A boundary layer topped by a density interface

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Abstract
A rough-wall turbulent boundary layer which grows into a temperature interface situated at the outer edge is investigated experimentally. Reynolds numbers based on boundary-layer thickness δ range from 4 × 103 to 104. Overall Richardson numbers Ri*, defined in terms of the friction velocity and the boundary-layer thickness, are in the range 0 ≤ Ri* [lsim ] 80. Measurements of the mean profiles and of the variances of the velocity fluctuations show that the interface acts in some respects like a moving wall: the velocity profile tends towards a turbulent Couette-type profile and the longitudinal r.m.s. turbulent velocity begins to be amplified at the base of the interfacial layer and reaches a maximum in about the centre. Time-lag correlations of fluctuating quantities taken just above the centre of the interfacial layer have a behaviour characteristic of internal waves, namely a 90° phase lag between vertical velocity and temperature fluctuations. These waves occur as short wave packets and propagate mainly horizontally. On the base of the interface the correlations exhibit the usual symmetric behaviour.The normalized entrainment velocity ue/u* decreases when Ri* increases but does not follow a power law in Ri*. This is consistent with momentum balance, which indicates that ue/u* also depends on the mean-flow Richardson number Ri0 = gΔTδ/TU02 and on the change in momentum and temperature defect. Momentum balance also shows that, when the undisturbed flow has zero pressure gradient, the boundary layer is expected to separate owing to entrainment when Ri0 ≅ 0.5