The nonlinear evolution process of new vortex structures at the late-stage of the transition, including the 3-D spatial structure of barrel-shaped vortex and "dark spots" structure observed by experiment research, has been confirmed by our computational results. The formation mechanisms of these structures have been explored. It is revealed that the new vortex structures, the ring-like vortex chain and induced disturbance velocities play a dominant role in the generation of turbulent spots. boundary layers, transition, barrel-shaped vortex, turbulent spots, direct numerical simulation PACS: 47.27.Cn, 47.27
By a simple transformation, (2+1)-dimensional Broer-Kaup equations are turned to a simple equation. Some new soliton solutions are obtained by combining the tra nsformation with the homogeneous balance method. The method given in this paper can be used to solve other nonlinear physical model.
The initial model of turbulent spots with the wall disturbance using the pulse form was proposed. A group of three-dimensional coupling compact difference schemes with high accuracy and high resolution were developed, and implemented to simulate the formation and development of turbulent spots in the near-wall shear flow by means of direct numerical simulation of the Navier-Stokes equations. Growing and decaying modes were used to analyze nonlinear evolution characteristics of the turbulent spots.The isolated local regions possessing some turbulent properties would appear in the near-wall shear flow under certain conditions [1] . Within the regions surrounded still by laminar flows, there were the turbulent properties, such as random pulse, Reynolds stress and vortex. The localized turbulent regions termed turbulent spots played an important role in the process of transition from laminar to turbulent flows. Since the phenomenon of turbulent spots was discovered in the 1950s, researchers had done a lot of work to understand properties of the turbulent spots [2][3][4] . However the complicated mechanism of the generation of turbulent spots and characteristics of nonlinear evolution still needed further research and exploration.After further studies on numerical simulation of the turbulent spots, two problems, the model of initial disturbance and the method of numerical simulation, became special interesting to researchs. There were various methods for introducing initial disturbances. Disturbance models of stirring up the turbulent spots were also explored. Utilization of disturbance waves under certain conditions and specialized enactment, such as consisting of several pairs of counter-rotating vortices [5] , was included. However, this created a very complex circumstance, and led to difficulties in the analysis and processing. It was considered that the wall disturbance might be an important triggered reason, and instantaneous pulse could trigger early turbulent spots discovered in the experiments [6] and was associated with the modeling of individual turbulent coherence structure in the wall re-
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