing has an important effect on the formation of mixed layer depth (MLD). The simulated maximum MLD is increased to 54 m and is only 1 m less than the observed value. The wave transport flux residue shows a dominant role in the mixed layer temperature (MLT) changing. The mean error of the MLT is reduced by 0.19 °C compared with the control experiment without wave mixing effects. The study shows that the effect of wave mixing should be included in the upper ocean structure modeling.

Significant wave height (SWH) prediction plays an important role in marine engineering areas such as fishery, exploration, power generation, and ocean transportation. For long-term forecasting of a specific location, classical numerical model wave height forecasting methods often require detailed climatic data and incur considerable calculation costs, which are often impractical in emergencies. In addition, how to capture and use the dynamic correlation between multiple variables is also a major research challenge for multivariate SWH prediction. To explore a new method for predicting SWH, this paper proposes a deep neural network model for multivariate time series SWH prediction—namely, CLTS-Net. In this study, the sea surface wind and wave height in the ERA5 dataset of the relevant points P1, P2, and P3 from 2011 to 2018 were used as input information to train the model and evaluate the model’s SWH prediction performance. The results show that the correlation coefficients (R) of CLTS-Net are 0.99 and 0.99, respectively, in the 24 h and 48 h SWH forecasts at point P1 along the coast. Compared with the current mainstream artificial intelligence-based SWH solutions, it is much higher than ANN (0.79, 0.70), RNN (0.82, 0.83), LSTM (0.93, 0.91), and Bi-LSTM (0.95, 0.94). Point P3 is located in the deep sea. In the 24 h and 48 h SWH forecasts, the R of CLTS-Net is 0.97 and 0.98, respectively, which are much higher than ANN (0.71, 0.72), RNN (0.85, 0.78), LSTM (0.85, 0.78), and Bi-LSTM (0.93, 0.93). Especially in the 72 h SWH forecast, when other methods have too large errors and have lost their practical application value, the R of CLTS-Net at P1, P2, and P3 can still reach 0.81, 0.71, and 0.98. The results also show that CLTS-Net can capture the short-term and long-term dependencies of data, so as to accurately predict long-term SWH, and has wide applicability in different sea areas.

A nonlinear Schrödinger equation (NLSE) describing the evolution of interfacial waves in a gravitationally stable, inviscid, incompressible, and irrotational two-layer fluid with arbitrary constant layer depths is derived using the multiple scale analysis method. The modulational instability (MI) of the interfacial waves is then analyzed using this NLSE. It is shown that the unstable region shrinks as the density ratio of the two layers increases and as each layer gets thinner. A requirement for unstable waves is that both the upper and lower layers are thicker than the critical depths for those layers. The critical depth of each layer as a function of the density ratio of two layers is obtained by curve fitting and used as a criterion for MI. Moreover, nine cases with various upper- and lower-layer depths are investigated. The relationships of the dark soliton to modulational stability and the bright soliton to MI are discussed in each case. In the unstable regions of the nine cases, it is found that the steepness of the perturbed interface amplitude increases, and the perturbed interface elevation decays more rapidly as the depth of each layer increases. Both the height and the steepness of the perturbed interface elevation increase with increasing density ratio of the two layers.

Both surface and internal freak waves can be regarded as special interfacial waves. Using a two-layer model, we investigated the influence of linear shear flow (LSF) in the upper layer on interfacial waves. Specially, the model was designed to study the effects of wind shear on surface freak waves and LSF on internal freak waves. Based on the model, a nonlinear Schrödinger equation was derived to describe interfacial-wave evolution. The unstable regions where interfacial freak waves occur were identified via analysis of modulational instability. According to these unstable regions, the elevation of interfacial freak waves was studied using the Peregrine Breather solution. It is found that the steepnesses and heights of surface freak waves decrease under positive vorticity and increase under negative vorticity during supercritical up-flow. In contrast, they increase under positive vorticity and decrease under negative vorticity during supercritical down-flow. The reason is that negative vorticity which has a convergent effect on the waves is easy to excite surface freak waves under supercritical up-flow, whereas positive vorticity has a convergent effect under supercritical down-flow. In addition, the steepnesses and heights of internal freak waves decrease under positive vorticity and uniform down-flow, whereas increase under negative vorticity and uniform up-flow. The convergent effect of negative vorticity and uniform up-flow promote the generation of internal freak waves.