The influence of initial phase of fundamental and subharmonic waves in a subharmonic resonant interaction is investigated for incompressible boundary layers with zero and adverse pressure gradient. Nonlinear parabolized stability equations (PSE) analyses are carried out for mean flow data of Blasius and Falkner-Skan solution. The pressure gradient parameter is chosen to reproduce the experimental amplification for both fundamental and subharmonic wave. Results for various initial phases of fundamental and subharmonic wave show that the amplification of subharmonic and higher modes is strongly dependent on the initial phase as observed in former experiments. There exists a certain combination of initial phases which leads to resonance or anti-resonance condition (the maximum or minimum amplification). From the results for various possible combinations of initial phases, the phase dependency is found to fall into a function of a single parameter representing initial phase difference between the fundamental and subharmonic wave. The amplification in subharmonic resonant interaction depends on the initial phase difference relationship rather than phase of either fundamental or subharmonic wave only. As proceeds to the end of parametric resonant stage, the phase difference converges toward value approximately ranging from 80 to 90 degrees regardless of initial phase difference. This feature is found to be same for boundary layers with zero and adverse pressure gradient. It implies that the pressure gradient does not affect basic mechanisms, properties, and phase dependency of subharmonic resonant interaction.
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