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Sodar Measurements of Wing Vortex Strength and Position

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  • 1 Physics Department, The University of Auckland, Auckland, New Zealand
  • | 2 Institute of Meteorology, University of Natural Resources and Applied Life Sciences, Vienna, Austria
  • | 3 Institute of the Built and Human Environment, University of Salford, Salford, United Kingdom
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Abstract

A method is developed for robust real-time visualization of aircraft vortex spatial and temporal development based on measurement data from a line array of sodars. The method relies on using a potential-flow vortex model, with spatial averaging according to the along-beam and transverse spatial resolution of the sodar. The model comprises the wing vortex pair, together with two image vortices below ground such that there is no flow through the ground surface. An analytic solution for the temporal–spatial evolution of this four-vortex system is obtained as an aid to establishing relevant scales and performance criteria for any sodar. Field results from an array of four sodars are used on an individual profile basis (every 2 s of real time) to fit the model parameters of vortex circulation, position, and spacing. This method gives vortex trajectories and strength as a function of real time without dependence on assumptions regarding interactions with the atmosphere. Estimates of parameter uncertainties are also produced in real time, and it is found that estimates of position and spacing can be obtained to around ±4 m and of vortex circulation to ±50 m2 s−1. Recommendations are given for optimizing sodars for vortex measurements using practical technology.

Corresponding author address: Stuart Bradley, Physics Department, The University of Auckland, Private Bag 92019, Auckland, New Zealand. Email: s.bradley@auckland.ac.nz

Abstract

A method is developed for robust real-time visualization of aircraft vortex spatial and temporal development based on measurement data from a line array of sodars. The method relies on using a potential-flow vortex model, with spatial averaging according to the along-beam and transverse spatial resolution of the sodar. The model comprises the wing vortex pair, together with two image vortices below ground such that there is no flow through the ground surface. An analytic solution for the temporal–spatial evolution of this four-vortex system is obtained as an aid to establishing relevant scales and performance criteria for any sodar. Field results from an array of four sodars are used on an individual profile basis (every 2 s of real time) to fit the model parameters of vortex circulation, position, and spacing. This method gives vortex trajectories and strength as a function of real time without dependence on assumptions regarding interactions with the atmosphere. Estimates of parameter uncertainties are also produced in real time, and it is found that estimates of position and spacing can be obtained to around ±4 m and of vortex circulation to ±50 m2 s−1. Recommendations are given for optimizing sodars for vortex measurements using practical technology.

Corresponding author address: Stuart Bradley, Physics Department, The University of Auckland, Private Bag 92019, Auckland, New Zealand. Email: s.bradley@auckland.ac.nz

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