Study on longitudinal modulation effects in Tollmien-Schlichting waves in a compressible boundary layer

Abstract

The objective of this project is to study the transition phenomena due to the longitudinal modulation effect in a flat plate. Transition is a process very complex and still not fully understood, such that the theories do not describe well the natural phenomena.The study of the transition phenomena started in XIX and there are models for very controlled situations. Its start is linked to the presence of perturbation, for example, in the velocity field, when determined frequencies can be amplified by the flow, generating after a non-linear process, a turbulent flow. Studies show that the natural transition may be better modeled as modulated tridimensional wave packet, a situation way more complex than that of a few monochromatic plane waves for which the theory is valid. The phenomenon complexity makes the use of computational tools indispensable. There are studies about transition due to a punctual source generating a wave but they produce results way too complex to be analysed. However there are also studies of a harmonic punctual source. It regards the analysis of a punctual source case with a wave pulse with constant frequency and controlled amplitude modulation, which allows us to make a bridge between the no modulation case and the pulse modulation case. The idea is that this study will enable a better understanding of the longitudinal modulation effect.The case will be analysed using a code previously developed to solve the Navier-Stokes equation through Direct Numerical Simulation (DNS). The results analysis will be done both in the physical and Fourier spaces. The work will allow comparisons with the already studied cases as well as with the experimental data, which are available to the group from previous works.