Wake Vortex Transport and Decay in Ground Effect: Vortex Linking with the Ground

15 Pages·2000·0.73 MB·English

by  Proctor, Fred H.

)
AIAA 2000-0757
Wake Vortex Transport and Decay in Ground
Effect: Vortex Linking with the Ground
Fred H. Proctor and David W. Hamilton
NASA Langley Research Center
Hampton, VA
Jongil Han
North Carolina State University
Raleigh, NC
I
i
Z ! ',¢ :,
:X
38th Aerospace Sciences
Meeting & Exhibit
January 10-13, 2000 / Reno, NV
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AIAA-2000-0757
Wake Vortex Transport and Decay in Ground Effect: Vortex Linking
with the Ground
Fred H. Proctor* and David W. Hamilton t
NASA Langley Research Center
Hampton, Virginia
Jongil Han _
North Carolina State University
Raleigh, NC
Abstract
become vertically oriented and which terminates at the
Numerical simulations are carried out with a three- ground. From the simulations eotutueted, the linkhlg time
dimensional Large-Eddy Simulation (LES) model to for IGE appears to be similar to the linking time for
explore the sensitivi_ of vortex decay and tran.wort in vortices inthe.free atmo.where: i.e., afunction ofambient
ground effect (IGE). The vortex decay rates are found to turbulence intensity.
be strongly enhanced following m(L_imum descent into
ground effect. The nmzdimensional decay rate isfi)und to Nomenclature
be insensitive to the initial values of circulation, height, B aircraft wing span
and vortex separation. The it!formation gained ./)'om b,, initial vortex separation - 7zB/4
these simulations is used to construct a sbnple decay g acceleration due to gravity
relationship. This relationship compares" well with Lx,Ly domain length in xand ydirections, respectively
observed data from an IGE ease study. Similarly, a L: domain depth
relationship for lateral drift due m ground £fJect is M mass of generating aircraft
constructed from the LES data. In the second part of this r radius from vortex center
paper, vortex linking with the ground isinvestigated. Our
r,. radius of peak tangential velocity
numerical simulations of wake vortices for IGE show that t time coordinate
avortex may link with its image beneath the ground, (fthe T nondimensional time - t VJbo
intensity of the ambient turbulence is moderate to high.
T,; T at z= Zmin
This linking with the ground (which is obsen,ed in real
cases) gives the appearance ofavortex tube that bends to Va airspeed of generating aircraft
Vo initial vortex descent velocity - F,,/(2 Jr bo)
x horizontal coordinate along flight path
*Research Scientist, Airborne Systems Competency, y horizontal coordinate lateral to fight path
AIAA member Y nondimensional lateral coordinate - y/b,,
*Research Scientist, Airborne Systems Competency z vertical coordinate
tResearch Scientist, Department of Marine, Earth, and Zmi, minimum altitude achieved during vortex descent
Atmospheric Sciences, AIAA member Z, initial height above ground of wake vortex
F vortex circulation
Copyright © 2000 by the American Institute of
F,, initial vortex circulation - M g/(b,,p Va)
Aeronautics and Astronautics. Inc. No copyright is
asserted in the United States under Title 17, U.S. Code. p air density
E ambient turbulence (eddy) dissipation rate
The Government has aroyalty-free license to exercise
_', x-component of vorticity
all rights under the copyright claimed herein for
v kinematic viscosity
Government purposes. All other rights are reserved by
q nondimensional eddy dissipation - (Ebo)"3 V,,l
the copyright owner.
