A computer model is developed to study the turbulence development behind an NACA4 airfoil that is used in a wind tunnel study. The existing moving grid model developed for bridge aerodynamics is modified to consider the movement of airfoil and the corresponding effect on the flow development behind the airfoil. The computer model is based on finite difference procedure. The turbulence is modeled using large eddy simulation. The airfoil is moved with known oscillations and the flow developed at one length of the airfoil from the tail is monitored and reported for better understanding. For sinusoidal oscillations the computer model is very stable and the computed velocity as well as the turbulence spectrum is documented. The challenges in numerical issues when known turbulence spectrum is used for the rotation are discussed.