A turbulent flow over a curved hill. Part 2. Effects of streamline curvature and streamwise pressure gradient

Abstract

The changes in turbulence in a flow over a two-dimensional curved hill, described in Part 1 (Baskaran, Smits & Joubert 1987), are analysed in the light of transport equations for the turbulent kinetic energy, $\frac{1}{2}\overline{q^2}$, and the primary shear stress, $-\overline{uv}$, in order to infer the way in which the extra strain rates due to streamline curvature and the streamwise pressure gradient contribute to the changes. Interaction between the two extra strain rates is also considered. The triple correlation data presented here are consistent with the fact already established in Part 1 that the upwind boundary-layer structure bifurcates to form two distinct turbulent zones over the hill, namely, an internal boundary layer and an external free turbulent flow. The source terms in the transport equations imply that the effects of streamline curvature and streamwise pressure gradient are felt differently on $\overline{q^2}$ and $-\overline{uv}$. The present experimental results show that the shear stress is more sensitive to streamline curvature than is the turbulent kinetic energy. The anisotropy parameter, $\overline{u^2}/\overline{v^2}$, plays a major role in determining the difference in the behaviour of $\overline{q^2}$ and $-\overline{uv}$ under the influence of streamline curvature. The distribution of turbulent lengthscales follows the general formulae suggested by Bradshaw (1969) for streamline curvature of either sign. The pressure-strain redistribution term deduced from the experimental data is in good agreement with the model of Zeman & Jensen (1987) for flows over hills. The influence of streamwise pressure gradient enters through the normal stress production terms, which appears only in the transport equation for $\overline{q^2}$. The transport terms are found to be affected by streamline curvature. To the thin shear layer approximation, the interaction between streamline curvature and streamwise pressure gradient appears to be weak.