## References

Blesbois, O., Chernyshenko, S. I., Touber, E. & Leschziner, M. A.
2013
Pattern prediction by linear analysis of turbulent flow with drag reduction by wall oscillation. J. Fluid Mech.
724, 607–641.10.1017/jfm.2013.165

Butler, K. M. & Farrell, B. F.
1993
Optimal perturbations and streak spacing in wall-bounded turbulent shear flow. Phys. Fluids A
5 (3), 774–777.10.1063/1.858663

Chernyshenko, S. I. & Baig, M. F.
2005
The mechanism of streak formation in near-wall turbulence. J. Fluid Mech.
544, 99–131.10.1017/S0022112005006506

Davis, R. E.
1974
Perturbed turbulent flow, eddy viscosity and the generation of turbulent stresses. J. Fluid Mech.
63 (4), 673–693.10.1017/S002211207400214X

Duque-Daza, C. A., Baig, M. F., Lockerby, D. A., Chernyshenko, S. I. & Davies, C.
2012
Modelling turbulent skin-friction control using linearised Navier–Stokes equations. J. Fluid Mech.
702, 403–414.10.1017/jfm.2012.189

Farrell, B. F., Gayme, D. F. & Ioannou, P. J.
2017
A statistical state dynamics approach to wall turbulence. Phil. Trans. R. Soc. Lond. A
375, 20160081.

Farrell, B. F. & Ioannou, P. J.
1993
Stochastic forcing of the linearized Navier–Stokes equations. Phys. Fluids A
5 (11), 2600–2609.10.1063/1.858894

Gaster, M., Kit, E. & Wygnanski, I.
1985
Large-scale structures in a forced turbulent mixing layer. J. Fluid Mech.
150, 23–39.10.1017/S0022112085000027

Gritsun, A. & Branstator, G.
2007
Climate response using a three-dimensional operator based on the fluctuation dissipation theorem. J. Atmos. Sci.
64, 2558–2575.10.1175/JAS3943.1

Hussain, A. K. M. F. & Reynolds, W. C.
1970
The mechanics of an organized wave in turbulent shear flow. J. Fluid Mech.
41 (2), 241–258.10.1017/S0022112070000605

Huynh, H. T.2007 A flux reconstruction approach to high-order schemes including discontinuous Galerkin methods. *AIAA Paper* 2007-4079, 1–42.

Kennedy, C. A., Carpenter, M. H. & Lewis, R. M.
2000
Low-storage, explicit Runge–Kutta schemes for the compressible Navier–Stokes equations. Appl. Numer. Maths
35 (3), 177–219.10.1016/S0168-9274(99)00141-5

Kim, J., Moin, P. & Moser, R.
1987
Turbulence statistics in fully developed channel flow at low Reynolds number. J. Fluid Mech.
177, 133–166.10.1017/S0022112087000892

Luchini, P.2018 An elementary example of contrasting laminar and turbulent flow physics. arXiv:1811.11877.
Luchini, P., Quadrio, M. & Zuccher, S.
2006
The phase-locked mean impulse response of a turbulent channel flow. Phys. Fluids
18 (12), 121702.10.1063/1.2409729

Malkus, W. V. R.
1956
Outline of a theory of turbulent shear flow. J. Fluid Mech.
1 (5), 521–539.10.1017/S0022112056000342

McKeon, B.
2017
The engine behind (wall) turbulence: perspectives on scale interactions. J. Fluid Mech.
817, P1.10.1017/jfm.2017.115

Moarref, R. & Jovanović, M. R.
2012
Model-based design of transverse wall oscillations for turbulent drag reduction. J. Fluid Mech.
707, 205–240.10.1017/jfm.2012.272

Newville, M., Stensitzki, T., Allen, D. B. & Ingargiola, A.2014 *LMFIT: Non-Linear Least-Square Minimization and Curve-Fitting for Python*. Zenodo. doi:10.5281/zenodo.11813.
Nikitin, N.
2018
Characteristics of the leading Lyapunov vector in a turbulent channel flow. J. Fluid Mech.
849, 942–967.10.1017/jfm.2018.418

Reynolds, W. C. & Hussain, A. K. M. F.
1972
The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical models and comparisons with experiments. J. Fluid Mech.
54 (2), 263–288.10.1017/S0022112072000679

Reynolds, W. C. & Tiederman, W. G.
1967
Stability of turbulent channel flow, with application to Malkus’s theory. J. Fluid Mech.
27 (2), 253–272.10.1017/S0022112067000308

Roshko, A.
1993
Instability and turbulence in shear flows. In Theoretical and Applied Mechanics 1992, pp. 1–24. Elsevier.

Russo, S. & Luchini, P.
2016
The linear response of turbulent flow to a volume force: comparison between eddy-viscosity model and DNS. J. Fluid Mech.
790, 104–127.10.1017/jfm.2016.4

Sen, P. K. & Veeravalli, S. V.
1998
On the behaviour of organised disturbances in a turbulent boundary-layer. Sadhana
23 (2), 167–193.10.1007/BF02745680

Sen, P. K. & Veeravalli, S. V.
2000
Behaviour of organised disturbances in fully developed turbulent channel flow. Sadhana
25 (5), 423–437.10.1007/BF02703624

Sen, P. K., Veeravalli, S. V., Carpenter, P. W. & Joshi, G.
2007
Organised structures in wall turbulence as deduced from stability theory-based methods. Sadhana
32 (1–2), 51–64.10.1007/s12046-007-0005-y

Trefethen, L. N., Trefethen, A. E., Reddy, S. C. & Driscoll, T. A.
1993
Hydrodynamic stability without eigenvalues. Science
261 (5121), 578–584.10.1126/science.261.5121.578

Vincent, P., Witherden, F., Vermeire, B., Park, J. S. & Iyer, A.
2016
Towards green aviation with python at petascale. In Proceedings of the International Conference for High Performance Computing, Networking, Storage and Analysis, p. 1. IEEE Press.

Witherden, F. D., Farrington, A. M. & Vincent, P. E.
2014
PyFR: an open source framework for solving advection–diffusion type problems on streaming architectures using the flux reconstruction approach. Comput. Phys. Commun.
185 (11), 3028–3040.10.1016/j.cpc.2014.07.011

Witherden, F. D., Vermeire, B. C. & Vincent, P. E.
2015
Heterogeneous computing on mixed unstructured grids with PyFR. Comput. Fluids
120, 173–186.10.1016/j.compfluid.2015.07.016