Burning Invariant Manifolds (BIMs) are one-way barriers to front propagation in fluid flows.

We describe these manifolds theoretically, and demonstrate their existence in experimental systems. The rest is application of this essential idea to many related problem areas.

What is an invariant manifold?

Let's restrict our discussion to two-dimensional flows where things are much simpler. If you remember the old video game "Snake":

http://i.imgur.com/dAtcCfH.gif

then you know that the snake will almost inevitably run into itself (this is why the game is hard). Similarly, a generic trajectory in a (time-independent) flow runs into itself. This means it is an invariant curve. In the 2D context, this is an invariant barrier (codimension 1 = can't just step around).

It is easy to find these invariant barriers in real fluids.

EXAMPLE PIC

These curves we have described are barriers to passive scalars. That is, a fluid parcel or tracer (think of abit of pepper floating on the fluid) will not penetrate such a barrier.

Our main research question is:

How do fronts propagating within such a flow interact with these (or other) invariant curves?

Recall how these manifolds are found for passive flows. We examinine the ODE looking for fixed points, and then the attached manifolds.

Reacting flows are often phrased in PDE rather than ODE form, making things much more difficult. So, we consider the simplest reacting flow model, which allows us to easily boil the PDE down to an ODE. In fact, it is easier to just phrase things in terms of the ODE directly.

This is the "front element dynamics" - the evolution equations for a little chunk along a reaction front.

TO BE CONTINUED