Coherent structures, uniform momentum zones and the streamwise energy spectrum in wall-bounded turbulent flows
Large-scale motions (LSMs) in wall-bounded turbulent flows have well-characterised instantaneous structural features (Kovasznay et al., J. Fluid Mech., vol. 41 (2), 1970, pp. 283–325; Meinhart & Adrian, Phys. Fluids, vol. 7 (4), 1995, pp. 694–696) and a known spectral signature (Monty et al., J. Fluid Mech., vol. 632, 2009, pp. 431–442). This work aims to connect these previous observations through the development and analysis of a representative model for LSMs. The model is constructed to be consistent with the streamwise energy spectrum (Monty et al. 2009) and amplification characteristics of the Navier–Stokes equations (McKeon & Sharma, J. Fluid Mech., vol. 658, 2010, pp. 336–382), and is found to naturally recreate characteristics of instantaneous turbulent structures, including a bulge shape (Kovasznay et al. 1970) and the presence of uniform momentum zones (Meinhart & Adrian 1995) in the streamwise velocity field. The observed structural similarity between the LSM representative model and instantaneous experimental data supports the use of travelling wave models to connect statistical and instantaneous descriptions of coherent structures, and clarifies a simple general equivalency between symmetry in a Reynolds-decomposed velocity field and asymmetry in the laboratory frame.
© 2017 Cambridge University Press. Received 12 May 2017; revised 20 June 2017; accepted 16 July 2017; first published online 15 August 2017. This work was made possible through the support of a National Defense Science and Engineering Graduate (NDSEG) Fellowship and United States Air Force grants FA9550-12-1-0060 and FA9550-16-1-0361. The authors would like to thank Dr S. Dawson for his work on the boundary layer resolvent code.