Boundary-layer Response To The Free-stream Turbulence And Simulation On Bypass Transition

Study on the entrainment of free-stream vortical disturbances(FSVD)in the boundary flows is of both theoretical and practical importance.However,the currently well-accepted mathematical model to describe this process,i.e.the continuous spectrum of Orr-Summerfeld(O-S)Equation,encounters some fatal errors,which were summarized as two non-physical phenomena(the 'Fourier entanglement' and the 'abnormal anisotropy').As pointed out by Dong & Wu(JFM 2013),both phenomena were caused by neglecting the non-parallel effect,which on the contrary,plays an equally important role as the convection terms through the entrainment process.They then proposed an asymptotic solution based on the edge layer theory,in which the non-physical phenomena are absent.This paper studies the spatial evolution of Dong & Wu's asymptotic solution in an incompressible boundary layer via direct numerical simulation(DNS).It is found that the perturbation field as was computed by DNS is generally in good agreement with that predicted by the asymptotic solution.The difference between them is only caused by the finite-Reynolds-number and the non-parallel effects.The errors caused by these effects are quantitatively predictable and would be vanished as it approaches downstream through our simulation.DNS on boundary-layer bypass transition is performed by introducing a large-amplitude & low-frequency disturbance and a series of small-amplitude & high-frequency disturbances in the external stream.In the early laminar stage,only the low-frequency FSVD has thick penetration depth,while the high-frequency FSVDs are expelled from the boundary layer due to the so-called 'shear-sheltering' phenomenon.The low-frequency disturbance in the boundary layer,appearing as streaks,is the dominant perturbation for quite a long distance until its breakdown.Meanwhile,the low-frequency disturbance distorts the mean flow,leading to the generation and rapid amplification of high-frequency disturbance due to the secondary instability mechanism.Since the streaks oscillate at low frequency,the secondary modes increases intermittently,leading to the re-laminarization(appearing as a turbulent-laminar interface)phenomenon during the transition process.In the turbulent stage,all the amplitudes of the disturbances tend to the same order of magnitude,and the mean profiles satisfy the classical log law of turbulent boundary layers.The implication is that no matter what route the transition is caused by,the statistics of turbulent boundary layers are identical.The simulation confirms that the asymptotic solution based on the edge-layer solution can be used as a proper inflow condition of bypass transition simulation.