Experiments on stably and neutrally stratified flow over a model three-dimensional hill

TLDR

The study focuses on the basic flow around three‑dimensional hills, with implications for estimating air‑pollutant dispersion. The paper aims to describe the flow structure over a bell‑shaped hill in stratified and unstratified environments. Experiments were conducted in large towing tanks with stratified saline solutions and in an unstratified wind tunnel, varying Froude numbers 0.1–1.7 and Reynolds numbers 400–275 000, using dye, shadowgraph, and bubble visualization to capture flow structure. At low Froude numbers the results confirm Drazin’s theory and delineate its limits, while at Froude numbers near unity the same lee‑wave and separated‑flow classifications from two‑dimensional studies extend to three‑dimensional hills.

Abstract

This paper describes the flow structure observed over a bell-shaped hill with height h (the profile of which is the reciprocal of a fourth-order polynomial) when it was placed first in a large towing tank containing stratified saline solutions with uniform stable density gradients and second in an unstratified wind tunnel. (A similarly shaped model hill was also studied in a small towing tank.) Observations were made at values of the Froude number F (≃ U/Nh) in the range 0·1 to 1·7 and at F = ∞, where U is the towing speed and N is the Brunt-Väisälä frequency, and at values of the Reynolds number from 400 to 275000. For F ≲ 0·4, the observations verify Drazin's (1961) theory for low-Froude-number flow over three-dimensional obstacles and establish limits of applicability. For Froude numbers of the order of unity, it is found that a classification of the lee-wave patterns and separated-flow regions observed in two-dimensional flows also appears to apply to three-dimensional hills. Flow-visualization techniques were used extensively in obtaining both qualitative and quantitative information on the flow structure around the hill. Representative photographs of dye tracers, potassium permanganate dye streaks, shadowgraphs, surface dye smears, and hydrogen-bubble patterns are included here. While emphasis is centred on obtaining a basic understanding of the flow around three-dimensional hills, the results are applicable to the estimation of air pollutant dispersion around hills.