An Investigation On Disturbance Evolutions And Transitions By Resonant-triad Interactions With Sideband Disturbances In A Boundary Layer

In usual studies on disturbance evolutions and transitions by resonant-triad interactions in the boundary layers,the disturbances in numerical simulation are pure.However,in practical engineering problems,there are always sideband components,whose frequencies are close to those of the dominant waves.When the amplitudes of sideband modes are high enough,it interacts with the dominant wave to generate a difference-frequency mode by nonlinear effects.The difference-frequency mode is quite “dangerous” because of its low frequency.It interacts with each wave such that the frequency bandwidths of all waves are broadened.Consequently,the evolutions of the dominant waves are modified.For the transition caused by resonant-triad,the sideband perturbations could change the transition location.In this thesis,the traditional incompressible parabolized stability equations(PSE)are modified.The parameter transform in spectral space is used in incompressible PSE,so that it can efficiently calculate the evolution of two disturbances with arbitrary frequencies,and we called it PSE for parameter transform(t PSE).Then,t PSE is used to calculate the evolution of a disturbance with a sideband mode.In this thesis,the influence of transitions caused by resonant-triad with sideband mode is studied.Firstly,the transitions caused by resonant-triad without sideband are calculated and the mechanism of transitions caused by resonant-triad is found.Then,we put the sideband mode of 2D dominant wave in calculation,and study its influence on the transitions by changing its amplitude.Finally,we analyze the roles of the waves in transitions and investigate the mechanism of transitions caused by resonant-triad with sideband mode.Based on the two parts of the study above,the results are obtained as follow:(1)When the amplitude of sideband mode becomes large enough,it can interact with the dominant disturbance to generate the difference-frequency mode and,it can influence the evolution of the fundamental waves.(2)In the transitions caused by resonant-triad,the “Steady-Spanwise-Waves-Working(SSWW)(SSWW)mechanism plays the necessary and essential role in transition process caused by resonant-triad.(3)In resonant-triad,it promotes transition when the amplitude of sideband mode becomes large enough.The relative amplitude of the side-frequency disturbance can affect the transition location substantially when it reaches 40%.(4)In the transitions caused by resonant-triad with sideband,the sideband disturbance promotes the effects of “SSWW” mechanism,such that the transition occurs earlier.