Klas Modin PRO
Mathematician at Chalmers University of Technology and the University of Gothenburg
Zeitlin's model for ideal hydrodynamics on the sphere
(Part 1: numerical experiments)
Klas Modin
Collaborator: Milo Viviani
SNS Pisa
\dot\omega = \{\psi,\omega \}, \quad \Delta \psi = \omega
Euler's equations
\dot W = [P,W], \quad \Delta_N P = W
Zeitlin's model
W,P \in \mathfrak{su}(N)
azimuth
elevation
Smooth, randomly generated initial data
azimuth
elevation
Smooth, vanishing angular momentum initial data
azimuth
elevation
...run it faster
Questions:
- How exactly is Zeitlin's model related to Euler?
- How accurate is it?
- Does it capture the right dynamics?
- Can it give new insights?
at fine scales: not at all!
...but no method is!
Example: canonical splitting
W = W_s + W_r \qquad (\omega = \omega_s + \omega_r)
W_s
W_r
projection onto stabilizer of \(P\)
Entire presentation at CUNY
Zeitlin's model for ideal hydrodynamics on the sphere
By Klas Modin
Zeitlin's model for ideal hydrodynamics on the sphere
CUNY Einstein seminar given 2021-12.
