Data-driven decomposition of the streamwise turbulence kinetic energy in boundary layers. Part 2. Integrated energy and $A_1$

Abstract

Scalings of the streamwise velocity energy spectra in turbulent boundary layers were considered in Part 1. A spectral decomposition analysis provided a means to separate out attached and non-attached eddy contributions and was used to generate three spectral sub-components, one of which is a close representation of the spectral signature induced by self-similar, wall-attached turbulence. Since sub-components of the streamwise turbulence intensity $\overline{u^2}$ follow from an integration of the velocity energy spectra, we here focus on the scaling of the former. Wall-normal profiles and Reynolds number trends of the three individual, additive sub-components of the streamwise turbulence intensity are examined. This allows for revisiting the scaling of the turbulence intensity in more depth, in comparison to evaluating the total streamwise turbulence intensity. Based on universal trends across all Reynolds numbers considered, some evidence is given for a Townsend--Perry constant of $A_1=0.98$, which would describe the wall-normal logarithmic decay of the turbulence intensity per Townsend's attached-eddy hypothesis. It is also demonstrated how this constant can be consistent with the Reynolds-number increase of the streamwise turbulence intensity in the near-wall region.

References in corpus (8)

• Direct numerical simulation of turbulent channel flow up to $R{e}_{\tau }\approx 5200$
• Wall-attached structures of velocity fluctuations in a turbulent boundary layer
• The persistence of viscous effects in the overlap region, and the mean velocity in turbulent pipe and channel flows
• Two-dimensional energy spectra in high Reynolds number turbulent boundary layers
• Streak instability in turbulent channel flow: the seeding mechanism of large-scale motions
• The streamwise turbulence intensity in the intermediate layer of turbulent pipe flow
• Comparison of turbulence profiles in high Reynolds number turbulent boundary layers and validation of a predictive model
• Large-scale motions from a direct numerical simulation of a turbulent boundary layer

Cited by in corpus (10)

• Data-driven decomposition of the streamwise turbulence kinetic energy in boundary layers. Part 1. Energy spectra
• Active and inactive components of the streamwise velocity in wall-bounded turbulence
• Statistical behaviour of self-similar structures in canonical wall turbulence
• Identification of the energy contributions associated with wall-attached eddies and very-large-scale motions in the near-neutral atmospheric surface layer through wind LiDAR measurements
• On the streamwise velocity variance in the near-wall region of turbulent flows
• A spectral-scaling based extension to the attached eddy model of wall-turbulence
• Model-based spectral coherence analysis
• Streamwise energy-transfer mechanisms in zero- and adverse-pressure-gradient turbulent boundary layers
• Wall-wake laws for the mean velocity and the turbulence
• Constructing wall turbulence using hierarchical hairpin vortices