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I.Introduction
showed only a weak sensitivity to the level of ambient
turbulence, and were in very-good agreement with Lidar-
Aircraft wake vortices are formed when vorticity derived observations. The results indicated that enhanced
generated by lift rolls up into two primary trailing decay from ground effect begins a few seconds after the
vortices. The two vortices have a characteristic initial vortices descend to their minimum height, with vortex
separation, b,, which is proportional to the wingspan of decay prior to these times being primarily influenced by
the generating aircraft. The wake vortices are considered stratification and ambient turbulence. The study also
to be "in ground effect" (IGE) when located within one found that vertical oscillations associated with vortex
initial separation of the ground (i.e., z < bo)._ The rebound were less prominent for higher levels of ambient
prediction for the location and intensity of these vortices turbulence, since the secondary vortices were more likely
is important for systems that are to manage safe aircraft to be diminished by the stronger turbulence. Also
spacings. addressed was the influence of ground stress on wake
vortex transport. The study determined that viscous
The complex influence of the ground onwake vortex stress reduced the velocity near the ground and acted to
behavior has been the focus of numerous investigations, decouple the primary vortices from their sub-ground
including the observations by Harvey and Perry,-" images. If ground stress was ignored, unrealistic
Hallock, _Kopp, 4Hallock and Burnham, _Burhnam and divergence of the vortex pairs ensued. The study, did not
Hallock, 6 and Rudis et al.,7 as well as the numerical address Crow instability, or similar linking instabilities,
studies bySchiling, 8Robins and Delisi, 9Zheng and Ash, _°
Corjon and Poinsot, _Corjon and Stoessel, _2and Proctor
Table 1. Salient Characteristics of TASS
and Han/3 Qualitative understanding of basic vortex
transport mechanisms for IGE isknown, but quantitative
relationships are needed. Wake vortex decay isknown to Primitiveequation /non-Boussinesq equationsetTime-
be enhanced byproximity to the ground, but much isto be dependent, nonhydrostatic, compressible.
learned about this behavior. 6
Meteorological framework withoption for either three-
dimensional ortwo-dimensional simulations.
Three-dimensional instability of wake vortices near
the ground islargely unexplored. Lateral linking of the Large Eddy Simulation model with 1st-order subgrid
vortex pair associated with Crow instability _ should be scale turbulence closure - Grid-scale turbulence
less likely due to the increased separation forced by the explicitly computed, while effects of aubgrid-scala
ground's presence. Ground linking -- the linking of a turbulenco modeled by Smegorinsky model with
modifications forstratificationand flowrotation.
vortex with its image vortex beneath the ground plane --
has been observed, =_but thought to be rare. _6 Linking
Ground stress based on Monin-OOukhov Similarity
instabilities can increase the uncertainty of a vortex's
theory.
position and may affect the vortex decay rate as well.
Optional boundary conditions- openconditions utilizes
Semi-empirical vortex prediction algorithms have mass-conservative, nonrefleotive radiation boundary
been developed by Robins etal.I that include the ground's scheme.
influence on lateral separation and vortex rebound.
Explicit numerical schemes, quadratic conservative,
Similar algorithms _7 have been incorporated within
time-split compressible- accurate as well as highly
NASA's Aircraft VOrtex Spacing System (AVOSS). 1s'192° efficient, and essentially free of numerical diffusion.
Improved accuracy of these prediction algorithms depend Space derivatives <x_r_uted on Arakawa C-grid
on the better understanding of vortex transport and decay staggered mesh with 4"-order accuracy forconvective
near the ground. Numerical experiments with a Large terms.
Eddy Simulation (LES) model are being conducted in
order to provide guidance for the enhancement of these Prognostic equations forvapor andatmospheric water
prediction algorithms. :_ substance (e.g. cloud droplets, rain, snow, hail, ice
crystals). Large set ofmicrophysical-parameterization
models.
This paper isacontinuation of the three-dimensional
LES study described in Proctor and Hart, _Jwith further Model applicable tomeso-ffandmicroscale atmospheric
focus on vortex decay within IGE. In Proctor and Han, phenomenon. Initialization modules for simulation of
we investigated the sensitivity over a wide range of convective storms, microbursts, atmospheric boundary
ambient turbulence levels of a wake vortex for a landing layers, turbulence, and aircraft wake vortices.
L-lOll that was observed on 26 September 1997 at
Dallas-Fort Worth (DFW) airport, z-' The simulations
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sincteheassumed
domain had a limited axial depth. In Thermodynamic Equation (Potential Temperature):
the present paper, we address the sensitivity of vortex 20 l _OPoa j 0 _PoUj
decay for IGE, by conducting LES of wake vortices with -- _ _ J¢
c]t Po "Oxj Po OxJ
different initial heights, separations and circulations. The
results are normalized and a simple analytical
+!_---S[p, 'K, °°1
representation for IGE decay isgiven. Similarly, a simple
Po xj Oxj
model based on the LES results is proposed for lateral
drift due toground effect. Inthe second part of this paper,
we examine the occurrence of ground linking and its with the Potential Temperatnre defined as:
sensitivity to ambient turbulence. 0 =r( )_
II. The Model and Initial Conditions
In the above equations, u_is the tensor component of
The numerical model used in this study isa three- velocity, tistime, pisdeviation from atmospheric pressure
dimensional LES model called the Terminal Area
P, z isatmospheric temperature, p isthe airdensity, Cpand
Simulation System 23(TASS), which has been adapted for
simulation of wake vortex interaction with the Cv are the specific heats of air at constant pressure and
atmosphere. 2_ The numerical model used in this study volume, gisthe earth's gravitafonal acceleration, Raisthe
differs from that in many previous investigations, in that: gas constant for dry air, Poo isaconstant equivalent to 1000
1)time-dependent computations are carried out in three- millibars (10"_pascals) of pressure. Environmental state
dimensional space, 2) the formulation isessentially free of variables, e.g., Po, Po and 0o, are defined from the initial
numerical diffusion, "-_3) the computations are LES and at input sounding and are functions of height only.
