Scalings of small-scale shear layers in temporally developing turbulent boundary layers

Small-scale shear layers in temporally developing turbulent boundary layers are investigated using direct numerical simulations at momentum-thickness Reynolds numbers from 2000 to 13 000. Flow statistics are evaluated in a local coordinate system aligned with each shear layer identified by the shear intensity. Conditional mean fields show that shear layers are embedded in a biaxial strain. Near the wall, these conditional fields further reveal two distinct regions of intense rigid-body rotation beneath the shear layer, leading to momentum transfer through a mechanism consistent with counter-rotating vortex pairs. Two distinct scalings are found for the shear layers. In the logarithmic and outer layers, the mean shear-related velocity jump

and its width

delta 3 δ 3 $\delta _3$

scale with the Kolmogorov velocity

u Subscript eta upper T u η T $u_{\eta T}$

and length

eta Subscript upper T η T $\eta _T$

evaluated in the turbulent region. In the buffer layer,

delta 3 δ 3 $\delta _3$

scales with the viscous length

delta Subscript nu Baseline equals nu divided by u Subscript tau δ ν = ν / u τ $\delta _\nu =\nu /u_\tau$

(

nu ν $\nu$

is the kinematic viscosity and

u Subscript tau u τ $u_\tau$

the friction velocity), and

normal upper Delta u 3 Δ u 3 $\Delta u_3$

scales with

delta Subscript nu Baseline divided by tau Subscript eta upper T δ ν / τ η T $\delta _\nu /\tau _{\eta T}$

, consistent with the predominance of shear in energy dissipation, where

tau Subscript eta upper T τ η T $\tau _{\eta T}$

is the Kolmogorov time scale. Velocity jumps associated with the biaxial strain exhibit Kolmogorov-based scaling in the logarithmic and outer layers. In the buffer layer, their widths scale with

delta Subscript nu δ ν $\delta _\nu$

, but their velocity jumps do not scale with

delta Subscript nu Baseline divided by tau Subscript eta upper T δ ν / τ η T $\delta _\nu /\tau _{\eta T}$

because strain contributes little to dissipation. Comparisons with turbulent jets indicate weak wall influence in the logarithmic and outer layers. These scalings provide a basis for predicting shear-layer properties, which is crucial for developing flow-control strategies that leverage small-scale shear instability.