**Weidong Cao \*, Zhixiang Jia and Qiqi Zhang**

Research Institute of Fluid Engineering Equipment Technology, Jiangsu University, Zhenjiang 212013, China **\*** Correspondence: cwd@ujs.edu.cn; Tel.: +86-139-5281-6468

Received: 26 June 2019; Accepted: 21 August 2019; Published: 23 August 2019

**Abstract:** The compact finite difference scheme on non-uniform meshes and the Fourier spectral hybrid method are used to directly simulate the evolution of vortex structures in a laminar boundary layer over a flat plate. To this end, two initial local vibration disturbances, namely, the positive–negative and the negative–positive models, at the wall were adopted. The numerical results show that the maximum amplitudes of vortex structures experience a process of linear growth and nonlinear rapid growth. The vertical disturbance velocity and mean flow shear and the derivative term of the stream-wise disturbance velocity and the span-wise disturbance velocity, are important factors for vortex structure development; the high- and low-speed stripe and the stream-wise vortex are consistent with structures seen in full turbulence. The maximum amplitude of the negative–positive model grows more quickly than that of the negative–positive model, and the detailed vortex structures are different for the two models. The mean flow profiles both become plump, which leads to the instability of the laminar boundary layer. The way in which the disturbance is generated with different local vibrations influences the dynamics of vortex structures in a laminar boundary layer.

**Keywords:** vortex structures; boundary layer; direct numerical simulation; amplitude; vortices
