## 1 Introduction
[PERSON] and [PERSON] [13; 14] applied the lifting line theory to study the ground effect of a three-dimensional wing near the free surface. Their results showed that the deformation of the free surface was significant at a low velocity, and that the lift coefficient fluctuates dramatically; at a high velocity, the deformation of the free surface could be neglected so that the free surface could be represented by a rigid wall. [PERSON] [15] developed the iterative boundary element method to investigate the effects of free surface both on 2-D airfoils and 3-D wings moving over a free surface. He concluded that the free surface would affect the aerodynamic characteristics of the airfoil and wing, and the Kelvin wave would also be generated on the surface. These researchers applied free surface boundary conditions in the study of ground effect, which is closer to the real scene, and made an important contribution to research into the ground effect. The sea is not calm most of the time, and there are always waves on the surface. The waves make the ground effect of WIG crafts more complicated. Therefore, some scholars have recently conducted research on the ground effect under wavy ground conditions. [PERSON] [16] studied the aerodynamics of the airfoil NACA 6409 moving over wavy ground by numerically solving the Euler equations; his results indicated that the aerodynamics of the airfoil became sensitive if the wave number or amplitude of the wavy ground was increased or if the proximity of the airfoil to the ground was lowered. [PERSON] [17] simulated a WIG craft flying at \(\alpha=3\)deg and \(\alpha=9\)deg over wavy ground employing compressible RANS equations and the Spalart-Allmaras turbulence model. [PERSON] [18] investigated the aerodynamics of a transonic airfoil above wavy ground and analyzed the change in aerodynamic characteristics caused by the interaction between shock waves and wavy ground. [PERSON] [19] employed a potential flow-based discrete vortex method to investigate heaving airfoils for a wing in ground effect over a rigid wavy surface and over progressive water waves, considering that a WIG craft may experience a periodic having motion induced by the presence of water waves. [PERSON] [20] conducted an experimental investigation on the aerodynamics and flow field of a NACA 0015 airfoil over a wavy ground. On this basis, [PERSON] [21] extended the airfoil experiment over a sinusoidal wavy ground to the investigation of the effect of a trailing-edge flap on the aerodynamics and flow field of a NACA 0015 airfoil. Most of the above scholars used rigid wavy ground instead of water waves to study the airfoil moving over waves. [PERSON] [22] applied the volume of fluid (VOF) method to numerically simulate the water wave to study the aerodynamics of the airfoil moving over waves. It should be noted that there is a strong coupling effect between the surface waves and the air near the water-air surface. Besides this, the spumes and bubbles generated as a result of wave breaking may affect the aerodynamics of the airfoil. [PERSON] [23] performed experiments to investigate the details of the momentum flux partitioning between turbulent, wave-coherent, and viscous stresses, and he [24] also developed vorticity equations to interpret the experimental data of fluid flow over wind-generated surface waves. [PERSON] [25] studied two-dimensional airflow velocity fields above the air-water interface and found a reversed, upwind sheltering effect near the water surface. [PERSON] [26] investigated the coupling processes between surface gravity waves and adjacent winds and currents in turbulent [PERSON] layers. [PERSON] [27] tried to reproduce the observed airflow dynamics induced by strongly forced wind waves through large-eddy simulation. Due to the strong coupling effect between the wave surface and the air, there are certain limitations in using wavy ground to simulate waves.