high Reynolds number, 4) the experiments are initialized
with realistic turbulence fields, and 5) realistic surface- Amodi fled Smagorinsky first-order closure isused for
stress and subgrid turbulence-closure formulations are the subgrid eddy viscosity as:
assumed. Salient characteristics of TASS are listed in
table 1. " I OUi- OU,i +C)Uj).2( OU_. )2
Model Equations
The TASS model contains aprognostic equation set x 41 -OQRis -or2Rir
for momentum, temperature and pressure, and employs a
compressible time-split formulation. Omitting moisture and The subgrid eddy viscosity for momentum, KM.ismodified
coriolis terms (which are not used inthese simulations), the by the Richardson numbers, for stratification, Ris, and for
TASS equation set in standard tensor notation isas follows:
flow rotation, Rir, with _q=3 and %= 1.5.
Momentum:
The subgrid length scale, Is, isdetermined from the
Ou, 4 H _p - OuiuJ +ui_UJ +g(H-l)_i37"-- grid volume and ismatched to the appropriate length scale
Ot Po _xi _xj dxj close to the ground where the flow isunder-resolved. That
is:
1 0 _tli Ouj 20tq
+---_-_ ,PoKMl--+ &j]
p,, xj Oxj Oxi 30x t
= trA[l+(or.A/kera z) 'n-l] z>_tzA/k
Buoyancy Ternl."
L k: :_<A=/2
n=[ 0 PC,, ]
Oo Po Cp
where k is yon Karman's constant, and where mand otare
Pressure Deviation: invariant constants with values defined as m = 3and ct=
0.15. The filter width isbased on the minimal resolvable
¢)p CpP Ouj
--4 - P,, gttj_j3 scale:
Ot Cv Oxj
A= [ 2Ax 2Ay 2Az 11/3
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where
At, AV,and Az are the numerical grid sizes in the is less than 3.0, and finally, performing an inverse FFr
respective x,y,zdirection. back to the physical space. At the same time, the
horizontal domain average temperature and velocity fields
The ground boundary is impermeable with nonslip are forced to maintain their initial vertical profiles by
velocity specifications. The surface stress due to the subtracting the difference every time step. Due tosubgrid
ground isdetermined locally from the wind speed, surface dissipation, the simulation can reach astatistically steady
roughness, and the local thermal stratification. Details of state, inthe sense that the mean turbulence kinetic energy
the surface formulation are in the appendix of reference oscillates in time around a constant value.
[13].
Figure 1shows aone-dimensional energy spectrum
Turbulence Initialization with a -5/3 slope of Kolmogorov's -'7spectrum when the
Prior to vortex initialization, an initial field of turbulent flow field has achieved a statistically steady
resolved-scale turbulence isallowed to develop under an state. Figure 1indicates that our approach can produce a
artificial external forcing at low wavenumbers. 2_The well-developed turbulent flow field that possesses
approach issimilar to that in recent studies with TASS, Kolmogorov's inertial subrange. The eddy dissipation rate
where wake vortex decay and the development of Crow e isestimated from the well-known technique of fitting
instability is examined within a Kolmogorov 27spectrum Kolmogorov's theoretical spectrum in the inertial
of homogeneous turbulence (Han etaL28"20). The method, subrange to the simulated spectra.
