Size and intensity of vortex structures in a simulated supercell as seen by the kinematic vorticity number
Lisa Schielicke, Peter Névir and Uwe Ulbrich Institute of Meteorology, Free University of Berlin, Germany
1. Problem of vortex 3. Model set-up 100 4. “Dancing Twisters”: Evolution of
) 200 a k detection The simulation of the supercells was P simulated supercell (2) as seen by W h (
300 e done with the WRF Model (Version 3.6.1) r u
s 400 s
On all scales, meteorological processes e using the implemented WRF test case of r 500 P are closely related to vortices within the 600 a quarter-circle supercell sounding 700 800 900 atmospheric fluid. The defining (Weisman and Klemp, 1982) as basis. The 1000 properties of these vortex structures are set of equations is convection permitting -20 -10 0 10 20 30 Temperature (°C) their size, circulation, lifetime and (fully-compressible, nonhydrostatic). The Fig.2a: Original sounding, travel speed. Although, intuitively it is model domain has a size of 250x200km temperature and dewpoint clear what a vortex is, it is rather with a resolution of 1km. The output was (adopted from Morrison, 2012) s
8 l (2) analysed on a 5 minutes basis over a 6 e complicated to find a (mathematical) v ) 4 (1) e l s /
duration of 3.5 hours. In order to study 2 l m e
definition and the issue is still open ( 0 (3) d d
n -20 -10 0 10 20 30 40 50 60 different vortex ensembles, we made 3 o
i -2
(Jeong and Hussain, 1995; Wu et al., w M - -4
experiments with modifications of the V 2007). Furthermore, the omnipresence of -6 sounding (Fig 2 a,b): -8 shear in atmospheric flows complicates -10 -12 the accurate detection of the vortex U-wind (m/s) (1) Original sounding (qcs) Fig.2b: Hodographs of original boundaries which can appear as (2) Doubled wind speed of (1) and modified soundings for WRF experiments, displayed elongated streamers. Vorticity thresholds (3) Linear shear (v-component=0) 10 m - 7.5 km in 100 m steps might work well in specific heights, however they need to be adjusted for different heights. Y ( km) ) In this work,we will introduce a method (km Fig. 3a X Y (km) ) that allows to extract vortex cores from (km Fig. 3b X Y ) (km) (km the 3-dimensional flow giving consistent Fig. 3c X sizes. The method has already been tested for large-scale flows (Müller et al., 2015, Schielicke et al. 2015) and will here be tested in high-resolution data of s l simulated supercells. e v e l
l e d o
2. Kinematic vorticity M number Wk
Mathematical basis is the velocity gradient tensor in two dimensions:
with the symmetric rate-of-strain tensor m) Y (km) (k T X ) Fig. 3d Y (km SS=(Vvv+(Vvv) )/2 and the antisymmetric (km) X Fig. 3e T m) (k vorticity tensor ΩΩ=(Vvv-(Vvv) )/2 which are Fig. 3a-i: Isosurfaces of (smoothed) vorticity Y (km) X -3 -1 Fig. 3f ) invariants of the velocity gradient tensor [(±1,±5)·10 s ] in the field of Wk>1 (lighter colors=low Y (k (km m) X values of ζ). Cells are viewed from the back (cell motion Fig. 3g m) (invariant under rotation/translation of Y ( (k indicated by black arrow) km) X Fig. 3h m) the reference system). Y (km) (k Fig. 3i X In 2D, the local motion around a point 5. Tracking of vortex structures – case (2) can be decomposed by an isotropic expansion, shearing and stretching Fig. 4A-c: show the deformation (S) and by a rigid body identified vortex structures (black rotation (Ω)Ω) (Fig. 1). Area-preserving motions contours) for some time steps at model level 7 (≈3.5 km above the surface). Tracks of cyclonic (red) and anti- cyclonic (blue) Isotropic Stretching Shearing vortices have been expansion added; '+' and 'x' denote the position Deformation of the vortex center Fig.1: Local motion around a point in the actual time step. Vorticity field The kinematic vorticity number Wk is is given in colors. Fig. 4a Fig. 4b Fig. 4c given by the ratio of the norms of vorticity tensor and strain rate tensor (Truesdell, 1954): 6. Statistics of vortex 7. Comparison with 7. Conclusions ensembles large-scale cyclones The Wk-method was tested in highly- resolved data (1 km) of numerically The Wk-method has been used previously For Wk>1, the local rate of rotation Vortices of the 3 different simulations modelled supercells. Main conclusions of in order to study large-scale cyclones prevails over the local rate of were analysed concerning their intensity this work are: (and anticyclones). The distribution of deformation. A pure shearing motion is (circulation) and their size distribution. The Wk-method defines a vortex as a The total ensembles show quite similar large-scale cyclones resemble that of given by Wk=1. If Wk<1, deformation region of rotation prevailing over vortex structures on the mesoscale in the prevails over rotation. behavior especially in the medium range deformation It therefore cuts out nicely experiments. It seems to give a universal (see Fig. 5a,b) even though their wind vortex regions. law for the moved mass (circulation*area profiles were quite different. However, While vorticity thresholds need to be or circulation*radius) which might the most intense case (2) with doubled adjusted in different heights, the Wk- 3. Methods describe the roll-up process of vortices wind speed of the original sounding method gives consistent sizes Vortex areas and intensities are detected shows different behavior at the lower (Fig. 6). with help of the Wk-fields as follows: throughout the atmosphere and allows and upper bounds of the distribution to estimate circulations i.e. intensities Vortex size is given Vortex intensity is with a tendency to larger sizes and by region of W >1 given by circulation The Wk-method allows to study vortex k intensities (as was expected). The around the center evolutions and interactions (“dancing Ω>0 : cyclonic distributions of anticyclonic cells are Ω<0 : anticyclonic C=∮ v⋅ds twisters”). equal to that of cyclonic cells. Statistics of vortex ensembles reveal Vortices are extracted for every level scale-free properties for vortex and later displayed on staggered fields. structures on different scales which are The tracking method connects areal maybe relatedto the self-similar roll-up overlaps of vortex regions for successive process of vortices time steps (time increment ∆t). References: Therefore, identified regions at time t (1) Jeong, Hussain, 1995: On the identification of a vortex, J. Fluid Mechanics, 285, 69-94. (2) Morrison, 2012: On the robustness of aerosol effects on an idealized supercell storm are advected by the mean wind inside simulated with a cloud system-resolving model. Atmos Chem Phys,12,7689-7705. (3) Müller, Névir, Schielicke, Hirt, Pültz, Sonntag, 2015: Applications of point vortex (a) (b) equilibria: Blocking events and the stability of the polar vortex. Submitted to Tellus. the region for ∆t/2 forwards and areas at (4) Schielicke, Névir, Ulbrich, 2015: Kinematic vorticity number – a tool for estimating vortex sizes and circulations. Submitted to Tellus. time t+1 are advected ∆t/2 backwards. (5) Truesdell,1954: The kinematics of vorticity, Indiana Univ Press, 232 p. Fig. 5a,b: Probability density distribution of (a) circulations, and Fig.6: Probability density distribution of (6) Weisman, Klemp, 1982: The dependence of numerically simulated storms on vertical wind shear and buoyancy, Mon Wea Rev, 110, 504-520. In case of overlapping areas, a track is (b) sizes of the different experiments mesoscale (blue, case 2) and large-scale (7) Wu, Ma, Zhou, 2007: Vorticity and vortex dynamics. Springer Science & Business Media. formed. (CFSR,0.5°, red; NCEP 2.5°,green) cyclones