Using the idea of general resonant triad of the hydrodynamic stability, the theoretical models for coherent structures in the wall region of a turbulent boundary layer is proposed. The interaction between coherent structures in the wall region of a turbulent boundary layer is studied by combining the compact finite differences of high numerical accuracy and the Fourier spectral hybrid method for solving the three dimensional Navier Stokes equations. In this method, the third order mixed explicit implicit scheme is employed for the time integration. The fifth order upwind compact finite difference schemes for the nonlinear convection terms in the physical space, and the sixth order center compact schemes for the derivatives in spectral space are descried, respectively. The fourth order compact schemes satisfied by the velocities and pressure in spectral space is derived. As an application, the method is implemented to the wall region of a turbulent boundary to study the interaction between coherent structures. It is found that the numerical results are satisfactory. The idea of ​​general resonant triad of the hydrodynamic stability, the theoretical models for coherent structures in the wall region of a turbulent boundary layer is proposed. The interaction between coherent structures in the wall region of a turbulent boundary layer is studied by combining the compact finite differences of high numerical accuracy and the Fourier spectral hybrid method for solving the three dimensional Navier Stokes equations. In this method, the third order mixed explicit implicit scheme is employed for the time integration. The fifth order upwind compact finite difference schemes for the nonlinear convection terms in the physical space, and the sixth order center compact schemes for the derivatives in spectral space are descried, respectively. The fourth order compact schemes satisfied by the velocities and pressure in spectral space is derived. As an application, the method is implemented to the wall region of a turbulent boundary to study the interaction between coherent structures. It is found that the numerical results are satisfactory.