however, isslightly different for the present study, due to
the inclusion of the ground. Since periodic boundary Vortex Initialization
conditions are assumed only at the horizontal boundaries, The initial wake vortex field is specified with a
the turbulence forcing is applied only to horizontal simple vortex system that isrepresentative of the post roll-
velocity over each horizontal plane. Nevertheless, the up, wake-vortex velocity field. The vortex system is
influence of the horizontal two-dimensional forcing initialized with the superposition of two counter-rotating
spreads quickly to the vertical direction as well as to the vortices that have no initial variation in the axial direction.
vertical velocity through the mass continuity. The tangential velocity, V,associated with each vortex, is
determined from:
101
V(r)=2_r[l-Exp[-lOI-_)°'75} I
100
where, r is the radius from the center of the vortex, F=
10 -1 the circulation at r >> re, and B is the span of the
generating aircraft. The above formula isbased on Lidar
observations of wake vortices measured early in their
evolution. The model isapplied only at r > r,. and is
matched with a Lamb model profile for r < rc. The
10-_
values assumed for initial vortex separation and
circulation are derived from an aircraft's weight, span,
i0 -4 and airspeed according to conventional formula based on
elliptical loading; i.e., b, =r,B/4, and F_ =4Mgl(rtBpV,,).
10¸ Appropriate vortex image conditions are applied to the
10-2 10-1 100 101 initial wake field to ensure consistency and mass
K2 continuity at the TASS model boundaries.
Figure 1. Turbulence energy xpectrton atz=14mbefi_re
vortex injection. Here, subscripts 2 and 3 denote Except when otherwise noted, the initial vortex
cros._flow and vertical directions, respectively. parameters (table 2) are taken from the observed aircraft
parameters for the L-1011, as was used in Proctor and
Because the TASS code uses a finite difference HanJ 3
numerical scheme, the forcing isachieved byperforming,
first, a two-dimensional fast Fourier transform (FFT) at All simulations are conducted with dimensional
every large time step, then adding aconstant amplitude to variables and assume turbulent flow with a rotational
all the modes with integer wavenumbers whose magnitude Reynolds number (FJr) of- 107.
4
Amencan Institute ofAeronautics and Astronautics
Amean average circulation isreported for each time
Table 2. Initial vortex parameters (baseline). interval bycomputing amean of the circulations from each
Parameter .......................................V...a..!.u..e_ ........................... crossflow plane:
Vortex spacing (b,,) 37 m =1N-
a,b ..ST._ ri a,b
Generating height (Z0 16m (0.432 bo)
• N i
Vortex circulation (F_,) 390 m-"s-_
Vortex core radius 3m (b,,/12.3) Similarly, a mean vortex position isreported for each
time interval by averaging the positions from each
Model Domain Parameters crossflow plane.
Two domain sizes are used for the experiments in
this paper. Ashort domain, which has been truncated in IlL IGE Sensitivity
the x-direction (Lx, Ly, L: = 81 m, 370 m, 81 m), and a
long domain (Lx, Ly, L: = 451 m, 337 m, 81m). For an Three sets of experiments are conducted inorder to
assumed initial vortex separation of b,,=37 m, this would determine the sensitivity of vortex decay within IGE The
translate into: (2.2 x 10x 2.2) bo for the short domain and short domain isassumed which will inhibit theoccurrence
(12.2 x 9.1 x 2.2) bo for the long domain. Both long and of linking instabilities. All of the simulations assume
neutral stratification, no mean ambient winds, and an
short domains are resolved bythe grid sizes listed in table
3. ambient turbulence dissipation rate of e =9.6 x 10_mz
s_. Other initial conditions for the simulations are listed
Table 3. Grid Resolution. in tables 2and 3.
Parameter Value
Sensitivity to Initialization Height
Vertical resolution (Az) 1.5 m
Five experiments are conducted for a vortex
Lateral resolution (zly) 1.5 m
initialization height (Z0 of: 0.32 bo,0.5 bo, 0.65 b,,, 0.84
Axial resolution (At) 2.0 m
b,,,and 1.0 b,,.Comparisons of the experiments are shown
in Fig. 2 as function of nondimensional time. Note that
The advantage of the short domain is that itallows the time coordinate for each experiment isoffset by the
economical calculations of vortex behavior and simplifies time of maximum descent into ground effect; i.e., by
the analysis of results. The longer domain, however, is T_;=T(_,min). The curves for normalized 5-15 m average
less likely to hinder three-dimensional linking instabilities. circulation, as well as the normalized lateral positions tend
A comparison of results from the two domain sizes is
to collapse, once the offset time T_;isaccounted for. As
shown in the appendix. also shown in our previous study, _3vortex decay is
significantly enhanced following maximum penetration
Determination of Vortex Position and Circulation
into IGE. In addition, these results show the decay rate to
Based on the vortex position ineach crossflow plain,
be more or less independent of the vortex initial height,
circulation iscomputed for each crossflow plane according
with the enhanced level of decay beginning roughly 0.25
tO: nondimensional time units following T,
F r( X )= __r(_ dydz
A formula for the decay of average circulation can
The circulation is not computed for any plane where the be obtained from these results as
vorticity vector isbeyond 30_'of the x-axis.
