Optimal perturbations and transition energy thresholds in boundary layer shear flows

Abstract

Subcritical transition to turbulence in spatially developing boundary layer flows can be triggered efficiently by finite amplitude perturbations. In this work, we employ adjoint-based optimization to identify optimal initial perturbations in the Blasius boundary layer, culminating in the computation of the subcritical transition critical energy threshold and the associated fully localized critical optimum in a spatially extended configuration, the so called minimal seed. By dynamically rescaling the variables with the local boundary layer thickness, we show that the identified edge trajectory approaches the same attracting phase space region as previously reported edge trajectories, and reaches the region more efficiently.

arXiv comment7 pages, 3 figures; fixed broken link; matches journal ref

References in corpus (9)

• Turbulence transition and the edge of chaos in pipe flow
• Low-dimensional dynamics embedded in a plane Poiseuille flow turbulence : Traveling-wave solution is a saddle point ?
• Snakes and ladders: localized solutions of plane Couette flow
• Minimal seeds for shear flow turbulence: using nonlinear transient growth to touch the edge of chaos
• An optimisation approach for analysing nonlinear stability with transition to turbulence in fluids as an exemplar
• Transition to turbulence in shear flows
• The vanishing of strong turbulent fronts in bent pipes
• A variational framework for flow optimization using semi-norm constraints
• Edge tracking in spatially developing boundary layer flows

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• Minimal seeds for turbulent bands
• Stability analysis of transitional flows based on disturbance magnitude
• Transient growth in a flat plate boundary layer under a stream with uniform shear
• On nonlinear transitions, minimal seeds and exact solutions for the geodynamo