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  • Journal of Fluid Mechanics, Volume 624
  • April 2009, pp. 33-44

Global stability of a jet in crossflow

  • SHERVIN BAGHERI (a1), PHILIPP SCHLATTER (a1), PETER J. SCHMID (a2) and DAN S. HENNINGSON (a1)
  • DOI: http://dx.doi.org/10.1017/S0022112009006053
  • Published online: 10 April 2009
Abstract

A linear stability analysis shows that the jet in crossflow is characterized by self-sustained global oscillations for a jet-to-crossflow velocity ratio of 3. A fully three-dimensional unstable steady-state solution and its associated global eigenmodes are computed by direct numerical simulations and iterative eigenvalue routines. The steady flow, obtained by means of selective frequency damping, consists mainly of a (steady) counter-rotating vortex pair (CVP) in the far field and horseshoe-shaped vortices close to the wall. High-frequency unstable global eigenmodes associated with shear-layer instabilities on the CVP and low-frequency modes associated with shedding vortices in the wake of the jet are identified. Furthermore, different spanwise symmetries of the global modes are discussed. This work constitutes the first simulation-based global stability analysis of a fully three-dimensional base flow.

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Corresponding author
Email address for correspondence: henning@mech.kth.se
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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

E. Åkervik , L. Brandt , D. S. Henningson , J. Hœpffner , O. Marxen & P. Schlatter 2006 Steady solutions of the Navier–Stokes equations by selective frequency damping. Phys. Fluids 18 (068102), 14.

D. Barkley 2006 Linear analysis of the cylinder wake mean flow. Europhys. Lett. 75, 750756.

J. M. Chomaz 2005 Global instabilities in spatially developing flows: non-normality and nonlinearity. Annu. Rev. Fluid Mech. 37, 357392.

R. Lehoucq , D. Sorensen & C. Yang 1998 ARPACK Users' Guide: Solution of Large-Scale Eigenvalue Problems with Implicitly Restarted Arnoldi Methods. SIAM.

C. D. Pruett , T. B. Gatski , C. E. Grosch & W. D. Thacker 2003 The temporally filtered Navier–Stokes equations: properties of the residual stress. Phys. Fluids 15 (8), 21272140.

P. J. Schmid 2007 Nonmodal stability theory. Annu. Rev. Fluid Mech. 39, 129162.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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