Browsing by Author "Bozatli, A. N."

Now showing 1 - 2 of 2
  • Thumbnail Image
    Nonlinear Interaction of Two Waves in Boundary-Layer Flows
    Nayfeh, Ali H.; Bozatli, A. N. (AIP Publishing, 1980)
    First_order nonlinear interactions of Tollmien-Schlichting waves of different frequencies and initial amplitudes in boundary_layer flows are analyzed using the method of multiple scales. Numerical results for flow past a flat plate show that the spatial detuning wipes out resonant interactions unless the initial amplitudes are very large. Thus, a wave having a moderate amplitude has little influence on its subharmonic although it has a strong influence on its second harmonic. Moreover, two waves having moderate amplitudes have a strong influence on their difference frequency. The results show that the difference frequency can be very unstable when generated by the nonlinear interaction, even though it may be stable when introduced by itself in the boundary layer.
  • Thumbnail Image
    Secondary Instability in Boundary-Layer Flows
    Nayfeh, Ali H.; Bozatli, A. N. (AIP Publishing, 1979)
    The stability of a secondary Tollmien–Schlichting wave, whose wavenumber and frequency are nearly one half those of a fundamental Tollmien–Schlichting instability wave, is analyzed using the method of multiple scales. Under these conditions, the fundamental wave acts as a parametric exciter for the secondary wave. The results show that the amplitude of the fundamental wave must exceed a critical value to trigger this parametric instability. This value is proportional to a detuning parameter which is the real part of k − 2K, where k and K are the wavenumbers of the fundamental and its subharmonic, respectively. For Blasius flow, the critical amplitude is approximately 29% of the mean flow, and hence many other secondary instabilities take place before this parametric instability becomes significant. For other flows where the detuning parameter is small, such as free‐shear layer flows, the critical amplitude can be small, thus the parametric instability might play a greater role.