Similarity treatment of moving-equilibrium turbulent boundary layers in adverse pressure gradients

Abstract

Dimensional analysis is applied to the velocity profile U(y) of turbulent boundary layers subjected to adverse pressure gradients. It is assumed that the boundary layer is in moving or local equilibrium in the sense that the free-stream velocity U∞ and kinematic pressure gradient α = ρ−1dP/dx vary only slowly with the co-ordinate x. This assumption implies a rather complicated general equation for the velocity gradient dU/dy which may be considerably simplified for several specific regions of the flow. A general family of velocity profiles is derived from the simplified equations supplemented by some experimental information. This family agrees well with almost all existing data on velocity profiles in adverse-pressure-gradient turbulent boundary layers. It may be used for the derivation of a skin-friction law which predicts satisfactorily the values of the wall shear stress at any non-negative value of the pressure gradient. The variation of the boundary-layer thickness with x is also predicted by dimensional considerations.

The relative importance of ejections and sweeps to momentum transfer in the atmospheric boundary layer

“…If S o does capture the statistical properties of the ejection-sweep cycle, then these properties are a "by-product" of how the boundary conditions produce non-uniformity in the first-and second-order velocity statistics. Within the canopy sublayer, the critical boundary condition is the fact that the drag of the canopy on the flow is extended in the vertical rather than being confined to the ground plane; within the outer layer, the critical boundary condition is the decay of turbulence near the ABL top; and within the surface layer, the critical condition is the balance between the control of the dynamics by the upper and lower boundary conditions (Kader and Yaglom 1978).…”

Direct numerical simulation of a separated turbulent boundary layer

“…Townsend (1961) refined the theory based on mixing length to the case of non-zero (but positive) wall shear stress and obtained a law with both squareroot and logarithmic parts based on u τ as a velocity scale. Kader & Yaglom (1978) extended the Stratford velocity profile to the case of positive wall stress. However, they kept the square-root law based on u p , and let the influence of a non-zero wall shear stress be accounted for by varying the constants.…”

The Continental-Shelf Bottom Boundary Layer

“…Generally, accelerated flows are treated separately, since their effects can involve relaminarization of the flow. The effects of adverse pressure gradients (see Kader & Yaglom 1978, Yaglom 1979 can be estimated using similarity theory in much the same way that stratified flows are treated. An additional length scale bp = pu!/ldp/dxl is introduced.…”