M.Sc Thesis


M.Sc StudentFederico Roizner
SubjectTransition in Plane Poiseuille Flow
DepartmentDepartment of Aerospace Engineering
Supervisor Full Professors Cohen Jacob


Abstract

This study examines the transition to turbulence via linear transient growth in plane Poiseuille flow. It is shown that four and five streamwise independent modes are sufficient to approximate the odd and even transient growth scenarios, respectively. The optimal odd or even disturbance corresponds to a single or a pair of streamwise independent counter-rotating vortices, respectively. Each optimal is used as a primary disturbance which modifies the base-flow by creating inflection points in the flow. Consequently, the modified base-flow becomes unstable to 3D secondary disturbances, which are calculated by performing a secondary stability analysis based on Floquet theory.


For each primary disturbance, a parametric study is performed where it is shown how the secondary disturbance characteristics vary with the spanwise and streamwise wavenumbers associated with the primary and secondary disturbances, respectively. It has been found that there are four different kinds of secondary disturbances for the even scenario and only one for the odd scenario. Each secondary disturbance corresponds to a different route to transition.


Because of the minimal number of modes participating in each transition scenario, it is possible to follow the transition stages analytically by employing a multiple time scales analysis. The analytical results are then compared to direct numerical simulations and demonstrate a very good agreement.


Comparison with similar results obtained for plane Couette flow ([Karp and Cohen, 2014]) shows that while most of the energy growth in plane Couette flow occurs during the growth of the secondary disturbance, in plane Poiseuille flow this growth occurs during the linear transient growth phase. Moreover, in plane Poiseuille flow the linear transient growth is sufficient to destabilize the flow, whereas in plane Couette flow the non-linear interactions between the transient growth modes are needed in order to obtain an unstable secondary mode.