F _Exp[-2(T-To,,) 2/t } (1)
F oo 5
A 5-15 meter averaged-circulation, is computed
according to:
where To, = T_;+0.25 (i.e., 0.25 nondimensional time
_J'_ -.labFr dr units following the time of maximum penetration into
S,_dr ground effect), and F,,,, is the circulation at
nondimensional time T,,,. The above formula is
independent of ambient turbulence and can only be
where a=5 m, and b = 15 m. The 5-15 m average
applied for T> T, +0.25.
circulation is chosen to characterize the intensity of the
vortex, since it quantifies the hazard faced by an
Differentiating the above gives the rate of decay as:
encountering aircraft 3°'31
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1 dF 4 _2(T_Too )2/3
-- -- = Exp{ 1 IGESensitivity TestforVarying VortexHeights (r1=0.091)
Foo dT 15(T_Too )1/3 5 VortexVerticalPositionHistory(Port)
(A)
Aplot of the curve from Eq. 1isshown also in Fig.
2c and agrees very well with the LES results. 09
0.8 _'_ "
An empirical relationship for lateral spread within '\ ...:.............
IGE can be determined from the LES results as well. The
vortices, which start at a lateral distance from the flight
path of y = _ Vzbo,diverge lateral with time due to the
0.4 ---'"
influence of the ground. Figure 2b indicates (in the 0.3 "'" ........... _=032bo
absence of crosswind) that the vortices asymptote toward 0.2 ....... _=065b=
y = 2bo; approaching a maximum separation ofabout 4bo. .... _=084b a
0.1 -- z_=1COb,
Based on these results, an empirical relationship for ; 'I .... ;
vortex drift due to ground effect is:
Nondlrnenslonal Time (T -Ta)
Y=1.385 (T-Tt;) °'227 for T > T_; + 0.25 (2) IGESensitivity TestforVaryingVortexHeights(r1=0,091)
Vortex LateralPosition History (Port)
where Y isthe normalized lateral position from the flight 2.5 (a)
path. The vortex separation, b = 2Ybo, also can be
predicted for IGE with Eq. 2. A plot of the curve from 2 S
2
Eq. 2iscompared with LES data in Fig. 2b. • 4 ''_+......
The lateral drift rate can be determined by
1.5
differentiating (2) giving:
|t
VG = d__Y = o.3173( T _ TG )-0.773 for T> T_; + 0.25 //7" _- _=0SOb,
dT '_o.s
7_=I00b_
where V,; is the nondimensional velocity for lateral drift -- Moc_ Fit
, ,,, I,,, i I,, l+l+l i I i i i |
due to ground effect (this velocity can be made 0 1 2 3 4
dimensional by multiplying by the initial vortex sink rate, NondlmenslonalTime(T-To)
Vo).
IGESensitivity TestforVaryingVortex Heights(q=0.091)
Vortex5-15mAveragedCirculationHistory(Port)
Sensitivity to Initial Vortex Spacing (c)
In order to further evaluate the sensitivity of our
results and test the validity of Eq. 1, three additional
experiments are conducted, which assume different initial 0.19 "-"IIL_. .-.-..-..-..-... Z__==oOs_obu.+
vortex spacings (bo) as listed in table 4. An initial '_+dk ....... Z=oeSbo
circulation of 400 m2sJ and an initial height of Z,= 0.432 "-o".8_ _ .I... z_=:i0o0bS,.°o
b, is assumed for each experiment. Values for Z, and 0.7 I _
nondimensional turbulence dissipation are slightly
different in these experiments due to the variation in bo.
Table 4. Initial vortex separation (bo)and corre,wondiug go0,.5 "'.%_.:_..:. ,_
0.4 """4.
initial altitude (Z,) and dintensionless turbulence intensi_.'
