Numerical study of some neutrally and unstably stratified boundary-layer flows over a valley at small Richardson number

A two-dimensional numerical model is utilized to investigate steady-state, three-dimensional turbulent flow over a valley under neutral and unstable thermal stratifications. Four case studies, three of which pertain to unstable conditions, are presented to show the effects of thermal stratification, wind angle, and valley geometry on flow at bulk Richardson numbers near zero.

The numerical results discussed include the channeling of flow by the valley and the distribution of surface shear stress and heat flux. Occurring under neutral conditions as well as unstable ones, channeling is a dynamical phenomenon. A smaller amount of channeling takes place under unstable conditions, with valleys of larger aspect ratio, and in flows whose incoming surface winds make angles in the vicinity of 0° or 90° with the valley axis. The distributions of surface shear stress and heat flux feature two local maxima at the two outer corners of the valley and two local minima at the two corners of the valley floor. The effects on these distributions caused by varying the model parameters are also noted. Results are in excellent qualitative agreement with Taylor’s results for flow over a valley under neutral conditions and, in a comparative neutral case study, in good quantitative agreement. The present work, however, being concerned largely with flows under unstable stratifications, is a considerable extension of Taylor’s paper, which neglects the energy equation since only neutral conditions are considered.