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Transient energy growth of a swirling jet with vortex breakdown

Published online by Cambridge University Press:  02 October 2018

Gopalsamy Muthiah  and
Arnab Samanta Open the ORCID record for Arnab Samanta [Opens in a new window]
Gopalsamy Muthiah
Affiliation:
Department of Aerospace Engineering, Indian Institute of Science, Bangalore 560012, India
Arnab Samanta*
Affiliation:
Department of Aerospace Engineering, Indian Institute of Science, Bangalore 560012, India
*
†Email address for correspondence: [email protected]
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Abstract

We investigate the existence of short-time, local transient growth in the helical modes of a rapidly swirling, high-speed jet that has transitioned into an axisymmetric bubble breakdown state. The time-averaged flow consisting of the bubble and its wake downstream constitute the base state, which we show to exhibit strong transient amplification owing to the non-modal behaviour of the continuous eigenspectrum. A pseudospectrum analysis mathematically identifies the so-called potential modes within this continuous spectrum and the resultant non-orthogonality between these modes and the existing discrete stable modes is shown to be the main contributor to such growth. As the swirling flow develops post the collapsed bubble, the potential spectrum moves further toward the unstable half-plane, which along with the concurrent weakening of exponential growth from the discrete unstable modes, increases the dynamic importance of transient growth inside the wake region. The transient amplifications calculated at several locations inside the bubble and wake confirm this, where strong growths inside the wake far outstrip the corresponding modal growths (if available) at shorter times, but especially at the higher helical orders and smaller streamwise wavenumbers. The corresponding optimal perturbations at initial times consist of streamwise streaks of azimuthal velocity, which if concentrated inside the core vortical region, unfold via the classical Orr mechanism to yield structures resembling core (or viscous) Kelvin waves of the corresponding Lamb–Oseen vortex. However, in contrast to that in Lamb–Oseen vortex flow, where critical-layer waves are associated with higher transient gains, here, such core Kelvin modes with the more compact spiral structure at the vortex core are seen to yield the maximum transient amplifications.

JFM classification

Instability: Instability Vortex Flows: Vortex Flows Vortex Flows: Vortex instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 856 , 10 December 2018 , pp. 288 - 322
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Copyright
© 2018 Cambridge University Press 

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