(r]) for sensitivity to initial vortex sFacin _ cases. 0.31 ,,, 0I,, 1 2 3 4 5
Nondlrnenslonal Tkne(T-Ta)
b. (m) Zi (m)
30 13 0.0671 Figure 2. Sensitivity to vortex initiation height.
37 16 0.0897
Nondimensional height (a), nondimensional lateral
49 21.2 0.1291 position (b), and nondimensional 5-15 m average
circulation (c) vs nondimensional time. "Decay mtMel" b_
(C)from Eq.1and "Curve fit" in (B)fi'om Eq.2.
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IGE Sensitivity Test for Varying Initial Separation (b0) IGE Sensitivity Test for Varying Initial Circulation
Vortex Vertical Position History (Zi=0.43bo) Vortex Vertical Position History (A)
1
(A)
1.4
0.9
1,2 0.8
,.%0.7
_0.6
08 _0.5
0.6
0.3 _ -- 1"=300m21s, q=0.1183
0.4 ....... I" •$S0 re:Is, q: 0.1014
0.2 .... I" •400 m:/s, q=0.0007
0.2 w_-- bboo==3479 mm,, qq==00..01828971 0.1 I" •450 re=Is, q=00789
O( L i i L1I .... 2I .... 3I .... 4I , , , , I5 0 .... 1I .... 2I .... 3I , , , , 4| _ , = , 5[
Nondlmenslonal Time (tb_/V.) Nondlmensional Time (!boP/o)
IGE Sensitivity Test for Varying Initial Separation (bo) IGE Sensitivity Test for Varying Initial Circulation
Vortex Lateral Position History (Zi=0.43bo) Vortex Lateral Position History
(B)
2.5 (B)
_._2
&
t.5
I,5
8
o. f
|i
_ _ -- I'. = 300 m:ls, q=0.1183
_0.5 ..........._-- bb=o•=3307 mm,, Tq1==00..00887817 0.5 ........... ll''. == 345000 mm=Z/lss,, qq==00..10001847
-- l+ = 450 mZls, q•0+0789
-- Mockll FR -- M_IF#
0( ' ' ' L1t ; B' I 2I .... 3I .... 4I .... 5I 01 i, i i 1I i i i I 2I .... 3I .... 4I .... 5I
Nondlmenslonal Time (tb,/V) Nondlmenslonal Time (tb_/+)
IGE Sensitivity Test for Varying Initial Separation (bo) IGE Sensitivity Test for Varying Initial Circulation
Vortex 5-15 mAverage Circulation History (Zi=0.43b0) Vortex 5-15 mAverage Circulation History
(c)
1.2 (c) 1.2
1 ._......_...._ b:o:=:130:mm, q:-_0.0:67l1:oT:: 1 .t..........i i [I =z 23_00 mmZZl/ss,, q_==00..11412803
....... I = 350 mZ/s, q=0.1014
0,8 0,8 ...._ [l"'' =•440500 mm==//ss,, qq•=00..00870879
o o
.0.6
0.4 04
0.2 0.2
0( , ; , ,1I b , , ,2I , _ R L3I .... 4I .... 5I 01 I, I I 1I I i i I 2I I ' ' '3I .... 4I .... 5I
No_lmens_nal Time (tb_=) Nondlmensional Time (tbJV=)
Figure 3. Same as Fig. 2, but.fi)r sensitivity to initial Figure 4. Same as Fig.2, but .fi)r ._'ensitivi_, to initial
vortex spacing. vortex circulatiort.
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The results presented in Fig. 3show that the curves intensity, or specifically, the eddy dissipation rate 2s,32._
again collapse to a similar value when normalized, and The goal of the experiments in this section isto examine
that the proposed formulas for IGE decay and lateral drift ground linking and any sensitivity that itmay have to the
are in excellent agreement with the LES results. level of ambient turbulence. All of the experiments
Enhanced levels of decay due to IGE begin at T=0.5 assume the long domain so as to permit linking
(which is T_;+0.25) for all three cases. instabilities. The experiments also assume the parameters
listed in tables 2and 3, as well as the initial sounding in
Sensitivity to Initial Circulation Fig. 5. The nondimensional turbulence strengths, rl, used
In the third set of experiments, five simulations with in these experiments, range from 0.233 to 0.75. These
different initial circulations are conducted (table 5). All values represent atypical range between moderate to very
else is assumed equal, with q being different due to its turbulent atmospheric boundary layers.
dependency on Fo.
