The generation and evolution of the turbulent spots are simulated by using Navier-Stokes equations in flat-plate boundary layer.An effective numerical approach for simulating the turbulent spot has been 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,and the fourth-order three-dimensional coupling central difference schemes are constituted.The fourth-order explicit upwind-biased compact difference schemes are used to overcome the difficulty of not adapting to boundary neighborhood for the general fourth-order central difference schemes.Different boundary conditions are processed carefully to retain the accuracy and stability.This approach is applied in the numerical investigation of the turbulent spots in overall flow domains including boundary neighborhood,and is used to simulate the evolutions of the turbulent spots in the flat-plate boundary layer flow.The results show the generation and evolution process and basic characteristics of the turbulent spots.