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Spatial structure of the Lamb vector in a separated three-dimensional shear flow around a wing

Juan Carlos Bilbao-Ludena* and George Papadakis†

  • *Contact author: j.bilbao-ludena17@imperial.ac.uk
  • †Contact author: g.papadakis@imperial.ac.uk
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Phys. Rev. Fluids 10, 074701 – Published 7 July, 2025

DOI: https://doi.org/10.1103/cqgv-lxq3

Abstract

The Lamb vector appears in the rotational form of the Navier-Stokes equations and is the source of vortical flow nonlinearity that results in the cascade of energy from large to small scales. We investigate the three-dimensional spatial structure of this vector in the near wake of a NACA0018 wing with square wingtip profile at 10∘ angle of attack and chord-based Reynolds number of 5000. At these conditions, a large recirculation zone forms in the wake and the flow transitions in the separating shear layer. We analyze the spatial footprint of the three components of the Lamb vector and its divergence (the latter for both the mean and the fluctuating velocity fields). By integrating the vertical component of the Lamb vector across the cross-stream direction (which is equal to the vorticity flux for two-dimensional flows) we obtain the local aerodynamic loading along the wing. The vorticity flux is equal to zero at the trailing edge, thereby confirming the Taylor-Sears condition away from the wing tip. We also apply Helmholtz decomposition to extract the potential and solenoidal parts of the Lamb vector. The former part is dominant in the attached and separated shear layers, while the latter is present downstream of the recirculation zone where the flow is turbulent. We decompose the Euclidean norms of the Lamb vector and its potential part into terms that are determined by the time-average field only, the fluctuating field only, as well as mixed terms. We find that the mixed terms play a dominant role and are the slowest to decay.

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Phys. Rev. Fluids 10, 074701– Published 7 July, 2025
  • Received 12 September 2024
  • Accepted 6 June 2025
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