Journal of Fluid Mechanics



Oblique transition in a laminar Blasius boundary layer


RUDOLPH A. KING a1 and KENNETH S. BREUER a2
a1 NASA Langley Research Center, Hampton, VA 23681, USA
a2 Division of Engineering, Brown University, Providence, RI 02912, USA

Abstract

Oblique transition was experimentally investigated in a Blasius boundary layer formed on a flat plate. This transition mechanism was provoked by exciting a pair of oppositely oriented oblique Orr–Sommerfeld (O–S) modes given by (ω/ωts, ±β/βts) = (1, ±1) in the frequency-wavenumber (spanwise) space. Surface waviness with height Δh and a well-defined wavenumber spectrum that is synchronized with the neutral O–S wavenumber at Branch I, (αw, ±βw) = (αts,I, ±βts,I), was used to provide a steady velocity perturbation in the near-wall region. A planar downstream-travelling acoustic wave of amplitude ε was created to temporally excite the flow near the resonance frequency, ωts(= 2πfo), of an unstable eigenmode corresponding to kts = kw (where k =±[α22]1/2). Possible mechanisms leading to laminar-to-turbulent breakdown were examined for various forcing combinations, εΔh. For small values of εΔh, a peak-valley structure corresponding to a spanwise wavenumber of 2βw was observed. As expected, the maximum r.m.s. narrow-band streamwise velocity fluctuations, ut(fo), occur at peak locations, which correspond to regions with mean streamwise velocity, U, deficits. For the largest value of εΔh, significant mean-flow distortion was observed in the spanwise profiles of U. Large spanwise velocity gradients, [mid R:]dU/dζ[mid R:], exist between peaks and valleys and appear to generate an explosive growth in the velocity fluctuations. The maximum values of ut no longer occur at peak locations of the stationary structure but at locations of spanwise inflection points. The magnitude of ut scales with [mid R:]dU/dζ[mid R:]. A nonlinear interaction of two non-stationary modes was conjectured as a possible mechanism for the enhancement of the streak ampliflcation rate.

(Received July 25 2000)
(Revised July 20 2001)



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