## 3 Results and Discussion  
### Aerodynamic Behavior  
The trailing edge point of the airfoil, which is taken as the reference point, is directly above the peak of wavy ground at the beginning. \(T\) is the time that is taken for the airfoil to move from one peak of wavy ground to the next. The variable t* = t/T is defined to describe the relative position between the airfoil and the wavy ground. The trailing edge point of the airfoil is directly above the peak at t* = 0 and t* = 1, hence the two moments are equivalent. Since the aerodynamics of the airfoil change periodically, one period is taken for analysis. The aerodynamic coefficients are the lift coefficient \(C_{I}\), the drag coefficient \(C_{d}\), and the moment coefficient \(C_{m}\). The point for calculating the moment is 1/4 chord length from the leading edge of the airfoil. The aerodynamic coefficients of different angles of attack in a period are shown in Figure 6. It can be seen that the trend of the aerodynamic coefficient at a 0\({}^{\circ}\) angle of attack is different from that at other angles of attack. The aerodynamic coefficients at other angles of attack have the same trend, similar to the sine curves. The lift coefficient increases with the increase in the angle of attack, but the rate of increase is decreasing, which is indicated by the smaller and smaller curve intervals in Figure 6. The lift coefficient curve no longer moves up from a 14\({}^{\circ}\) angle of attack, and the fluctuation amplitude increases obviously. The moment coefficient curve moves down with the increase in the angle of attack, and the fluctuation amplitude increases. The interval between the moment curves increases with the increase in the angle of attack, indicating that the rate of change is increasing. The time-averaged value and fluctuation amplitude of the drag coefficient change little in the range of 0-8\({}^{\circ}\) angles of attack. When the angle of attack exceeds 10\({}^{\circ}\), the drag coefficient increases rapidly, and the fluctuation amplitude also increases with the angle of attack. Figure 6: The change in aerodynamics in a period: (**a**) lift coefficient, (**b**) moment coefficient, (**c**) drag coefficient. The fluctuation amplitude of the aerodynamic coefficient is defined as \(A\) and \(R\). \(A\) is the absolute amplitude of the aerodynamic coefficient, and \(R\) is the relative amplitude of the aerodynamic coefficient. Their definitions are shown in Equations (3) and (4), respectively. \(C_{max}\) and \(C_{min}\) are the maximum and minimum aerodynamic coefficients in a period, respectively, and \(C_{time-averaged}\) is the time-averaged value of the aerodynamic coefficient in a period. The time-averaged value is the integral of the coefficient over time in one period divided by \(T\), as shown in Equation (5). \[A=C_{\max}-C_{\min}, \tag{3}\]  
\[R=\left(C_{\max}-C_{\min}\right)/C_{time-averaged}, \tag{4}\]  
\[C_{time-averaged}=\int\limits_{T}Cdt/T. \tag{5}\]  
Figure 7 presents the fluctuation amplitude of an aerodynamic coefficient varying with the angle of attack. The left longitudinal axis is the absolute amplitude, and the right longitudinal axis is the relative amplitude. At a 0\({}^{\circ}\) of attack, the absolute amplitude of the lift coefficient is large, while the time-averaged lift coefficient is small, resulting in the maximum relative amplitudes among all angles of attack. The absolute amplitude of the lift coefficient increases with the increase in angle of attack from 2\({}^{\circ}\), varies slightly within the range of 6\({}^{\circ}\) to 10\({}^{\circ}\), then increases rapidly from 12\({}^{\circ}\). The relative amplitude decreases from 2\({}^{\circ}\) to 10\({}^{\circ}\) and increases from 10\({}^{\circ}\) to 18\({}^{\circ}\), reaching the minimum of 10.8% at 10\({}^{\circ}\). The absolute amplitude of the drag coefficient is smallest when the angle of attack is 2\({}^{\circ}\)and gradually increases with angle of attack from 2\({}^{\circ}\).