Large eddy simulations of atmospheric vortex streets

Atmospheric vortex streets which are also known as Kármán vortex streets consist of a double row of opposite rotating, mesoscale eddies. They can develop in the leeward region of a steep island or an isolated topography in the atmospheric boundary layer. Numerous observations reveal that the marine boundary layer is well mixed during the occurrence of a vortex street. It is further characterised by an elevated inversion which lies below the island top and strong steady winds are blowing from a roughly constant direction. Furthermore, the boundary layer is often capped by stratocumulus clouds which act as natural tracer for the eddies. For the first time, atmospheric vortex streets were simulated under the realistic meteorological situation of an elevated inversion by means of large eddy simulation (LES). The parallelised LES model PALM was used. In contrast to mesoscale models which were mainly used in previous numerical studies, LES models resolve the main part of the turbulence spectrum. Thus, it was possible to study the influence of turbulence on atmospheric vortex streets directly. The topography consists of an idealised island having the shape of a two-dimensional Gaussian distribution. We performed LES of a dry boundary layer because clouds are not essential for this phenomenon.

As the formation and separation of eddies in the wake of large islands depends on the Froude number of the flow, it was determined by applying the concept of the dividing streamline using profile data. The calculation of characteristic properties like the distances between cyclonic and anti-cyclonic vortices, the propagation speed of the eddies or the shedding period of a vortex pair, requires the automatic identification and tracking of the eddies. Hence, appropriate analysis techniques had to be developed. They are based on horizontal cross-sections which are coarsened and smoothed at first because the eddies are superimposed by the small scale, turbulent signal in the data. It is known from satellite observations that the vortices span the whole depth of the boundary layer. The high areal resolution of the simulations permits to take a step further and to examine especially the vertical structure of single eddies. Thus, the spatially averaged structure of single eddies in a mature state is presented here for the first time.

The simulation results show that the properties of the vortex streets are almost constant with height and that the eddies extend throughout the whole depth of the boundary layer. The eddies are further characterised by vertical axes, warm cores and pressure minima independent of their sense of rotation. There is a continuous updraft in the order of 10 cm/s in the centre of the vortex. This causes a divergent outflow at the vortex' top where a maximum of potential temperature is located which originates from the lowering of the capping inversion due to the flow divergence. This may be responsible for the cloud-free centres of many observed vortices in satellite pictures. The influence of the turbulence on the vortex streets is small. Merely the mean radius of the eddies descends with increasing turbulence indicating a faster decay of the eddies. This can be ascribed to higher mixing which is associated with higher turbulence. Variations of the wind speed in the simulations affects the Froude number of the flow and therewith its character. In addition to a vortex street, a wavy wake could be simulated due to the exceeding of the critical Froude number of the flow.