Linearly stratified flow past a horizontal circular cylinder

Abstract

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.