Drag force on a circular cylinder in stratified flow: A two-dimensional numerical study

Using two-dimensional numerical simulations, we investigate a circular cylinder in a stratified flow with a pycnocline of a smooth density profile. We are particularly concerned about the difference between stratified flows and their homogeneous, or unstratified, counterparts in drag coefficients. It is well known that the characteristics of a stratified flow depend on the Reynolds number Re and the internal Froude number Fr. First, we change the incoming flow velocity, with the Reynolds number and the internal Froude number varying simultaneously, in the ranges of 76≤Re≤579 and 0.14≤Fr≤1.046, respectively. We find that the flow experiences a sequence of flow patterns, namely “multiple centerline structures,” “isolated mixed regions,” and “vortex shedding,” as we increase this combination, agreeing well with the previous experiments in the low Re and Fr ranges. Meanwhile, the mean drag coefficient decreases, and it drops below the value for a homogeneous state as an empirical stability parameter, k, drops below unity, indicating the transition from a lee-wave dominant wake to an unsteady, vortex shedding wake. This unique variation of drag coefficient is more clearly shown in another situation, when we fix the Reynolds number at Re = 234 while varying the Froude number within 0.094≤Fr≤4.192. In such a situation, we observe a stable “double eddy” pattern at Fr = 1.87, around which a minimum of mean drag coefficient is reached. At this critical point, we understand that the stratification in the flow inhibits lee-side separation, while the internal waves have not yet played a significant role. Although we observe turbulence-like, strong mixing regions in the far downstream wake for some specific cases, it is argued that the current two-dimensional simulations might not be able to resolve the high Reynolds number or high Froude number cases.