TRANSMISSION COEFFICIENT OF TOLLMIEN-SCHLICHTING WAVES UNDERGOING SMALL INDENTATION/HUMP DISTORTION

摘要

Behaviours of Tollmien-Schlichting (T-S) waves experiencing small localized imperfection distortions within the boundary layer along a flat plate are investigated. According to the theoretical results [1], for hump and indentation distortions, transmission of T-S waves shows that +h (hump) can stabilize T-S waves and h (indentation) can destabilize T-S waves. Here, we consider the properties of the boundary layer distorted by small-scale localized imperfection with the width scale d which is less than T-S wavelength lTS. We analysis the shear stress distribution on the wall from both a theoretical and a numerical point of view. Then, the transmission behaviours of T-S waves are investigated numerically. We observe that for h .≤σ(xRe 5=8), both hump and indentation have destabilizing effects. By observing the profiles of the T-S wave transmission coefficient distributions around short rapid distortions, we observe that recovering the Blasius boundary layer profile is only required after a long distance from the rapid distortion position and the distance is far greater than σ(xRe 3=8) , since the shear stress distribution has a profound influence on both upstream and downstream of the rapid distortion position. Therefore, there is no Blasius boundary layer velocity profiles on the scale σ(xRe 3=8), then, estimating theoretically T-S wave transmission coefficient for the current configuration h ≤ σ(xRe 5=8) is inapplicable. Therefore, the classical linearised triple-deck theory can not be employed to formulate a universal analytical expression of the transmission coefficient. Finally, it is concluded that the mechanism of the T-S wave destabilization is shown to be independent of roughness types.