Vorticity field of a 2D fluid on a sphere
A frame of the evolution of the intensity of the vorticity field of a 2D homogeneous, inviscid, incompressible fluid on a sphere, represented in grey scale on a zonal-colatitude coordinates grid

New algorithms for hydrodynamic problems

​In his PhD thesis, Milo Viviani has combined aspects of geometry and numerical analysis to better understand the 2D ideal hydrodynamics. This is of great relevance in, for example, model predictions of the climate dynamics.

Milo Viviani​Fluid dynamics is a large and very active field of research both in pure and applied mathematics. Milo quotes Richard Feynman: “the problem of turbulence [of fluids] is still the most important unsolved problem of classical physics”. The approach presented in his thesis is to use structure-preserving algorithms to solve differential equations that can be applied to hydrodynamic problems. Hydrodynamics is about fluids that are incompressible, as water, but also fluids like the atmosphere. The problem addressed is more specifically about 2D ideal hydrodynamics on a sphere, which is fundamental in modelling oceanic and atmospheric circulation, even for non-terrestrial planets like Jupiter.

New insights into open questions

Of the four papers included, two focus on numerical analysis and two on hydrodynamics. In the first part, Milo develops a new class of numerical schemes for Hamiltonian and non-Hamiltonian isospectral flows. In the latter part, he uses this new tool to better understand hydrodynamics theoretically and efficiently simulate the 2D Euler equations of fluid dynamics on a sphere. This work has given new insights and hints into open questions, as the controversial persistent unsteadiness of the statistical state of a fluid. These findings may suggest that a more complex theory than the current one is needed. This would have a clear impact in model predictions of atmospheric and climate dynamics.

Milo has liked mathematics ever since elementary school. He did his master’s thesis in Bergen, Norway, in an Erasmus exchange programme and there he was introduced to and got interested in the research area he has worked with as a PhD student. A visiting colleague of his current supervisor told about the position in Gothenburg, which he applied for and received.

Ups and downs of being a PhD student

– When I started as a PhD student I was curious about the parts of research that involve participating in conferences, travels and meeting people, and I have been well satisfied in this. Sweden does not always have the best weather, but I had been to Norway during the winter and so I knew what to expect. I also got to know some very good friends from whom I have learned a lot of new perspectives and who made me personally grow, and over all I have really had a fun time!

That said, research work can often be unsatisfactory. After about two years, Milo began to feel lost in his project and started to lose faith in his own work. Then it turned again, and he is really glad for the last years of his programme: he has got resources and support to continue his work to the best. This process is not uncommon among PhD students and Milo speculates that maybe it is something you must go through. But since the process to some extent is predictable, it could probably be studied and handled.

Next, Milo is going to Scuola Normale Superiore in Pisa for a two-years postdoctoral position at the Ennio De Giorgi Mathematical Research Center.

Milo Viviani will defend his PhD thesis “Symplectic methods for isospectral flows and 2D ideal hydrodynamics” on June 9 at 10.00 via Zoom. Supervisor is Klas Modin.

Text: Setta Aspström
Photo: private
Picture: Milo Viviani

Published: Wed 03 Jun 2020.