Multi-scale characteristics and inter-scale interaction in a transitional boundary layer over an axisymmetric body of revolution

Abstract

The present work focuses on the evolution of multi-scale characteristics and inter-scale interaction in a transitional curve-wall boundary layer, which was triggered by free-stream turbulence (FST), via time-resolved two-dimensional (2D) particle image velocimetry measurement. Using multi-component variational mode decomposition, 2D velocity fields are decomposed into three intrinsic mode functions (IMFs). The proper orthogonal decomposition was then applied to each IMF to reveal the corresponding statistical representative structures with various characteristic length scales. It is found that the first IMF primarily depicts low-frequency large-scale motions inside the boundary layer, which are characterized as the Klebanoff mode in the pre-transition region, as well as inclined shear layer and lift-up of low-speed streaky structures in the nonlinear stage. Meanwhile, the second IMF is characterized as mild-to-high-frequency small-scale motions, whose quick amplification leads to the secondary streak instability. Analysis of the amplitude and frequency modulation effects shows that the top-down and bottom-up scenarios alternately govern the inter-scale interaction in various transition stages. Before the transition onset, a reversal top-down scenario depicts that the small-scale fluctuations in FST positively modulate Klebanoff-mode streaky structures in the near-wall region, while in the nonlinear transition stage, the bottom-up modulation is characterized as positive amplitude and frequency modulation in the near-wall region, as well as negative ones in higher flow layer, the latter of which is attributed to the lift-up of near-wall streaky structures and their subsequent burst and breakdown.