Assessing the frictional and baroclinic contributions to stratified wake formation

It is well known that wake formation in stratified flows can occur through either of two processes: (i) frictional coupling between the fluid and obstacle surface; and/or (ii) baroclinic processes in the fluid interior. Here we explore the relative contributions of these two effects in the context of idealized flows past hills of various widths and heights.

We first map the parameter space dependence for flows both with and without applied surface friction as a function of the non-dimensional height Nh/U and slope h/L of the hill. For the free-slip problem wakes occur only for sufficiently large Nh/U, with the threshold height for the wake increasing with increasing h/L. For all h/L the transition to the wake regime is nearly coincident with the appearance of upstream blocking. With the addition of surface friction a second wake regime appears at small Nh/U and large h/L. The critical obstacle slope for this regime is smallest at N = 0 and increases with increasing Nh/U. The parameter dependence of the surface drag (both pressure and skin friction) and vertical momentum flux is also discussed.

Several of the large Nh/U cases are re-examined using a method for separating the vorticity and flow fields into baroclinic and frictional parts. It is shown that for small h/L the wake is driven primarily by baroclinic effects. However, with increasing obstacle slope the role of the frictional flow becomes gradually more pronounced. For slopes at laboratory scales (h/L = 2.0) the frictional part of the flow appears to dominate while baroclinicity plays a secondary role.