Identifying skin-friction generation structures in turbulent channel flows via canonical correlation decomposition

TL;DR

This work addresses the problem of linking skin-friction generation in wall-bounded turbulence to specific flow structures. It introduces Canonical Correlation Decomposition (CCD) as an observable-targeted method that identifies flow features most correlated with skin friction, offering a stark contrast to energy-based decompositions like POD/DMD. Applied to DNS of turbulent channel flows at $Re_\tau \approx 180$ and $550$, with and without opposition control, CCD reveals that the leading modes form spanwise-localized streamwise streaks near the observable and that the spectrum exhibits strong low-rank behavior, with the first four CCD modes capturing $>80\%$ of the $c_f$ variation, far surpassing POD. Under opposition control, CCD shows a pronounced structural reorganization—lifted primary streaks, shorter lengths, and a secondary opposite-phase streak beneath—consistent with observed drag reduction and supporting CCD as a diagnostic tool for drag-control design in wall-bounded turbulence.

Abstract

Flow structures directly responsible for local skin-friction generation in turbulent channel flows are identified using the newly developed Canonical Correlation Decomposition (CCD) method. The dominant structures take the form of streamwise streaks that are spanwise-localised around the position where the skin-friction is targeted and exhibit significantly shorter streamwise extent than those revealed using POD. The resulting CCD spectrum shows a clear low-rank behaviour; flow reconstruction using only the first 4 CCD modes recovers more than 80\% of the examined skin friction, as opposed to 2\% recovered by the leading 4 POD modes. When the opposition control technique is used to reduce drag, the application of CCD shows that drag reduction is achieved by lifting the original streak structures and generating smaller streaks with opposite phases underneath. These findings demonstrate that CCD isolates the causally relevant flow structures governing skin-friction generation and modification, which is expected to find use in various drag control applications in wall-bounded turbulence.

Figures (11)

• Figure 1: The spectra of (a) CCD and (b) POD modes when $Re_\tau\approx180$.
• Figure 2: Reconstruction of the skin friction coefficient (fluctuation part) using the first 4 CCD (a) and POD (b) modes when $Re_\tau\approx180$, respectively.
• Figure 3: Front (a,c,e,g) and left (b, d, f, h) views of the first four CCD modes when $Re_\tau\approx180$. $z=0$ for (a, c, e, g) while $x=0$ for (b, f) and $x=1/3\pi$ for (c, h).
• Figure 4: Isosurface of the 1st- to 4th- order (a to d) CCD modes when $Re_\tau\approx180$. The red and blue isosurfaces represent $50\%$ and $-50\%$ of the fluctuation amplitude, respectively.
• Figure 5: Front (a) and left (b) views of the first POD mode when $Re_\tau\approx180$. $z=0.6$ for (a) while $x=0$ for (b).