Experimental study of upstream influence in the two‐dimensional flow of a stratified fluid over an obstacle†

Linearly stratified flow past a horizontal circular cylinder

The flow of a linearly stratified fluid past a long circular cylinder in a channel is considered experimentally. The characteristics of the flow depend on the internal Froude number F i the Reynolds number Re and the cylinder diameter to fluid depth ratio, d/H . A wide range of characteristic flow fields are observed in the parameter space investigated; i.e. 0.02 ⩽ F i ⩽ 13 , 5 ⩽ Re ⩽ 4000 and 0.03 ⩽ d / H ⩽ 0.20 . A flow regime diagram of F i against Re for these characteristic flows is developed. Some of the lower F i Re experiments are compared with numerical experiments. A theory is advanced which indicates that the dimensionless length, x b ∗ = x b / d of the blocked region ahead of the cylinder should scale as x b ∗ ≈ ( δ / d ) 5 R e F i − 2 , where δ is the thickness of the shear layer between the external flow and the approximately stagnant blocked region; the results of an experimental programme that support this scaling are presented. Measurements are made which indicate that for the range of parameter space in which lee waves occur, the lee wavelengths are predicted to a good approximation by linear theory. A scaling analysis is carried out which suggests that the height of the rotors above the streamwise centreline, Z r ∗ = Z r / d , scales with F i experiments aire in good agreement with this prediction. For conditions under which the wake of the cylinder is turbulent, scaling arguments suggest that the dimensionless maximum width of the wake, γ m ∗ = γ m / d , and the dimensionless streamwise distance at which this maximum occurs, β m ∗ = β m / d , scale as F i 1 2 Experiments are presented which support this scaling.

Obstacle drag in stratified flow

This paper describes an experimental study of the drag of two- and three-dimensional bluff obstacles of various cross-stream shapes when towed through a fluid having a stable, linear density gradient with Brunt-Vaisala frequency, N . Drag measurements were made directly using a force balance, and effects of obstacle blockage ( h / D , where h and D are the obstacle height and the fluid depth, respectively) and Reynolds number were effectively eliminated. It is shown that even in cases where the downstream lee waves and propagating columnar waves are of large amplitude, the variation of drag with the parameter K ( = ND /π U ) is qualitatively close to that implied by linear theories, with drag minima existing at integral values of K . Under certain conditions large, steady, periodic variations in drag occur. Simultaneous drag measurements and video recordings of the wakes show that this unsteadiness is linked directly with time-variations in the lee and columnar wave amplitudes. It is argued that there are, therefore, situations where the inviscid flow is always unsteady even for large times; the consequent implications for atmospheric motions are discussed.