Constant Vorticity – The Saga Continues…

Looking at the real part of the growth rate \left(\mathcal{R}\left\lbrace\lambda\right\rbrace\right) vs. the Floquet parameter \left(\mu\right) for increasing matrix truncations sizes \left(N\right)

The above picture shows the real part of the growth rate \lambda vs. the Floquet parameter \mu for increasing truncation of the Floquet/Fourier/Hill matrix.

After a lengthy discussion with Richard Kollar, we have agreed that there seem to be two separate issues here.  The first is that one must be careful when restricting the Floquet Multiplier \mu \in \left[0,\frac{1}{2}\right] in conjunction with the size of the truncated matrix for the Fourier/Floquet/Hill method.  The second is that there is still some other type of instability that may be present (the “moving” instability).

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Constant Vorticity (Update)

In the quest to understand what happens to the stability as the strength of the vorticity increases, it’s important to predict precisely where the first instability will arise (in terms of the Floquet parameter \mu.

animation
Intersecting lines of opposite signature could give rise to a potential instability.  The two black dots follow the first to collisions; both of which yield instabilities for non-trivial solutions.

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AIMS 2018: Taipei (Day 2)

Chris posing with the conference banner.

Today, I attended a session organized by Christian Kharif on water-waves. Three of the speakers were colleagues: Vishal, Vera, and Chris. While quite a few topics were discuss, I personally found the conversations that happened between talks the most useful.  I discussed various projects with various permutations of people.  The following contains a brief summary of some of the topics/projects/questions discussed.

 

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