70,a8170o,b8t O[
Again, the curves collapse with atight spread (Fig.
4), and the proposed IGE decay and drift formulas are in
excellent agreement with LES results.
60 l 60
Table 5. hdtial circulation (Fo) attd corresponding _o _ _5o
dimensionless turbulence intensi_for Fosensitivity cases. 40_ , =_=,o_ 1
F,, (m2s"j) ............. 11 .....................................
250 0.1420
300 0.1183 20
350 0.1014
400 0.0887 10 1
450 0.0789
..... 30 3 0 1 2
0v(K) v(m/s)
IV. Comparison with Observed Case. Figure 5. hzitial pr_file of a) ambient potential
temperature and b) crosswind for DFW, 26 September
In this section, the new formula for IGE decay 1997, 20:09 UTC.
(Eq. I) iscompared with the LES simulation for alanding
L-lOll, which was observed at 20:09 UTC on 26
September 1997 at Dallas-Fort Worth (DFW) airport. DALLAS 1997INGROUND EFFECTCASE
97/09/2620:09:24 GMT
The input sounding for temperature and crosswind is Vortex 5-15mAveragedCirculation Comparison
shown in Fig. 5. The simulation isconducted with the
short domain and with the parameters listed in tables 2 400 Clrn Q
and 3. The simulation includes an ambient turbulence "[3 .... [] L3_DOLbEsS PoPro_(rqt-(-'0q=O23233)5)
field with, e =1.654 x I0'_m2s_ (rl =0.2349), which is 300 _1_[] ......... DLES Slat(q=0233)
Decay Mod_
very close to the ambient value observed at z=40 m. The
average circulation from both the port and starboard
vortices is show in Fig. 6. The slightly faster decay for
the starboard vortex may be due to the opposite sign
vorticity of the ambient crosswind. Also included in Fig. °1o 0
6 for comparison, is measured Lidar data for the port
vortex. The LES results and Lidar data show reasonable
agreement with the circulation decay given by Eq. 1. t , , I , i II , L , I , , , I i , , , Ii L
1 2 3 4 5
Nondimensional Time (tb,,/V°)
V. Ground Linking Experiments
Figure 6. Average circulation vs mmdimen.sional time
In the free atmosphere, the linking process begins as Jor observed DFW case. Cmnparison of LES, Lidar, and
the counter-rotating circulations of avortex pair connect, IGE decay model (Eq. 1).
producing crude vortex rings. The time at which this
linking takes place isa known function of the turbulence
8
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ETA = 0.3_B6 (T= 0.0 -- 4.0)
T (_) TOP VIEW SIDE VIEW
liD-
,:
o.o-_I
I++... . .__ .... +_____--.__:...,,__:: _--"....
o ...... ....
-tooW].+.
150 _- Ill +_ i" +, ff
,., m-r---+ _; ..... -. _._ ......... ,,.Tm'MlllLdi_a_l_,li, Tl_,_l+_J#,+J
1.u oi. -_- - - L_ ..... T ..... _1.,
:::]- •....
tlol - _ . . _ +i Ilil_ll______!_+_,', "" +' _+ _ _ l _,_ ,£ r
-_lo't I
150_I . - . ,,',_+- .._i lid __ii : r _ .,.... , +, ' + +'+i I¢-<• '
"- z,_r,.+ __,._3m,...* t,..+ . +_,
2.o_,__
::-+-1 - - :IIl|l :_
Iii11 11, • " +
100 _ ° _ "+ _- . " "
+ ,+_,++_ , '+
2D+, r
-1BO'L /
+L+
,,L._)+'._+_1:_,,
3.5 * + +. ' "P.P ,_'+t
.f- +, , +_ , .
104 " "_il_,_O '+
-_1 " -
4.0 _L "; "t:+ " ' + _ -b '1
_ . _ _-,_-.,+._ ;,.--_.--+2-D+i:_
-Ioo , f. , ;
-_ -1'1:0 0 1'_
Figure 7. Timeevolution within IGEofwake vortex pair.lor rl=0.388. Top (xy)andside (._+,zv)iewqfwake vorriee.+
at increments 0.5 nondimensional time units.
9
American Institute of Aeronautics and Astronautics