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Boundary-layer separation and adverse pressure gradient for 2-D viscous incompressible flow

Publication ,  Journal Article
Ghil, M; Liu, JG; Wang, C; Wang, S
Published in: Physica D: Nonlinear Phenomena
October 1, 2004

We study the detailed process of bifurcation in the flow's topological structure for a two-dimensional (2-D) incompressible flow subject to no-slip boundary conditions and its connection with boundary-layer separation. The boundary-layer separation theory of M. Ghil, T. Ma and S. Wang, based on the structural-bifurcation concept, is translated into vorticity form. The vorticily formulation of the theory shows that structural bifurcation occurs whenever a degenerate singular point for the vorticity appears on the boundary; this singular point is characterized by nonzero tangential second-order derivative and nonzero time derivative of the vorticity. Furthermore, we prove the presence of an adverse pressure gradient at the critical point, due to reversal in the direction of the pressure force with respect to the basic shear flow at this point. A numerical example of 2-D driven-cavity flow, governed by the Navier Stokes equations, is presented; boundary-layer separation occurs, the bifurcation criterion is satisfied, and an adverse pressure gradient is shown to be present. © 2004 Elsevier B.V. All rights reserved.

Duke Scholars

Published In

Physica D: Nonlinear Phenomena

DOI

ISSN

0167-2789

Publication Date

October 1, 2004

Volume

197

Issue

1-2

Start / End Page

149 / 173

Related Subject Headings

  • Fluids & Plasmas
  • 4903 Numerical and computational mathematics
  • 4902 Mathematical physics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics
 

Citation

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Ghil, M., Liu, J. G., Wang, C., & Wang, S. (2004). Boundary-layer separation and adverse pressure gradient for 2-D viscous incompressible flow. Physica D: Nonlinear Phenomena, 197(1–2), 149–173. https://doi.org/10.1016/j.physd.2004.06.012
Ghil, M., J. G. Liu, C. Wang, and S. Wang. “Boundary-layer separation and adverse pressure gradient for 2-D viscous incompressible flow.” Physica D: Nonlinear Phenomena 197, no. 1–2 (October 1, 2004): 149–73. https://doi.org/10.1016/j.physd.2004.06.012.
Ghil M, Liu JG, Wang C, Wang S. Boundary-layer separation and adverse pressure gradient for 2-D viscous incompressible flow. Physica D: Nonlinear Phenomena. 2004 Oct 1;197(1–2):149–73.
Ghil, M., et al. “Boundary-layer separation and adverse pressure gradient for 2-D viscous incompressible flow.” Physica D: Nonlinear Phenomena, vol. 197, no. 1–2, Oct. 2004, pp. 149–73. Scopus, doi:10.1016/j.physd.2004.06.012.
Ghil M, Liu JG, Wang C, Wang S. Boundary-layer separation and adverse pressure gradient for 2-D viscous incompressible flow. Physica D: Nonlinear Phenomena. 2004 Oct 1;197(1–2):149–173.
Journal cover image

Published In

Physica D: Nonlinear Phenomena

DOI

ISSN

0167-2789

Publication Date

October 1, 2004

Volume

197

Issue

1-2

Start / End Page

149 / 173

Related Subject Headings

  • Fluids & Plasmas
  • 4903 Numerical and computational mathematics
  • 4902 Mathematical physics
  • 4901 Applied mathematics
  • 0102 Applied Mathematics