A semi-nonlinear theoretical model for wind-generated waves in the marginal ice zone

The wind–wave generation process in the marginal ice zone (MIZ) is a component of the evolution of polar marine environments. To more accurately describe this physical phenomenon, we conducted research on the stability and transition theories for shear flows and proposed a semi-nonlinear theoretical model for wind-generated waves in the MIZ. This model decomposes the wind speed over the sea ice surface into a nonlinear velocity profile consisting of boundary layer flow and small disturbances, incorporates the ice layer as a viscoelastic layer, and incorporates the seawater component as a nonviscous fluid. A no-slip boundary condition was applied at the air–ice interface. We solved the coefficient matrix by employing varying coefficients and the kinematic boundary conditions at the air–ice interface to obtain the solution to the dispersion equation of the theoretical model. Additionally, we analyzed the impact of sea ice properties on the wind–wave generation process in the MIZ, identifying key factors that influence the generation of wind waves. Our model can provide technical support and theoretical foundations for the accurate prediction of wave levels in polar marginal ice zones.