A Novel Velocity-Vorticity Method for Simulating Boundary-Layer Disturbance Evolution and Control

  • Christopher Davies
  • Peter W. Carpenter
  • Duncan A. Lockerby
Conference paper
Part of the IUTAM Symposia book series (IUTAM)


For a wide class of wall-bounded incompressible fluid flows it is possible to derive a system of governing equations that involves only two vorticity transport equations, for two vorticity components, together with a Poisson equation for a single velocity component. This system of three equations in three unknowns remains fully equivalent to the usual primitive variables form of the Navier-Stokes equations. The reduction in the number of equations to be solved and the number of variables that require storage makes the formulation attractive for computational purposes. In addition, some difficulties that are associated with more conventional velocity-vorticity formulations can be avoided.

The utility of the new formulation has been demonstrated by numerical simulations conducted for disturbance development and control in boundary-layers involving steady suction and blowing slots, interactive MEMS devices, compliant surfaces and absolute instability.


Secondary Variable Absolute Instability Compliant Wall Suction Slot Parabolized Stability Equation 
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  1. 1.
    Herbert, Th. (1997) Parabolized stability equations. Ann. Rev. Fluid Mech. 29, 245–283MathSciNetADSCrossRefGoogle Scholar
  2. 2.
    Kleiser, L., Zang, T. (1991) Numerical simulation of transition in wall-bounded shear flows. Ann. Rev. Fluid Mech. 23, 495–537ADSCrossRefGoogle Scholar
  3. 3.
    Lingwood, R. J. (1995) Absolute instability of the boundary layer on a rotating disc. J. Fluid Mech. 299, 17–33MathSciNetADSMATHCrossRefGoogle Scholar
  4. 4.
    Lingwood, R. J. (1996) An experimental study of absolute instability of the rotating-disk boundary-layer flow. J. Fluid Mech. 314, 373–405ADSCrossRefGoogle Scholar
  5. 5.
    Gaster, M., Linnick, M. N. (1995) The perturbations produced in a boundary layer by wall suction. Bull. Amer. Phys. Soc. 40, 1915Google Scholar
  6. 6.
    Metcalfe, R. W., Battistoni, F., Ekeroot, J., Orszag, S. A. (1991) Evolution of boundary layer flow over a compliant wall during transition to turbulence. In: Boundary Layer Transition and Control, Cambridge, UK. Royal Aeronautical Soc., London, 36. 1–36. 14Google Scholar
  7. 7.
    Davies, C., Carpenter, P. W. (1997) Numerical simulation of the evolution of Tollmien-Schlichting waves over finite compliant panels. J. Fluid Mech. 335, 361–392MathSciNetADSMATHCrossRefGoogle Scholar
  8. 8.
    Rathnasingham, R. Breuer, K. S. (1997) Coupled fluid-structural characteristics of actuators for flow control. AIAA J. 35, 832–837Google Scholar
  9. 9.
    Fasel, H., Rist, U., Konzelmann, U. (1990) Numerical investigation of the three-dimensional development in boundary-layer transition. AIAA J., 28, 29–37MathSciNetADSCrossRefGoogle Scholar
  10. 10.
    Rist, U., Fasel, H. (1995) Direct numerical simulation of controlled transition in a flat-plate boundary layer. J. Fluid Mech. 298, 211–248ADSMATHCrossRefGoogle Scholar
  11. 11.
    Davies, C., Carpenter, P. W. (1997) A novel velocity-vorticity formulation of the Navier-Stokes equations with applications to numerical simulation of boundary layer disturbance evolution. Fluid Dynamics Research Centre Tech. Rep., 97/2, University of Warwick, UK.Google Scholar
  12. 12.
    Carpenter, P. W., Davies, C., Lockerby, D. A. (1998) A novel velocity-vorticity method for simulating the effects of MEMS actuators on boundary layers. In: Proc. 3rd Asian CFD Conf., Bangalore, India. Indian Inst., Bangalore, 44–49.Google Scholar
  13. 13.
    Cooper, A. J., Carpenter, P. W. (1997) The stability of rotating-disc boundary-layer flow over a compliant wall. Part 2. Absolute instability. J. Fluid Mech. 350, 261–270MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Christopher Davies
    • 1
  • Peter W. Carpenter
    • 2
  • Duncan A. Lockerby
    • 2
  1. 1.School of Mathematical and Information ScienceCoventry UniversityCoventryUK
  2. 2.Fluid Dynamics Research CentreUniversity of WarwickCoventryUK

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