Measurements of streamwise and spanwise fluctuating velocity components in a high Reynolds number turbulent boundary layer

Measurements of the streamwise and spanwise fluctuating velocity components are obtained in a high Reynolds number turbulent boundary layer using custom made sub-miniature hot wires. These measurements are made over a range of Reynolds numbers from Reτ ≈ 3,000 to Reτ ≈ 10,500, but at fixed unit Reynolds number U∞/ν (Reτ = δUτ/ν; where ν is the kinematic viscosity, Uτ is the friction velocity and δ is the boundary layer thickness). In this way the measurement volumes of the probes are approximately fixed for all Reτ at 14×14×7 viscous units. This gives sufficiently resolved velocity measurements, allowing observation of Reτ trends in isolation from spatial resolution effects. The resulting velocity measurements show clear scale separation in both streamwise and spanwise velocities at Reτ ≈ 10,500. The pre-multiplied spectra for both components show a near-wall peak which is fixed in viscous units and an outer region peak fixed in outer scaling, which grows in magnitude with Reτ. The large scale wavelengths associated with the outer site extend all the way down to the near-wall region for both components demonstrating the presence of large scale motions with a footprint that stretches to the surface for both of the streamwise and spanwise fluctuations. Introduction The broad-band nature of turbulence, and the increased scale separation between the smallest and largest energetic scales as Reynolds number increases, mean that it is highly challenging to obtain well resolved measurements of fluctuating components in high Reynolds number flows. Hot-wire anemometry using a single-wire has been successfully applied to obtain sufficiently resolved streamwise velocity components at a high Re [4]; however, there is a dearth of measurements for the other two velocity components at similarly high Re. Here, we attempt to redress this issue by simultaneously measuring the streamwise and spanwise fluctuating velocity components using subminiature cross-wires. For this paper, we highlight the similarities and the differences in Reynolds number trends for the streamwise and spanwise components. We consider in particular, the contribution from small and large scales in the flow to the turbulence intensities and the pre-multiplied spectra. Here, we use superscript ‘+’ to denote viscous scaling of length (e.g. z = zUτ/ν), velocity (e.g. U = U/Uτ) and time (e.g. t = tU2 τ/ν). Capitalisation (e.g. U) and overbar (e.g. u2) indicate time averaged quantities, while lower case (e.g. u) shows fluctuating components. We employ the co-ordinate system x, y and z to refer to streamwise, spanwise and wall-normal directions; with u, v and w the corresponding fluctuating velocities.