(a) Wind-tunnel facility with the cavity section in close-up. (b) High-speed PIV setup.
A snapshot for TR-PIV data, in a cross-stream plane (x, y), for the case L/θ0 = 76. Colors scale dimensionless vorticity fluctuations and vector field represents velocity fluctuations.
Primary Strouhal numbers based on L are displayed as functions of dimensionless cavity length L/θ0; self-sustained oscillations frequencies (black), side-band peaks (gray), and low frequencies (white). Rectangle dimensions represent uncertainties. The shaded area (yellow) is drawn a posteriori such as to segregate self-sustained oscillation frequencies from most side-band peaks. It is delimited by , with the centerline Strouhal number. Hatched regions highlight side-band frequencies departing from the general scheme.
(a) Mean velocity streamlines colored by normalized mean velocity modulus . Normalized Reynolds tensor components (in %). (b) , (c) , (d) .
Shear-layer local features along streamwise coordinate x/D: (a) cross-stream profiles fitted by a hyperbolic-tangent law; (b) twice the mean velocity 2U m (·), shear strength ΔU (+), and (○); (c) vorticity thickness δω/θ0; (d) the most destabilizing frequency f c = 0.44 c/(πδω) (·), estimated as in a free shear layer, the wave celerity being given by c = U m (x), and the dominant frequency f a L/U 0 = 0.96 (–·–) of the spectrum (on the right).
Normalized power spectral distribution of (a) u ′ from LDV (black) together with an averaged PSD over the 15 PIV series (gray) extracted at the LDV point (x/D = 1.4, y/D = 0.1); (b) fluctuations u ′ (black) and v′ (gray, blue), out of the PIV time series and space-averaged over the impingement vicinity (1.3 ⩽ x/D ⩽ 1.5 and −0.23 ⩽ y/D ⩽ 0.23). Line thickness corresponds to the 99%-confidence interval.
(a) TR-PIV time-series for configuration L/θ0 = 76 for both fluctuating velocity components u ′/U 0 (light) and v′/U 0 (dark) extracted at point (x p /L = 0.96, y p /D = 0); and their corresponding time-frequency diagrams for (b) u ′/U 0 and (c) v′/U 0, respectively. Vertical black lines delimit the time-window used for Sec. V B .
Wave properties of the main frequencies of the flow along the shear layer. (a) Phase evolution with respect to x/L, solid lines corresponding to linear fits. (b) Amplitude variation with respect to x/L. Contributions are shifted vertically for the sake of legibility and straight lines correspond to fits of the exponential form . See text for details.
Iso-surfaces of vorticity fluctuations in the space-time volume (x, y, t), issued of time-resolved PIV data for configuration L/θ0 = 76. (light, yellow) and (dark, blue). Only an abstract of the entire set, such as , is displayed.
A close-up ( ) from Fig. 9 , shown from upstream (a) and below (b).
Space-time diagrams and time-series issued of time-resolved PIV data for configuration L/θ0 = 76, with the same close-up in time as Fig. 9 ( ). The space-time diagrams are obtained at (a) y/D = 0, (b) y/D = −0.3, (c) y/D = −0.7 (streamwise) and at (d) x/L = 0.96, (e) x/L = 0.33 (crosswise). Contour levels of vorticity fluctuations range from (a) −4 (dark)–5.5 (light); (b) −2–2.2; (c) −3–4; (d) −5–5; and (e) −2–2. Three characteristic time-series, for both streamwise and crosswise velocity fluctuations u ′/U 0 and v′/U 0, are extracted at intersections of these space-time planes: at the impingement, (a ∩ d); in the inflow along the downstream wall, (b ∩ d); inside the main recirculation, (c ∩ e). Schematic (f) locates extraction regions.
Real (left) and imaginary (right) parts of global Fourier modes for shear layer frequencies. Arrows represent velocity fluctuations and colors encode vorticity fluctuations normalized by their maximum. (a) and (b) F a (x, y) associated with the dominant peak f a ; (c) and (d) F a2(x, y) associated with its first harmonic 2 f a ; (e) and (f) F ℓ(x, y) associated with the left side-band peak ; (g) and (h) F 2ℓ(x, y) associated with the second left side-band peak ; (i) and (j) F +(x, y) associated with the right side-band peak f + = f a + f b .
Space-averaged spectra of velocity fluctuations, u ′ (black) and v′ (gray, blue), out of time-resolved PIV data. Space averaging is performed over three regions of interest of the cross-stream (xy)-plane: above the cavity near the impingement (a), the downstream half of the cavity (b), and the upstream half of the cavity (c). PSDs are displayed as functions of Strouhal number St D = f D/U 0. Line thickness corresponds to the 99%-confidence interval.
Real part (left) and imaginary part (right) of global Fourier modes for low frequencies in a cross-stream plane (xy). Arrows represent velocity fluctuations, colors encode vorticity fluctuations normalized by their maximum. (a) and (b) associated with ; and (c) and (d) associated with .
Real part (left) and imaginary part (right) of the global Fourier mode , associated with the frequency Hz ( ) out of the broad-band peak.
Dimensionless parameters with uncertainties.
Wave properties measured at y/D = 0.05.
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