Moderately stable flow over a three-dimensional hill A comparison of linear theory with laboratory measurements

Abstract

Several series of experiments were performed in a stratified towing tank to study the near-field flow of a linearly stratified fluid over an isolated three-dimensional hill. Streamlines were obtained in the laboratory using a stereographic method to determine the paths of plumes of dye released upstream of the hill. Velocities over the hill centre were obtained by analysis of video recordings of dye plumes and with a propeller anemometer. The results of these experiments are compared with numerical solutions, computed using Fast Fourier Transforms, of the linearized equations of motion for an inviscid fluid. Numerical solutions were obtained using two different upper boundary conditions: one represents flow in a fluid of infinite depth and the other flow in a fluid of finite depth. Near the hill surface, the predicted streamline deflections were quite similar in both cases except for Froude numbers close to one in the lee of the hill. Good agreement with the measurements is found for Froude numbers (based on the hill height) greater than about 2.0. For Froude numbers greater than about 4.0, flow patterns were observed to differ only slightly from those for neutral flow.