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Stokes problems for moving half-planes. (English) Zbl 0843.76015

New exact solutions of Navier-Stokes equations describing the impulsive and oscillatory driven flows in a half-space or in a channel are presented. These solutions have a two-dimensional structure in the region near to the contact between the half-infinite plates. The exact fundamental solutions are also obtained for the flow in a half-space driven by the tangential edgewise motion of half-infinite plate. These solutions are then used to find the solutions for the channel flows which can be obtained by adding an infinite series solution derived from a reflection procedure, by using the fact that the non-slip boundary condition is satisfied on the top wall.

MSC:

76D05 Navier-Stokes equations for incompressible viscous fluids
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[1] DOI: 10.1016/0021-9290(94)90010-8
[2] Stokes, Trans. Camb. Phil. Soc. 9 pp 8– (1851)
[3] Kerczek, J. Fluid Mech. 62 pp 753– (1974)
[4] Hall, J. Fluid Mech. 146 pp 347– (1984)
[5] Dewey, Trans. ASME 103 pp 177– (1981)
[6] DOI: 10.1146/annurev.fl.08.010176.000421
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