Nonlinear optimal perturbations in plane Couette flow

• Subcritical transition to turbulence can occur in a variety of wall-bounded shear flows when the laminar base state is not subject to linear instability. In this case, perturbations to the base state with a finite but very small amplitude can be amplified by non-normal effects, up to a level where nonlinear interactions come into play. Since transition is often undesired, leading to a dramatic increase in wall drag, it is important to know which kind of (weak) perturbations are susceptible to trigger it if we wish to delay it. A vast amount of litterature has described the linear mechanisms responsible for disturbance amplification. Optimisation methods have yielded linear optimal disturbances[1, 2], the disturbances which exhibit the largest linear growth. Yet the focus has been on linear amplification rather than on actual transition, which requires full nonlinearity to be taken into account. In this study, we go back to the original question of which perturbation is most likely to trigger transition to turbulence. We are hence investigating nonlinear optimal disturbances, those with smallest initial energy which effectively lead to a highly disordered flow. In the recent years, progress in the understanding of subcritical transition was made using the concept of ’edge states’, originating from dynamical systems theory. ’Edge state’ refers to the flow regime reached asymptotically by critical trajectories at the exact onset of transition. It is an unstable flow state and cannot be observed in experiments, but its stable manifold determines the basin of attraction of the base state. Direct numerical simulation in minimal domains of plane Couette flow has shown that the flow at the onset of transition asymptotically approaches an unstable finite-amplitude steady state solution, characterised by wavy streaks and streamwise rolls [3]. Using a shooting method, approach to such steady states is the way to characterise whether a transitional trajectory in phase space is actually an ’edge’ trajectory.

Ämnesord

TEKNIK OCH TEKNOLOGIER  -- Maskinteknik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Mechanical Engineering (hsv//eng)

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Engineering mechanics

Teknisk mekanik

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