, 44:86 | Cite as

Development of a potential vortex-hazard index to predict cruise-level wake turbulence encounters

  • J Saravanakumar
  • C Arshad Shameem
  • T N VenkateshEmail author


A pair of counter-rotating trailing vortices formed as a consequence of lift generation poses a potential threat to the encountering aircraft. In recent years, incidents/accidents involving wake turbulence confrontation at cruise altitude are increasing due to increase in the number of super-heavy category aircraft. The vertical separation distance between two airplanes guided by the Federal Aviation Administration (FAA) could be inadequate in certain cases. In this article, a new approach has been proposed to predict the probable area of the persistence of trailing vortices produced by large aircraft. It includes the development of an index with multiple atmospheric effects on the vortices. Also, the impact of the wake from a distinct airplane is incorporated. The performance assessment of the index in predicting the cruise-level wake vortex encounters has been made using various scenarios that happened in the recent past. Weather Research and Forecasting (WRF) model is employed to simulate the atmospheric flow conditions of chosen situations. We found that the method successfully predicts all the cases considered in this study.


Aviation weather hazards aircraft wake vortices potential vortex-hazard index cruise-level encounters wake turbulence WRF 



wingspan of the generating aircraft (m)


turbulence kinetic energy (J/kg)


acceleration due to gravity (\(\hbox {m/s}^2\))


atmospheric turbulence intensity percentage


constant for shear production


\(\Delta z\), length scale for shear production (m)


mass of the generating aircraft (kg)


measure of the turbulence kinetic energy (m/s)


initial separation distance between the vortices

(m); for elliptical loading, \((\pi /4)b\)


half of the initial separation distance between

the vortices (m)


distance along the flight path of the generating

aircraft (km)


time in UTC


magnitude of atmospheric velocities along the

flight path of the generating aircraft (m/s)


velocity component of wind in x, y and z directions,

respectively, along the flight path of the

generating aircraft (m/s)


cruise velocity of the generating aircraft (m/s)


cross-wind along the flight path of the

generating aircraft (m/s)


tail wind along the flight path of the

generating aircraft (m/s)


descent velocity of the vortices at any

given \(\tau \) (m/s)


initial descent velocity (m/s)


centre of the elliptical area enclosing air masses


lateral position of the port and starboard

vortices, respectively


vertical position of the port and starboard

vortices, respectively

\(\Gamma \)

circulation value of the vortices at any

given \(\tau \) (m2/s)

\(\Gamma _0\)

initial circulation value of the vortices

\(\Gamma _1,\Gamma _2\)

circulation value of the port and starboard

vortices, respectively

\(\Theta \)

angle of rotation

\(\theta \)

aircraft heading concerning the positive x-axis

\(\rho _c\)

density at cruise altitude (\(\hbox {kg/m}^3\))

\(\tau \)

time in seconds (s)

\(\tau _{max}\)

maximum time the vortices can

persist in the atmosphere (s)

\(\varphi ,\lambda ,h\)

latitude, longitude and altitude of the

generating aircraft, respectively, at any given t

\(\psi \)

potential vortex-hazard index

\(\Omega \)

angular velocity



This work was carried out as a part of SERB/DST Project Number SB/S4/AS-145/2014. The support is gratefully acknowledged. The authors are thankful to Ms Asha V and Ms K Veena for their support. They also thank NCAR for making WRF available in the public domain and NCEP for providing the FNL datasets. They further thank Prof Joseph Mathew and Dr V Ramesh for their valuable comments. They appreciate the valuable comments and suggestions by the anonymous reviewer, which have led to improvements of this paper.


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Copyright information

© Indian Academy of Sciences 2019

Authors and Affiliations

  • J Saravanakumar
    • 1
  • C Arshad Shameem
    • 1
  • T N Venkatesh
    • 1
    Email author
  1. 1.CTFD DivisionCSIR-National Aerospace LaboratoriesBengaluruIndia

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