Very large-scale motion in the outer layer

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.

Three-dimensional vortex organization in a high-Reynolds-number supersonic turbulent boundary layer

“…Ganapathisubramani et al (2007b) even report lengths up to 40δ at y/δ = 0.2 in their supersonic boundary layer visualization based on high repetition rate PIV measurements and using Taylor's hypothesis. Long low-speed zones have also been found in incompressible turbulent boundary layers and pipe flow using a single hot-film (Kim & Adrian 1999) or a spanwise array of 10 hot wires to account for meandering of the low-speed zones (Hutchins & Marusic 2007). The width of the low-speed zones observed in the present experiments varies between 0.25δ and 0.4δ, which is consistent with earlier studies (Spina et al 1991;Tomkins & Adrian 2003;Ganapathisubramani et al 2006;Ringuette et al 2008), and the spanwise spacing between low-speed zones is typically between 0.5δ and 1.0δ.…”

“…Furthermore the energy contained in this length scale is approximately constant up to y/δ = 0.7, after which it decreases with distance from the wall. For y/δ = 0.1 a peak is observed near λ x /δ = 9, which indicates the presence of VLSM at that height in the boundary layer (Kim & Adrian 1999). The energy contained in the very large scales decreases with distance from the wall, so that they are visible only as a small bump in the power spectra up to y/δ = 0.5.…”

“…temperature and density) across the boundary layer is taken into account in the scaling (Smits & Dussauge 2006). More recently, Ganapathisubramani, Clemens & Dolling (2006) performed PIV in a plane parallel to the wall showing very long high and low-speed regions consistent with the VLSM model (Kim & Adrian 1999) for subsonic flow, which again suggests the presence of hairpin vortices aligned in the streamwise direction. Although the occurrence of hairpins in the supersonic boundary layer has been suggested previously on the basis of flow visualization, a direct observation in velocity measurements is lacking presently.…”

“…They have been referred to as very large-scale motions (VLSM) or superstructures. Based on their signatures in onedimensional hot-wire signals, it has been conjectured that the elongated structures result from streamwise aligned hairpin packets (Kim & Adrian 1999). It should be noted that here, and throughout the paper, the term hairpin is used to represent cane, hairpin, horseshoe and omega shaped vortices (following Adrian et al 2000), which are believed to be variations of the same basic structure.…”

“…These reports were subsequently followed by particle image velocimetry (PIV) and hot-wire observations of even larger scale motions ranging up to 40δ in streamwise direction (e.g. Kim & Adrian 1999;Guala, Hommema & Adrian 2006;Hutchins & Marusic 2007;Ganapathisubramani, Clemens & Dolling 2007b;Balakumar & Adrian 2007), which manifest long regions of low velocity. They have been referred to as very large-scale motions (VLSM) or superstructures.…”