Abstract
The linear and nonlinear stability with respect to 2D and 3D perturbations is investigated for the natural-convection flow of air in a differentially heated enclosure, with a height over width ratio of four, and assumed periodicity in the lateral direction. At the high Rayleigh numbers considered, the flow consists of boundary layers along all walls and a thermally stratified core region. The solution of the 3D, unsteady Navier-Stokes equations is numerically approximated by Chebyshev-Fourier expansions. After computing a 2D base flow, 3D perturbations are introduced. The linear growth is examined by linearization of the convection terms, and the nonlinear growth is computed by retaining the nonlinear convection. 3D perturbations turn out to be less stable than 2D perturbations. The 3D structures consist of counter-rotating longitudinal convection rolls in the boundary layers along the horizontal walls.
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© 1996 Kluwer Academic Publishers
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Henkes, R.A.W.M., Le Quéré, P. (1996). Linear and Nonlinear Unstable 3D Waves for Boundary Layers in Differentially Heated Enclosures. In: Duck, P.W., Hall, P. (eds) IUTAM Symposium on Nonlinear Instability and Transition in Three-Dimensional Boundary Layers. Fluid Mechanics and Its Applications, vol 35. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-1700-2_6
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DOI: https://doi.org/10.1007/978-94-009-1700-2_6
Publisher Name: Springer, Dordrecht
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