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.
Highlights
At the beginning of a transition in shear flow, a large number of vortex structures are formed.The formation mechanism and dynamic characteristics of vortex structures are still key issues in fluid mechanics research.Lee presented direct comparisons of experimental results on transitions in wall-bound flows obtained by flow visualizations, hot-film measurement, and Particle Image Velocimetry (PIV), along with a brief mention of relevant theoretical progresses, based on a critical review of about 120 selected publications
Wedin studied finite-amplitude coherent structures with a reflection symmetry in the span-wise direction of a parallel boundary layer flow; some states computed displayed a span-wise spacing between streaks of the same length scale as turbulence flow structures observed in experiments [3]
A direct numerical simulation of the nonlinear evolution of vortex structures in a laminar went up, and the influencing areas gradually diffused, followed by strong ejection and sweeping at boundary layer induced by different local micro-vibrations on the wall was carried out
Summary
At the beginning of a transition in shear flow, a large number of vortex structures are formed.The formation mechanism and dynamic characteristics of vortex structures are still key issues in fluid mechanics research.Lee presented direct comparisons of experimental results on transitions in wall-bound flows obtained by flow visualizations, hot-film measurement, and Particle Image Velocimetry (PIV), along with a brief mention of relevant theoretical progresses, based on a critical review of about 120 selected publications. At the beginning of a transition in shear flow, a large number of vortex structures are formed. Sharma presented a new theory of coherent structures in wall turbulence. The theory is the first to predict packets of hairpin vortices and other structures in turbulence and their dynamics, based on an analysis of the Navier–Stokes equations, under an assumption of a turbulent mean profile [2]. Wedin studied finite-amplitude coherent structures with a reflection symmetry in the span-wise direction of a parallel boundary layer flow; some states computed displayed a span-wise spacing between streaks of the same length scale as turbulence flow structures observed in experiments [3]. Wu presented a mathematical theory to describe the nonlinear dynamics of coherent structures. Mcmullan implemented large eddy simulations of the plane mixing layer
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