Oblique transition in a laminar Blasius boundary layer

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/ω_ts, ±β/β_ts) = (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, (α_w, ±β_w) = (α_ts,I, ±β_ts,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, ω_ts(= 2πf_o), of an unstable eigenmode corresponding to k_ts = k_w (where k =±[α²+β²]^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 2β_w was observed. As expected, the maximum r.m.s. narrow-band streamwise velocity fluctuations, u_t(f_o), 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 ]dU/dζ[mid ], exist between peaks and valleys and appear to generate an explosive growth in the velocity fluctuations. The maximum values of u_t no longer occur at peak locations of the stationary structure but at locations of spanwise inflection points. The magnitude of u_t scales with [mid ]dU/dζ[mid ]. A nonlinear interaction of two non-stationary modes was conjectured as a possible mechanism for the enhancement of the streak ampliflcation rate.