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.

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Bratislava

My first day in Bratislava was pretty rough.

The first disaster was that related to my luggage falling from overhead.  Not only did I get a bruise on my eye, I broke my glasses.  I had recently switched back to glasses because my contacts had been causing really bad headaches.  And while I was strongly resistant to buying *those* particular frames, they really grew one me.  So, I’m in a city and should be conducting research, but I can’t see.  At least I have one contact with me 🙂

The second ‘adventure’ was that I was ticketed 50 Euro! I thought you paid for your bus ticket on the bus.  I had my money out ready to pay; except, that machine was only for validation.  As soon as the doors closed, I got a ticket!  I was totally embarassed!

That said, research has been good, and I like my office.  Here are some pics for fun!

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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It’s been a while (again)…

It’s definitely been a while.  Renting/moving out of the house, packing, and then finally settling into Vienna has been overwhelming.

We initially traveled to Prague for some tourism.  After Prague, we rented a car and drove to Vienna via the Wachau Valley.  Finally, we made it to Vienna and got settled in.

Now, to write some updates about research!

 

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