Session: 06-16-01 Wave Mechanics, Modeling and Wave Effects - I

Submission Number: 175557

Incorporating Nonlinear Interactions in Lagrangian-Based Real-Time Ocean Wave Prediction 

One of the central challenges in marine science and ocean engineering is the real-time prediction of the ocean surface wave field, a problem of fundamental and practical importance. Reliable wave forecasts play a critical role in the safe operation of surface vessels, the optimization of ocean wave energy conversion systems, and the design and control of marine structures such as offshore floating wind turbines (FOWTs). In particular, the optimal control and load mitigation strategies for floating wind turbines depend heavily on accurate short-term forecasts of the instantaneous ocean surface elevation. Consequently, the ability to understand and predict the instantaneous nonlinear state of ocean waves is essential, especially under strongly nonlinear sea conditions characterized by large wave steepness.

The Lagrangian approach has proven to be an effective tool for representing nonlinear surface gravity waves. Compared to Eulerian methods, the Lagrangian formulation offers improved computational efficiency at high orders of nonlinearity. The Lagrangian approach is especially advantageous for accurately describing strongly nonlinear wave motions and capturing the statistical characteristics of random wave fields with reduced computational cost.

Based on these advantageous aspects, several studies have proposed phase-resolved real-time wave prediction algorithms using nonlinear Lagrangian-based models that incorporate essential nonlinear effects. Among these, the Improved Choppy Wave Model (ICWM) has shown that retaining selected nonlinear properties, such as Stokes drift and mean vertical displacement, can improve both computational efficiency and predictive accuracy. Importantly, the redefinition of Lagrangian reference particles mitigates phase errors that arise from the nonlinear dispersion relation, thus enabling longer and more stable prediction horizons. Recent efforts have further confirmed that this approach achieves accurate and efficient real-time predictions across a range of sea conditions. Validation against dedicated tank-scale experiments has shown that incorporating nonlinear interaction terms in the improved models yields a more accurate representation of surface elevations in both unidirectional and directional sea states.

More recently, an explicit Complementary Improved Choppy Wave Model (CICWM) has been developed to extend the ICWM framework by considering all combinations between aligned and non-aligned wave vector components in three-dimensional random wave systems. This model successfully reproduces free-surface elevations measured in the tank-scale experiments, achieving higher predictive accuracy than earlier formulations. However, previous implementations did not fully incorporate the horizontal interaction terms, as these were considered numerically unstable and inconsistent with second-order Eulerian solutions. This omission, while stabilizing computations, limited the model’s ability to provide better description of nonlinear wave motions.

In the present study, we extend the CICWM framework by fully including the horizontal interaction terms in the Lagrangian description to achieve a more complete nonlinear representation of sea states. This development enables a more physically consistent treatment of nonlinear coupling effects, leading to improved predictions of energy transfer. We investigate the influence of these nonlinear terms on the accuracy and stability of real-time phase-resolved ocean wave prediction under a range of realistic sea conditions. Results demonstrate that incorporating full nonlinear interactions significantly enhances prediction performance in severe sea states characterized by high steepness, confirming that nonlinear dynamics play a crucial role in short-term deterministic wave forecasting. The findings highlight the potential of advanced Lagrangian-based models to support real-time operational forecasting.

Presenting Author: In-Chul Kim Pukyong National University

Presenting Author Biography: Dr. In-Chul Kim is an Assistant Professor in the Department of Ocean Engineering at Pukyong National University, Busan, South Korea.

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