Elucidation and control of near-wall turbulence-A new approach by saddle solutions

点击翻译按钮获取中文摘要

In this research project, recently found appealing saddle solutions (unstable equilibrium or periodic solutions) were recomputed in plane Couette, plane Poiseuille, and autonomous wall systems to compare their properties. It has been shown that in spite of diffrernce in the way of driving the systems, there exist universal saddle solutions in wall-bounded shear flow. These solutions have been shown to be classified into two families, one of which is an upper-branch solution characterized by dominant streamwise vortical motion and the other of which is a lower-branch solution characterized by dominant streaky structures. The former represents well structures and statistics for near-wall turbulence, while the latter exhibits wall shear rate much less than that for a turbulent state. In numerical experiments of plane Couette flow, the lower-branch solution (unstable periodic solution) with much less wall shear rate has been stabilized by the use of a chaos control theory to accomplish a s … More ignificant reduction of skin friction drag in turbulent flow. The linear stability analysis of the lower-branch solution for the plane Couette system has been performed to demonstrate that the solution has only one unstable eigenvalue. At subcritical Reynolds numbers the lower-branch solution and its stable manifold form the basin boundary between laminar and turbulent attractors. It has been shown that turbulent flow can be laminarized if a small-amplitude control input is imposed on the flow during its transient approach to the lower solution and so to the basin boundary. The properties of the upper-branch solution (unstable periodic solution) representing near-wall turbulence was examined in plane Couette flow to show that the solution reproduces the universal statistical law of near-wall turbulence, i.e., the Prandtl wall law. Furthermore, the same kind of an upper-branch solution has been discovered in periodic-box turbulence with the high-symmetry to confirm that the statistics of the solution is in good agreement with that in a turbulent state. It has been found that the upper-branch solution also reproduces the universal statistical law of isotropic turbulence, i.e., the Kolmogorov similarity law. Less