Cambridge University Press apologise for an error with the supplementary material of the above article. Additional materials from an unrelated article were erroneously published alongside the intended supplementary material. This has been corrected.

The turbulent boundary layer (TBL) development over an air cavity is experimentally studied using planar particle image velocimetry. The present flow, representative of those typically encountered in ship air lubrication, resembles the geometrical characteristics of flows over solid bumps studied in the literature. However, unlike solid bumps, the cavity has a variable geometry inherent to its dynamic nature. An identification technique based on thresholding of correlation values from particle image correlations is employed to detect the cavity. The TBL does not separate at the leeward side of the cavity owing to a high boundary layer thickness to maximum cavity thickness ratio (δ/t_max = 12). As a consequence of the cavity geometry, the TBL is subjected to alternating streamwise pressure gradients: from an adverse pressure gradient (APG) to a favourable pressure gradient and back to an APG. The mean streamwise velocity and turbulence stresses over the cavity show that the streamwise pressure gradients and air injection are the dominant perturbations to the flow, with streamline curvature concluded to be marginal. Two-point correlations of the wall-normal velocity reveal an increased coherent extent over the cavity and a local anisotropy in regions under an APG, distinct from traditional APG TBLs, suggesting possible history effects.

Different air phase regimes are formed by controlled air injection in a spatially developing flat plate turbulent boundary layer (TBL). The air is introduced via a slot type injector without the use of a backward-facing step or cavitator upstream of the air injection position. The effect of different incoming liquid flow characteristics on the different regimes is investigated by varying both the liquid freestream velocity and the incoming TBL thickness. The latter is realized through changing the position of the air injection along the length of the water tunnel facility. That resulted in a downstream distance based Reynolds number from 1 to 5 million. Three different air phase regimes are identified under different air flow rates and freestream velocities: the bubbly regime, the transitional, and the air layer regime. The morphological differences of each one are described and quantitative analysis is performed based on the non-wetted area in each condition. The incoming TBL as well as the flow around the air layer are measured with planar particle image velocimetry. The latter enabled the determination of the air layer thickness. In addition, the ratio of the air layer to the incoming boundary layer thickness t_air/δ is also calculated (≈ 0.04 – 0.5). This is a significant dimensionless parameter for scaling, which indicates the extent to which the air layer is embedded within the incoming TBL. Depending on the incoming flow conditions, a two or three branch air layer is formed. The length of the air layer is found to increase with increasing liquid freestream velocities. A good agreement between the air layer length and a half gravity wave predicted by the dispersion relation is found. An increase of the air layer length is observed with a decreasing incoming TBL thickness. This is attributed to a decrease in the local mean velocity at the air–water interface due to the TBL growth. Finally, increasing the incoming TBL thickness delays the onset of the air layer regime.

An air layer within a liquid turbulent boundary layer (TBL) is formed by controlled air injection underneath a flat plate. The incoming boundary layer as well as the flow around the air layer were measured with planar particle image velocimetry (PIV). The effect of different incoming liquid flow characteristics on the air layer geometry is investigated by varying both the freestream velocity and the streamwise development length of the TBL. The latter was realized through changing the position of the air injection along the length of the water tunnel facility. Increasing the freestream velocity resulted in an increase of the air layer length, while its maximum thickness remained relatively unaltered. An increase in the TBL development length, had a similarly marginal effect on the resulting maximum air layer thickness but led to a shorter air layer length. The latter could be attributed to a decrease in local mean velocity due to the TBL growth, reflected in a decrease of the air layer to boundary layer thickness ratio (from 0.27 to 0.17). The results of this study are expected to provide insight on the design conditions of an air layer drag reduction system installed in the hull of a ship.