Joint Centre for Mesoscale Meteorology (JCMM)
Vorticity and potential vorticity in stratified flows interactng with an isolated obstacle
by Jorge A Gutierrez and Alan J Thorpe
The production of vorticity and potential vorticity is studied in a low Froude number stratified flow over and around an isolated bell-shaped mountain with a circular base. The effects of background rotation and surface friction have been considered. Without background rotation and shear and using a free-slip lower boundary condition for inviscid flow, the baroclinic mechanism is the main source of horizontal vorticity. This horizontal vorticity is tilted into the vertical and generates two counter-rotating lee-vortices. Only small vertical vorticity is found on the upwind side of the orography. With rotation the baroclinic mechanism remains an important source of horizontal vorticity but it is closely followed by additional tilting terms which depend on the Coriolis parameter. Including rotation weakens the vertical vorticity field in this area.
Simulations of viscous flow using a no-slip boundary condition show that the baroclinic term is then not an important contributor to the horizontal vorticity budget. Much larger values of vertical vorticity are found on the upwind side of the orography than in the other two cases, due to the tilting of the horizontal vortex tubes created by the no-slip boundary condition.
For a westerly flow in the northern hemisphere, negative potential vorticity is produced on the northern flank of the orography and positive potential vorticity is produced on the southern flank. A quantity called normalised potential vorticity is defined to allow the relation between the amount of vorticity and potential vorticity being produced to be quantified. it is produced from early in the integration for both non-rotating and rotating inviscid flows, due to the implicit diffusion implied by the numerical method. In the viscous flow more normalised potential vorticity is produced due to the inclusion of friction.
The onset of vortex shedding due to asymmetries in the flow is also studied. The asymmetries were introduced by including background rotation creating an asymmetry in the upwind flow allowing the lee eddies to be shed.