Report - Participation in the Trimester "Mathematical Developments in Geophysical Fluid Dynamics" in Paris by Philomène Dufour

After attending the introductory school at the CIRM in Marseille in April, near the beautiful site of the Calanques, I went to Paris to participate in the third workshop of this programme.

I was particularly pleased that this workshop was held in Paris, as it was an opportunity to see some of my old friends from the Master's programme at Sorbonne University and to come back to this city to which I am particularly attached.

The third workshop lasted one week and took place at the Institut Henri Poincaré, in the Latin Quarter of Paris, which is well known for its intellectual and student atmosphere. We were sitting in the Charles Hermite amphitheatre, one of the oldest lecture halls of the institute, which has hosted many renowned mathematicians and physicists.

During this workshop, I attended many talks and presented my poster on an attempt at deriving the α -modified Craik–Leibovich equations using geometric generalised Lagrangian mean theory. This work aims to develop a mathematical model describing wave–mean current interactions while accounting for the effects of turbulence through an α-regularisation. Because the poster combines ideas from Craik–Leibovich theory, α -models of turbulence and geometric GLM, it attracted researchers with rather different backgrounds, including oceanographers, applied mathematicians and specialists in mechanics. These discussions helped me to better identify which aspects of the work are the most accessible to different audiences and which questions naturally arise from each community.

I was very happy to see that this subject raised the interest of many people; it encouraged me a lot to continue. As the poster was displayed throughout the whole week, it also enabled me to continue discussions with people afterwards. This experience also highlighted the importance of poster sessions for presenting ongoing work, receiving feedback and establishing new scientific contacts.

Although the event in Paris was completely free of charge, lunches were organised directly next to the amphitheatre, which greatly facilitated discussions and informal interactions. One of the highlights of the week was undoubtedly the cocktail on the rooftop of the Maison Poincaré, where discussions continued in a relaxed atmosphere. Participants were also offered free admission to the Maison Poincaré's mathematics museum. I visited it with a few other participants and enjoyed discovering its interactive exhibitions.

The scientific programme covered a broad range of themes. The talks ranged from reduced models for strongly stratified turbulence, derived using asymptotic analysis, to the treatment of boundary conditions in wave–structure interactions. They showcased a variety of mathematical tools, including turbulence modelling, asymptotic methods, geometric mechanics, and numerical simulations. Although the topics were diverse, they all shared the common objective of improving our understanding of the fundamental mechanisms governing geophysical flows. At this stage of my PhD, this workshop helped me better understand how my research fits within the broader field of geophysical fluid dynamics.

In the following week, there will be a satellite conference, *Perspectives and Challenges in Geophysical Fluid Dynamics*, at the École normale supérieure. I am looking forward to meeting other members of the TRR and many other researchers there.

The workshop also gave me the opportunity to learn about future events of the community. Several participants recommended the Advanced Summer School on Mathematical Fluid Dynamics in Cargèse next year, which I hope to attend.