## The Dispersion Relationship for N-layers of Linear Shear

It would be interesting to use the AFM formulation to quickly derive not only the dispersion relationship for N-layers of linear shear, but also develop numerical simulations of traveling waves and relationships between the pressure and other internal wave properties.

## Constant Vorticity – The Saga Continues…

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).

Continue reading “Constant Vorticity – The Saga Continues…”

## 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 $\mu$.

## Stability and Constant Vorticity

When the constant vorticity is strong enough to induce a region of lower pressure under the crest, is the wave stable?

## AIMS 2018: Taipei (Day 2)

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.