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Beaume C, Chini GP, Julien K, et al. Reduced description of exact coherent states in parallel shear flows. Phys Rev E Stat Nonlin Soft Matter Phys. 2015;91(4):043010doi: 10.1103/PhysRevE.91.043010.
Beaume, C., Chini, G. P., Julien, K., & Knobloch, E. (2015). Reduced description of exact coherent states in parallel shear flows. Physical review. E, Statistical, nonlinear, and soft matter physics, 91(4), 043010. https://doi.org/10.1103/PhysRevE.91.043010
Beaume, Cédric, et al. "Reduced description of exact coherent states in parallel shear flows." Physical review. E, Statistical, nonlinear, and soft matter physics vol. 91,4 (2015): 043010. doi: https://doi.org/10.1103/PhysRevE.91.043010
Beaume C, Chini GP, Julien K, Knobloch E. Reduced description of exact coherent states in parallel shear flows. Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Apr;91(4):043010. doi: 10.1103/PhysRevE.91.043010. Epub 2015 Apr 15. PMID: 25974583.
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Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Apr;91(4):043010. doi: 10.1103/PhysRevE.91.043010. Epub 2015 Apr 15.

Reduced description of exact coherent states in parallel shear flows.

Physical review. E, Statistical, nonlinear, and soft matter physics

Cédric Beaume, Gregory P Chini, Keith Julien, Edgar Knobloch

Affiliations

  1. Department of Aeronautics, Imperial College London, London SW7 2AZ, UK.
  2. Department of Mechanical Engineering and Program in Integrated Applied Mathematics, University of New Hampshire, Durham, New Hampshire 03824, USA.
  3. Department of Applied Mathematics, University of Colorado at Boulder, Boulder, Colorado 80309, USA.
  4. Department of Physics, University of California, Berkeley, California 94720, USA.

PMID: 25974583 DOI: 10.1103/PhysRevE.91.043010

Abstract

A reduced description of exact coherent structures in the transition regime of plane parallel shear flows is developed, based on the Reynolds number scaling of streamwise-averaged (mean) and streamwise-varying (fluctuation) velocities observed in numerical simulations. The resulting system is characterized by an effective unit Reynolds number mean equation coupled to linear equations for the fluctuations, regularized by formally higher-order diffusion. Stationary coherent states are computed by solving the resulting equations simultaneously using a robust numerical algorithm developed for this purpose. The algorithm determines self-consistently the amplitude of the fluctuations for which the associated mean flow is just such that the fluctuations neither grow nor decay. The procedure is used to compute exact coherent states of a flow introduced by Drazin and Reid [Hydrodynamic Stability (Cambridge University Press, Cambridge, UK, 1981)] and studied by Waleffe [Phys. Fluids 9, 883 (1997)]: a linearly stable, plane parallel shear flow confined between stationary stress-free walls and driven by a sinusoidal body force. Numerical continuation of the lower-branch states to lower Reynolds numbers reveals the presence of a saddle node; the saddle node allows access to upper-branch states that are, like the lower-branch states, self-consistently described by the reduced equations. Both lower- and upper-branch states are characterized in detail.

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