Boundary layer turbulence in the ocean plays a crucial role in regional and global climate by influencing heat, momentum, and gas fluxes at the air-sea interface. Among these processes, Langmuir turbulence is one of the most significant, with spacing from several to dozens of meters. However, due to its relatively small scale, Langmuir turbulence cannot be directly resolved in mainstream ocean circulation models and its effects must be implemented by parameterization schemes. Unfortunately, most existing schemes are based on simplified physical models under ideal sea-states, making them less effective in complex surface forcing conditions, leading to large biases in representing the upper ocean dynamics in real-world scenarios.

  In this study, we use large eddy simulations to generate training data and develop a parameterization scheme for Langmuir turbulence in tropical cyclone conditions. This is achieved by leveraging neural network models that incorporate a deep integration of physical experience, ultimately aiming to establish a parameterization scheme of Reynolds stress, namely turbulence closure scheme. Our results reveal two major defects in turbulence closure schemes based on the eddy-viscosity assumption (or the Boussinesq assumption) in complex wind and wave conditions: one is the misalignment between Reynolds stress and Lagrangian shear, and the other is the excessive turbulence viscosity coefficients in the high-wind conditions. To address these issues, we categorize the data into three groups based on wind speed, the Reynolds stress-Lagrangian shear angle, and boundary layer thickness, and subsequently construct three neural network models to parameterize Reynolds stress for each category. The proposed neural network model outperforms traditional parameterization schemes by effectively remedying these defects. Our study provides a novel framework for the development of turbulence closure scheme with integrating physical prior information with statistical algorithms.