Modulated patterns in a reduced model of a transitional shear flow

Article English OPEN
Beaume, C ; Knobloch, E ; Chini, GP ; Julien, K (2016)
  • Publisher: IOP Publishing
  • Subject:
    arxiv: Physics::Fluid Dynamics

We consider a close relative of plane Couette flow called Waleffe flow in which the fluid is confined between two free-slip walls and the flow driven by a sinusoidal force. We use a reduced model of such flows constructed elsewhere to compute stationary exact coherent structures of Waleffe flow in periodic domains with a large spanwise period. The computations reveal the emergence of stationary states exhibiting strong amplitude and wavelength modulation in the spanwise direction. These modulated states lie on branches exhibiting complex dependence on the Reynolds number but no homoclinic snaking.
  • References (27)
    27 references, page 1 of 3

    [1] P. Assemat, A. Bergeon and E. Knobloch, Fluid Dyn. Res., 40 (2008) 852-876

    [2] C. Beaume, Proc. Geophysical Fluid Dynamics Program, Woods Hole Oceanographic Inst. (2012) 389-412

    [3] C. Beaume, E. Knobloch and A. Bergeon, Phys. Fluids, 25 (2013) 114102

    [4] C. Beaume, E. Knobloch and A. Bergeon, Phys. Fluids, 25 (2013) 124105

    [5] C. Beaume, E. Knobloch, G. P. Chini and K. Julien, Fluid Dyn. Res., 47 (2015) 015504

    [6] C. Beaume, G. P. Chini, K. Julien and E. Knobloch, Phys. Rev. E, 91 (2015) 043010

    [7] A. Bergeon, J. Burke, E. Knobloch and I. Mercader, Phys. Rev. E, 78 (2008) 046201

    [8] M. Chantry, L. S. Tuckerman and D. Barkley, arXiv:1506.05002 (2015)

    [9] J. H. P. Dawes, SIAM J. Appl. Dyn. Syst., 8 (2009) 909-930

    [10] P. G. Drazin and W. H. Reid, Hydrodynamic Stability, Cambridge University Press (1981)

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