Experimental studies of strongly stratified flow past three-dimensional orography

Abstract

Stably stratified flows past three-dimensional orography have been investigated using a stratified towing tank. Flows past idealized axisymmetric orography in which the Froude number, Fh=U/Nh (where U is the towing speed, N is the buoyancy frequency and h is the height of the obstacle) is less than unity have been studied. The orography considered consists of two sizes of hemisphere and two cones of different slope. For all the obstacles measurements show that as Fh decreases, the drag coefficient increases, reaching between 2.8 and 5.4 times the value in neutral flow (depending on obstacle shape) for Fh[les ]0.25. Local maxima and minima in the drag also occur. These are due to the finite depth of the tank and can be explained by linear gravity-wave theory. Flow visualization reveals a lee wave train downstream in which the wave amplitude is O(Fhh), the smallest wave amplitude occurring for the steepest cone. Measurements show that for all the obstacles, the dividing-streamline height, zs, is described reasonably well by the formula zs/h=1−Fh. Flow visualization and acoustic Doppler velocimeter measurements in the wake of the obstacles show that vortex shedding occurs when Fh[les ]0.4 and that the period of the vortex shedding is independent of height. Based on velocity measurements in the wake of both sizes of hemisphere (plus two additional smaller hemispheres), it is shown that a blockage-corrected Strouhal number, S2c =fL2/Uc, collapses onto a single curve when plotted against the effective Froude number, Fhc=Uc/Nh. Here, Uc is the blockage-corrected free-stream speed based on mass-flux considerations, f is the vortex shedding frequency and L2 is the obstacle width at a height zs/2. Collapse of the data is also obtained for the two different shapes of cone and for additional measurements made in the wake of triangular and rectangular at plates. Indeed, the values of S2c for all these obstacles are similar and this suggests that despite the fact that the obstacle widths vary with height, a single length scale determines the vortex-street dynamics. Experiments conducted using a splitter plate indicate that the shedding mechanism provides a major contribution to the total drag (∼25%). The addition of an upstream pointing ‘verge region’ to a hemisphere is also shown to increase the drag significantly in strongly stratified flow. Possible mechanisms for this are discussed.