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Weakly nonlinear optimal perturbations

Published online by Cambridge University Press:  12 November 2015

Jan O. Pralits ,
Alessandro Bottaro  and
Stefania Cherubini
Jan O. Pralits*
Affiliation:
DICCA, Università di Genova, Via Montallegro 1, 16145 Genova, Italy
Alessandro Bottaro
Affiliation:
DICCA, Università di Genova, Via Montallegro 1, 16145 Genova, Italy
Stefania Cherubini
Affiliation:
DynFluid, Arts et Metiers ParisTech, 151, Bd. de l’Hôpital, 75013 Paris, France
*
†Email address for correspondence: jan.pralits@unige.it
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Abstract

A simple approach is described for computing spatially extended, weakly nonlinear optimal disturbances, suitable for maintaining a disturbance-regeneration cycle in a simple shear flow. Weakly nonlinear optimals, computed over a short time interval for the expansion used to remain tenable, are oblique waves which display a shorter streamwise and a longer spanwise wavelength than their linear counterparts. Threshold values of the initial excitation energy, separating the region of damped waves from that where disturbances grow without bounds, are found. Weakly nonlinear optimal solutions of varying initial amplitudes are then fed as initial conditions into direct numerical simulations of the Navier–Stokes equations and it is shown that the weakly nonlinear model permits the identification of flow states which cause rapid breakdown to turbulence.

JFM classification

Instability: Instability Instability: Nonlinear instability Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 785 , 25 December 2015 , pp. 135 - 151
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Copyright
© 2015 Cambridge University Press 

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