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Spatial instability of a wall-bounded flow with fluid injection through porous walls

Köken, Ozan
One of the important and yet least understood fields in fluid mechanics research more than a century is hydrodynamic stability. The main objectives in this field are to investigate the breakdown of laminar flows, their subsequent development as the flow evolves along downstream and eventual transition to the fully turbulent flows. The origin of the turbulence and the transition from laminar to turbulent flow is of crucial importance for the whole science of fluid mechanics as well as aviation and marine industries since the flow regime has an impact on the steady operating conditions of many vehicles concerned of those sectors. The focus of the current study is on the stability of an incompressible, homogenous, two-dimensional, planar wall-bounded flow driven by inflow through its porous walls. The non-parallelism of the mean flow and its effect on stability conditions are studied by using two stability approaches, namely, local and nonlocal. Chebyshev collocation method is used to discretize the wall-normal direction, while 1st order-accurate backward difference scheme is used in streamwise marching procedure. Codes for the mean flow calculation, local approach and non-local approach (parabolized stability equations) are written in MATLAB to investigate stability of a non-parallel base flow. Instead of using perturbation of the primitive flow variables, disturbance streamfunction is used in the formulation. The validation of the codes is performed by comparing the numerical results with the literature.