Time irreversibility in a transitional boundary layer

Laminar to turbulent flow transition is a complex phenomenon that is currently widely investigated in the field of fluid dynamics. In particular, the study of time irreversibility - intended as statistical asymmetry of signals under time reversal - of a transitional boundary layer can offer new perspectives in the analysis of turbulence and non-stationary processes. Therefore, the connection between the turbulent structure of the boundary layer and the irreversibility of the velocity signals is an important subject of research. This thesis proposes a quantitative and point-to-point analysis of the time irreversibility of a transitional boundary layer and makes use of numerical data from the John Hopkins Turbulence Database (JHTDB), which simulate an incompressible flow on a flat plane subject to a bypass transition induced by isotropic turbulence at the inlet. Time series of the velocity components u, v and w are transformed into graphs using different Visibility Graph methods, which are able to represent and study the geometric structure of signals using the tools of graph theory. Time irreversibility is quantified through the Kullback-Leibler divergence Ik of the ingoing and outgoing degree probability distributions of the nodes and measured by comparison with a reversible null model through its Z-Score Ik,r. The results show that the regions exhibiting the highest levels of irreversibility are located in the transition zone and close to the wall and coincide with regions characterised by high turbulent fluctuations, particularly in the buffer layer. It is also observed that irreversibility does not depend directly on the amplitude of the fluctuations, rather it is influenced by their temporal asymmetry and by the geometric structure of the signal. A local analysis by means of temporal windows suggests a correlation between irreversibility and the overlap regions between laminar and turbulent parts of the signal. These results offer a new point of view on the interpretation of turbulent transition using graph theory, thereby providing a first step towards the understanding of time irreversibility and its connection to the turbulent structures of a boundary layer. Future studies may extend the analysis to the time-space dynamics of a single spot and its evolution along the plate, in order to unveil the mechanisms through which local asymmetries and coherent structures contribute to the global irreversibility of the flow.