On the spatial organization of hairpin packets in a turbulent boundary layer at low-to-moderate Reynolds number

Abstract

The present study is devoted to characterizing the coherent organization of vortical structures, which can be fitted into the paradigm of the hairpin-packet model, in the streamwise–wall-normal plane of a canonical turbulent boundary layer at $Re_{\unicode[STIX]{x1D70F}}=377{-}1093$. Proper orthogonal decomposition (POD) of the planar velocity fields measured via two-dimensional particle image velocimetry, together with a spatio-temporal coherence analysis, shows that the first four leading-order POD modes share both geometric similarity and dynamic coherence and jointly depict the downstream convection of the large-scale Q2/Q4 events, which can be regarded as the low-order imprints of the hairpin packets. A simple low-order indicator is then proposed to extract the inclined interfaces of the hairpin packets, based on which a two-point conditional correlation analysis forms a statistical picture of the spatial organization of multiple prograde vortices aligned along the interface within one packet. A saturation of the self-similar growth of the streamwise gap between two neighbouring vortices is seen. This implies a detachment of the hairpin packets from the inner layer. Both the detachment height and the saturated streamwise spacing are found to scale as $Re_{\unicode[STIX]{x1D70F}}^{1/2}$.

Sand-turbulence interaction in a high-Reynolds-number turbulent boundary layer under net sedimentation conditions

“…Such a scenario also explains the observation in figure 10(c) that the critical layer is next to the right end of the log-layer u rms plateau (or bump) in the TBL. According to Deng et al (2018), the detachment of LSMs from the wall marks a quick drop of the magnitude of u rms and a cease of the u rms plateau. If the role of LSMs on the sandgrain vertical motion is valid, the detachment of LSMs will also lead to a significant weakening of the occurrence probability of the sand-grain Q2 events, which exactly occurs beyond the critical layer (see figure 14b).…”

Wall-Normal Variation of Spanwise Streak Spacing in Turbulent Boundary Layer With Low-to-Moderate Reynolds Number

“…In the present study, Proper Orthogonal Decomposition (POD) is used as an alternative. POD has been used as a scale-filtering tool to isolate large-scale structures from small-scale ones in wall-bounded turbulence [ 45 , 97 ]. In essence, it decomposes a given space-time realization into a linear combination of a set of orthogonal bases whose spatial and temporal dimension are fully decoupled as: …”

“…Since the POD modes are ranked by their relative TKE contribution with the eigenvalue of the n th mode, a cumulative energy cut-off threshold can be set to separate all the POD modes into a leading-order group including the first s modes and a high-order group containing the rest ones. Similar to Wu and Christensen [ 45 ] and Deng et al [ 97 ], velocity field reconstruction using these two mode groups via the right part of Equation ( 1 ) is taken. This separates the original full-order into a leading-order and a high-order .…”

Experimental study on low-speed streaks in a turbulent boundary layer at low Reynolds number

“…For a turbulent boundary layer, Wu (2014) pointed out that instantaneous large-scale turbulence structures are the main contributors to the first two POD modes based on analysis of a 2-D PIV dataset. Deng et al (2018) also determined that the first four leading-order POD modes jointly depict the downstream convection of the large-scale ejection/sweep events, which were regarded as the low-order imprints of the hairpin packets. The decomposition can be written as…”