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Numerical study of viscous starting flow past wedges

Abstract

This paper presents a numerical study of vortex formation in the impulsively started viscous flow past an infinite wedge, for wedge angles ranging from $60^{\circ }$ to $150^{\circ }$. The Navier–Stokes equations are solved in the vorticity-streamfunction formulation using a time-splitting scheme. The vorticity convection is computed using a semi-Lagrangian method. The vorticity diffusion is computed using an implicit finite difference scheme, after mapping the physical domain conformally onto a rectangle. The results show details of the vorticity evolution and associated streamline and streakline patterns. In particular, a hierarchical formation of recirculating regions corresponding to alternating signs of vorticity is revealed. The appearance times of these vorticity regions of alternate signs, as well as their dependence on the wedge angles, are investigated. The scaling behaviour of the vortex centre trajectory and vorticity is reported, and solutions are compared with those available from laboratory experiments and the inviscid similarity theory.

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Corresponding author
Email address for correspondence: lingxu@umich.edu
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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

J. D. Anderson Jr. 2005 Ludwig Prandtl’s boundary layer. Phys. Today (December) 58 (12), 4248.

T. S. Jespersen , J. Q. Thomassen , A. Andersen  & T. Bohr 2004 Vortex dynamics around a solid ripple in an oscillatory flow. Eur. Phys. J. B 38, 127138.

G. Strang 1968 On the construction and comparison of difference schemes. SIAM J. Numer. Anal. 5 (3), 506517.

L. Xu  & M. Nitsche 2015 Start-up vortex flow past an accelerated flat plate. Phys. Fluids 27, 033602.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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