Abstract
It is demonstrated that the vertical profile of gradient Richardson number, Ri, can be shaped by control of the working-section inlet temperature profile. In previous work (Hancock and Hayden in Boundary-LayerMeteorol 168:20–57, 2018; 175:93–112, 2020; 180:5–26, 2021) the inlet temperature profile had been specified but without control of the profile of Ri in the developed-flow region of the working section. Control of the inlet temperature profile is provided by 15 inlet heaters (spread uniformly across the height of the working section), allowing control of the temperature gradient over the bulk of the boundary layer, and the overall temperature level above that of the surface. The bulk Richardson number for the 11 cases covers the range 0.01–0.17 (there is no overlying inversion). In the upper ≈ 2/3 of the boundary layer, the Reynolds stresses and turbulent heat flux are controlled by the gradient in mean temperature, while in the lower ≈ 1/3 they are controlled both by this gradient and by the level above the surface temperature. In three examples, Ri is approximately constant at 0.07, 0.10 and 0.13 across the bulk of the layer. The previous observation of horizontally homogenous behaviour in the temperature profiles in the top ≈ 2/3 of the boundary layer but not in the lower ≈ 1/3 is repeated here, except when, tentatively, Ri does not exceed 0.05 over the bulk of the boundary layer. Favourable validation comparisons are made against two sets of local scaling systems and field data over the full depth of the boundary layer, over the range 0.006 ≤ Ri ≤ 0.3, or, in terms of height and local Obukhov length, 0.005 ≤ z/L ≤ 1.