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Viscous-Inviscid Interactions in a Boundary-Layer Flow Induced by a Vortex Array

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Abstract

In this paper, we investigate the asymptotic validity of boundary-layer theory. For a flow induced by a periodic row of point-vortices, we compare Prandtl’s boundary-layer solution to Navier-Stokes solutions with different Reynolds numbers. We show how Prandtl’s solution develops a finite-time separation singularity. On the other hand, the Navier-Stokes solutions are characterized by the presence of two distinct types of viscous-inviscid interactions that can be detected by the analysis of the enstrophy and of the pressure gradient on the wall. Moreover, we apply the complex singularity-tracking method to Prandtl and Navier-Stokes solutions and analyze the previous interactions from a different perspective.

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Acknowledgement

The work of the authors has been partially supported by the GNFM of INDAM.

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Authors and Affiliations

  1. CNR, Istituto per l’Ambiente Marino Costiero (IAMC), Via L. Vaccara 61, 91026, Mazara del Vallo, TP, Italy

    Francesco Gargano

  2. Dipartimento di Matematica e Informatica, Università degli studi di Palermo, Via Archirafi 34, 90100, Palermo, Italy

    Marco Sammartino & Vincenzo Sciacca

  3. Department of Mechanical, Materials, and Aerospace Engineering, Illinois Institute of Technology, 10 West 32nd Street, Chicago, IL, USA

    Kevin Cassel

Authors
  1. Francesco Gargano
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  2. Marco Sammartino
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  3. Vincenzo Sciacca
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  4. Kevin Cassel
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Correspondence to Francesco Gargano.

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In honor of Professor Salvatore Rionero, on the occasion of his 80th birthday.

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Gargano, F., Sammartino, M., Sciacca, V. et al. Viscous-Inviscid Interactions in a Boundary-Layer Flow Induced by a Vortex Array. Acta Appl Math 132, 295–305 (2014). https://doi.org/10.1007/s10440-014-9904-1

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