Very large-scale motion in the outer layer

TLDR

Very large‑scale motions appear as long streamwise velocity fluctuations in the outer layer of turbulent pipe flow, and are thought to arise from coherent alignment of turbulent bulges or hairpin vortex packets. Hot‑film anemometry reveals a bimodal one‑dimensional spectrum of streamwise velocity, with one component representing large‑scale motion and the other capturing smaller turbulent scales. The large‑scale mode’s wavelength grows through the logarithmic layer to about 12–14 pipe radii—an order of magnitude larger than the largest integral scale—and then shrinks to roughly two pipe radii at the centerline.

Abstract

Very large-scale motions in the form of long regions of streamwise velocity fluctuation are observed in the outer layer of fully developed turbulent pipe flow over a range of Reynolds numbers. The premultiplied, one-dimensional spectrum of the streamwise velocity measured by hot-film anemometry has a bimodal distribution whose components are associated with large-scale motion and a range of smaller scales corresponding to the main turbulent motion. The characteristic wavelength of the large-scale mode increases through the logarithmic layer, and reaches a maximum value that is approximately 12–14 times the pipe radius, one order of magnitude longer than the largest reported integral length scale, and more than four to five times longer than the length of a turbulent bulge. The wavelength decreases to approximately two pipe radii at the pipe centerline. It is conjectured that the very large-scale motions result from the coherent alignment of large-scale motions in the form of turbulent bulges or packets of hairpin vortices.