On the stabilization of the most amplified Gortler vortex on a concave surface by spanwise oscillations

In the present work the effect of spanwise oscillations on the most unstable Gortler vortex is studied. The wavenumber of the most unstable disturbance is very large, so that the parabolic character of the problem is eliminated. After the disturbances are expanded in a Fourier series in time, the eigenvalue problem is solved for various amplitudes and frequencies of the oscillation. Due to numerical difficulties the treatment of very high amplitudes and/or very low frequencies becomes prohibitively expensive. Therefore an approximate formulation was developed for high magnitudes of the spanwise speed of the oscillation E. The results, which were obtained in all cases, indicate that the disturbances move away from the wall in a logarithmic way, reducing the effects of the oscillation. Consequently, it is impossible to stabilize the flow completely. However, it is shown that a large reduction of the growth rate can be achieved even for moderate values of E.