Large-scale modes of turbulent channel flow: transport and structure

Abstract

Turbulent flow in a rectangular channel is investigated to determine the scale and pattern of the eddies that contribute most to the total turbulent kinetic energy and the Reynolds shear stress. Instantaneous, two-dimensional particle image velocimeter measurements in the streamwise-wall-normal plane at Reynolds numbers Reh = 5378 and 29 935 are used to form two-point spatial correlation functions, from which the proper orthogonal modes are determined. Large-scale motions – having length scales of the order of the channel width and represented by a small set of low-order eigenmodes – contain a large fraction of the kinetic energy of the streamwise velocity component and a small fraction of the kinetic energy of the wall-normal velocities. Surprisingly, the set of large-scale modes that contains half of the total turbulent kinetic energy in the channel, also contains two-thirds to three-quarters of the total Reynolds shear stress in the outer region. Thus, it is the large-scale motions, rather than the main turbulent motions, that dominate turbulent transport in all parts of the channel except the buffer layer. Samples of the large-scale structures associated with the dominant eigenfunctions are found by projecting individual realizations onto the dominant modes. In the streamwise wall-normal plane their patterns often consist of an inclined region of second quadrant vectors separated from an upstream region of fourth quadrant vectors by a stagnation point/shear layer. The inclined Q4/shear layer/Q2 region of the largest motions extends beyond the centreline of the channel and lies under a region of fluid that rotates about the spanwise direction. This pattern is very similar to the signature of a hairpin vortex. Reynolds number similarity of the large structures is demonstrated, approximately, by comparing the two-dimensional correlation coefficients and the eigenvalues of the different modes at the two Reynolds numbers.

Effects of free-stream turbulence intensity on laminar separation bubbles

“…This type of analysis was introduced to the fluids community by Lumley [168] and has since been used extensively in analyzing turbulent and transitional flows (e.g., Refs. [23,38,133,[169][170][171]). The methodology of POD is outlined in detail by Berkooz et al [169] but, the method used in this investigation is based on the snapshot method as discussed by Sirovich [172].…”

The role of coherent structures in subgrid-scale energy transfer within the log layer of wall turbulence

“…These observations provide further evidence that vortex organization is a dominant feature of the outer layer. With regard to transport, Liu et al 9 found that large-scale motions having length scales on the order of the channel half-height can be reconstructed with only a few low-order proper orthogonal decomposition ͑POD͒ modes. These low-order modes contained half of the turbulent kinetic energy and over two-thirds of the Reynolds shear stress in the outer region.…”

Three-dimensional structure of a low-Reynolds-number turbulent boundary layer

“…As a given portion of a turbulent flow is composed of structures of varying age and levels of activity, ensemble-averaged approaches may present a more complicated or confused picture of the flow than actually exists. Liu, Adrian & Hanratty (2001), Adrian, Meinhart & Tomkins (2000) and Zhou et al (1999) have provided insight on the generation of coherent hairpin vortex packets containing a multiplicity of spatially organized hairpin-like vortices in channel and boundary-layer flows. The earlier observations by Bandyopadhyay (1980) and Head & Banyopadhyay (1981) on these packets with a characteristic upstream interface, sloping at about 12 • to 20 • , were confirmed using numerical simulations and PIV experiments.…”