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Numerical study of viscous starting flow past wedges

  • Ling Xu (a1)

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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Anderson, J. D. Jr. 2005 Ludwig Prandtl’s boundary layer. Phys. Today (December) 58 (12), 4248.
Davies, P. A., Dakin, J. M. & Falconer, R. A. 1995 Eddy formation behind a coastal headland. J. Coast. Res. 11, 154167.
Falcone, M. & Ferretti, R. 1998 Convergence analysis for a class of high-order semi-Lagrangian advection schemes. SIAM J. Numer. Anal. 33, 909940.
Hudson, J. D. & Dennis, S. C. R. 1985 The flow of a viscous incompressible fluid past a normal flat plate at low and intermediate Reynolds numbers: the wake. J. Fluid Mech. 160, 369383.
Jespersen, T. S., Thomassen, J. Q., Andersen, A. & Bohr, T. 2004 Vortex dynamics around a solid ripple in an oscillatory flow. Eur. Phys. J. B 38, 127138.
Koumoutsakos, P. & Shiels, D. 1996 Simulation of the viscous flow normal to an impulsively started and uniformly accelerated flat plate. J. Fluid Mech. 328, 177227.
Luchini, P. & Tognaccini, R. 2002 The start-up vortex issuing from a semi-infinite flat plate. J. Fluid Mech. 455, 175193.
Pierce, D. 1961 Photographic evidence of the formation and growth of vorticity behind plates accelerated from rest in still air. J. Fluid Mech. 11, 460464.
Pullin, D. I. 1978 The large-scale structure of unsteady self-similar rolled-up vortex sheets. J. Fluid Mech. 88, 401430.
Pullin, D. I. & Perry, A. E. 1980 Some flow visualization experiments on the starting vortex. J. Fluid Mech. 97, 239255.
Strang, G. 1968 On the construction and comparison of difference schemes. SIAM J. Numer. Anal. 5 (3), 506517.
Xu, L. & Nitsche, M. 2014 Scaling behaviour in impulsively started viscous flow past a finite flat plate. J. Fluid Mech. 756, 689715.
Xu, L. & Nitsche, M. 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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