Author:
ANDERSSON PAUL,BRANDT LUCA,BOTTARO ALESSANDRO,HENNINGSON DAN S.
Abstract
A scenario of transition to turbulence likely to occur during the development of
natural disturbances in a flat-plate boundary layer is studied. The perturbations at
the leading edge of the flat plate that show the highest potential for transient energy
amplification consist of streamwise aligned vortices. Due to the lift-up mechanism
these optimal disturbances lead to elongated streamwise streaks downstream, with
significant spanwise modulation. Direct numerical simulations are used to follow the
nonlinear evolution of these streaks and to verify secondary instability calculations.
The theory is based on a linear Floquet expansion and focuses on the temporal,
inviscid instability of these flow structures. The procedure requires integration in the
complex plane, in the coordinate direction normal to the wall, to properly identify
neutral modes belonging to the discrete spectrum. The streak critical amplitude,
beyond which streamwise travelling waves are excited, is about 26% of the free-stream
velocity. The sinuous instability mode (either the fundamental or the subharmonic,
depending on the streak amplitude) represents the most dangerous disturbance.
Varicose waves are more stable, and are characterized by a critical amplitude of about
37%. Stability calculations of streamwise streaks employing the shape assumption,
carried out in a parallel investigation, are compared to the results obtained here
using the nonlinearly modified mean fields; the need to consider a base flow which
includes mean flow modification and harmonics of the fundamental streak is clearly
demonstrated.
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics
Cited by
348 articles.
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