Investigation of inviscid shear layer by linear stability theories

Topbaş, Ahmet Emre
ThisIn this thesis, spatial and temporal instabilities of the inviscid shear layer flows are investigated using the linear stability theory. Utilizing the small and wavy disturbances, Rayleigh equation was derived from the Helmholtz vorticity equation. For the hyperbolic-tangent velocity profile, the Rayleigh equation was solved by using space and time amplification approaches by an in-house Fortran code involving RK4 and simplex method algorithm. Eigenvalues of various disturbance frequencies were calculated both for spatial and temporal amplification theories. Results of two theories were compared and the most strongly amplified disturbance frequencies were calculated. Eigenfunctions of spatial theory were plotted for various disturbance frequencies. For the most strongly amplified disturbance frequency, eigenfunctions were calculated for both theories and compared. In spatial amplification case, derivatives of the eigenfunctions and the vorticity amplitudes were also calculated for different disturbance frequencies. By using the vorticity amplitudes, constant vorticity distributions of spatial amplification were plotted at different times in order to demonstrate the mechanism of instability. At the most strongly amplified disturbance frequency of spatial theory, the motion of particles at different locations in the shear layer were investigated. To investigate the motions of the particles and the characteristics of the instability clearly, the pathlines and the streaklines of the disturbed shear layer were calculated and the streakline patterns were drawn. The pathlines and streaklines were also compared in terms of their ability to reflect the instability mechanism. The streaklines of the shear layer at different disturbance frequencies were compared. Results calculated by the help of the Fortran code were compared with experimental and numerical data in the literature and seen that they are in agreement. The Fortran code was also tested with the different velocity profiles to check its capability. The reasons why the code could not solve the parabolic velocity profiles were discussed.


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Citation Formats
A. E. Topbaş, “Investigation of inviscid shear layer by linear stability theories,” M.S. - Master of Science, Middle East Technical University, 2018.