Lecture 8: Edge Tracking – Walking the Tightrope
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چکیده
In the subcritical transition scenario, there is typically a regime where the linearly stable basic state coexists with the turbulent state. The simplest model of this is a 1D system ẏ = y(12 − y)(y − 1) where the basic state is y = 0, the ‘turbulent’ state is y = 1 and there is an intermediate state y = 12 which separates initial conditions which become turbulent (if y(0) > 12 then y(t) → 1 as t → ∞) from those which laminarise (if y(0) < 1 2 then y → 0 as t → ∞). The state y = 1 2 is special in that it separates these two different types of behaviour and corresponds to neither (if y(0) = 1/2, y(t) = 1/2 ∀ t). Identifying initial conditions which lead to this intermediate behaviour is crucial for understanding transition. An extra dimension is needed in our model to allow this intermediate behaviour to be non-trivial so consider the 2D system
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تاریخ انتشار 2011