The generation and evolution of turbulent spots in the open-channel flow are simulated numerically by using the Navier-Stokes equations. An effective numerical method with high accuracy and high resolution is developed. The fourth-order time splitting methods with high accuracy is proposed. Three-dimensional coupling difference methods are presented for the spatial discretization of the Poisson equation of pressure and Hemholtz equations of velocity, therefore, the fourth-order three-dimensional coupling central difference schemes are constituted. The fourth-order explicit upwind-biased compact difference schemes are designed to overcome the difficulty for the general higher-order central difference scheme which is inadaptable in the boundary neighborhood. The iterative algorithm and overall time marching is used to enhance efficiency. The method is applied in the numerical simulation of turbulent spots at various complex boundary conditions and flow domains. The generation and the developing process of turbulent spots are given, and the basic characteristics of turbulent spots are shown by simulating the evolution of the wall pulse in inclined open-channel flow. The generation and evolution of turbulent spots in the open-channel flow are simulated numerically by using the Navier-Stokes equations. An effective numerical method with high accuracy and high resolution is developed. The fourth-order time splitting methods with high accuracy is proposed. Three-dimensional coupling difference methods are presented for the spatial discretization of the Poisson equation of pressure and Hemholtz equations of velocity, therefore, the fourth-order three-dimensional coupling central difference schemes are composed. The fourth-order explicit upwind-biased compact difference schemes are designed to overcome the difficulty for the general higher-order central difference scheme which is inadaptable in the boundary neighborhood. The iterative algorithm and overall time marching is used to enhance efficiency. The method is applied in the numerical simulation of turbulent spots at various complex boundary conditions and flow domains. The generation and the dev eloping process of turbulent spots are given, and the basic characteristics of turbulent spots are shown by simulating the evolution of the wall pulse in inclined open-channel flow.