The unsteady laminar boundary layer on a semi-infinite flat plate due to small fluctuations in the magnitude of the free-stream velocity

Author:

Ackerberg R. C.,Phillips J. H.

Abstract

Asymptotic and numerical solutions of the unsteady boundary-layer equations are obtained for a main stream velocity given by equation (1.1). Far downstream the flow develops into a double boundary layer. The inside layer is a Stokes shear-wave motion, which oscillates with zero mean flow, while the outer layer is a modified Blasius motion, which convects the mean flow downstream. The numerical results indicate that most flow quantities approach their asymptotic values far downstream through damped oscillations. This behaviour is attributed to exponentially small oscillatory eigenfunctions, which account for different initial conditions upstream.

Publisher

Cambridge University Press (CUP)

Subject

Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics

Reference12 articles.

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2. Ligiiteill, M. J. 1954 The response of laminar skin friction and heat transfer to fluctuations in the stream velocity.Proc. Roy. Soc. A 224,1–23.

3. Lam, S.H. & Rott, N. 1960 Theory of linearized time-dependent boundary layers.Cornell University QSAE Rep. AFOSR TN-60–1100.

4. Ackerberg, R. C. 1970 Boundary-layer separation at a free streamline. Part 1.J. Fluid Mech. 44,211–225.

5. Cole, J. D. 1968 Perturbation Methods in Applied Mathematics.Waltham, Mass. :Blaisdell.

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