Kovasznay flow

Kovasznay flow corresponds to an exact solution of the Navier–Stokes equations and are interpreted to describe the flow behind a two-dimensional grid. The flow is named after Leslie Stephen George Kovasznay, who discovered this solution in 1948.[1] The solution is often used to validate numerical codes solving two-dimensional Navier-Stokes equations.

Normalized streamline () contours of the Kovasznay flow for . Color contours denote normalized vorticity .

Flow description

Let be the free stream velocity and let be the spacing between a two-dimensional grid. The velocity field of the Kovaszany flow, expressed in the Cartesian coordinate system is given by[2]

where is the root of the equation in which represents the Reynolds number of the flow. The root that describes the flow behind the two-dimensional grid is found to be

The corresponding vorticity field and the stream function are given by

Similar exact solutions, extending Kovasznay's, has been noted by Lin and Tobak[3] and C. Y. Wang.[4][5]

References

  1. Kovasznay, L. I. G. (1948, January). Laminar flow behind a two-dimensional grid. In Mathematical Proceedings of the Cambridge Philosophical Society (Vol. 44, No. 1, pp. 58-62). Cambridge University Press.
  2. Drazin, P. G., & Riley, N. (2006). The Navier-Stokes equations: a classification of flows and exact solutions (No. 334). Cambridge University Press. page 17
  3. Lin, S. P., & Tobak, M. (1986). Reversed flow above a plate with suction. AIAA journal, 24(2), 334-335.
  4. Wang, C. Y. (1966). On a class of exact solutions of the Navier-Stokes equations. Journal of Applied Mechanics, 33(3), 696-698.
  5. Wang, C. Y. (1991). Exact solutions of the steady-state Navier-Stokes equations. Annual Review of Fluid Mechanics, 23(1), 159-177.
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