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How linear is wall-bounded turbulence?
1. A. N. Kolmogorov, “The local structure of turbulence in incompressible viscous fluids a very large Reynolds numbers,” Dokl. Akad. Nauk SSSR 30, 301–305 (1941);
8. K. M. Butler and B. F. Farrell, “Optimal perturbations and streak spacing in wall-bounded shear flow,” Phys. Fluids A 5, 774–777 (1993).
12. S. Corrsin, “Local isotropy in turbulent shear flow,” NACA Research Memorandum 58B11, Washington, 1958.
15. P. J. Schmid and D. S. Henningson, Stability and Transition in Shear Flows (Springer, 2001), pp. 55–58.
16. W. M. Orr
, “The stability or instability of the steady motions of a perfect liquid and of a viscous liquid. Part I: A perfect liquid
,” Proc. R. Ir. Acad. A 27
25. J. Jiménez, G. Kawahara, M. P. Simens, M. Nagata, and M. Shiba, “Characterization of near-wall turbulence in terms of equilibrium and ‘bursting' solutions,” Phys. Fluids 17, 015105 (2005).
31. B. F. Farrell and P. J. Ioannou, “Stochastic forcing of the linearized Navier–Stokes equations,” Phys. Fluids A 5, 2600–2609 (1993).
40. P. G. Drazin and W. H. Reid, Hydrodynamic Stability (Cambridge University Press, 1981).
42. A. A. Townsend, The Structure of Turbulent Shear Flow, 2nd ed. (Cambridge University Press, 1976), Chap. 3.12.
43. B. F. Farrell and P. J. Ioannou, “Optimal excitation of three-dimensional perturbations in viscous constant shear flow,” Phys. Fluids A 5, 1390–1400 (1993).
44. H. Tennekes and J. L. Lumley, A First Course in Turbulence (MIT Press, 1972).
49. A. Lozano-Durán, O. Flores, and J. Jiménez, “The three-dimensional structure of momentum transfer in turbulent channels,” J. Fluid Mech. 694, 100–130 (2012).
50. R. García-Mayoral and J. Jiménez, “Hydrodynamic stability and breakdown of the viscous regime over riblets,” J. Fluid Mech. 678, 317–347 (2011).
53. S. Hoyas and J. Jiménez, “Scaling of the velocity fluctuations in turbulent channels up to Reτ = 2003,” Phys. Fluids 18, 011702 (2006).
55. P. K. Yeung, S. B. Pope, A. G. Lamorgese, and D. A. Donzis, “Acceleration and dissipation statistics of numerically simulated isotropic turbulence,” Phys. Fluids 18, 065103 (2006).
60. H. Lamb, Hydrodynamics, 2nd ed. (Cambridge University Press, 1895).
61. G. K. Batchelor, An Introduction to Fluid Dynamics (Cambridge University Press, 1967).
62. This limit is obtained by noting that the motion conserves the energy log |sin (2z0)|, and equating the energies of the two configurations in which the rows are either aligned along the centerline, z0 = π/4, or maximally separated at z0 = iH.
64. R. García-Mayoral and J. Jiménez, “Scaling of turbulent structures in riblet channels up to Reτ ≈ 550,” Phys. Fluids 24, 105101 (2012).
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The relevance of Orr's inviscid mechanism to the transient amplification of disturbances in shear flows is explored in the context of bursting in the logarithmic layer of wall-bounded turbulence. The linearized problem for the wall normal velocity is first solved in the limit of small viscosity for a uniform shear and for a channel with turbulent-like profile, and compared with the quasiperiodic bursting of fully turbulent simulations in boxes designed to be minimal for the logarithmic layer. Many properties, such as time and length scales, energy fluxes between components, and inclination angles, agree well between the two systems. However, once advection by the mean flow is subtracted, the directly computed linear component of the turbulent acceleration is found to be a small part of the total. The temporal correlations of the different quantities in turbulent bursts imply that the classical model, in which the wall-normal velocities are generated by the breakdown of the streamwise-velocity streaks, is a better explanation than the purely autonomous growth of linearized bursts. It is argued that the best way to reconcile both lines of evidence is that the disturbances produced by the streak breakdown are amplified by an Orr-like transient process drawing energy directly from the mean shear, rather than from the velocity gradients of the nonlinear streak. This, for example, obviates the problem of why the cross-stream velocities do not decay once the streak has broken down.
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