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M3: Towards Consistent Subgrid Momentum Closures

Principal investigators: Prof. Sergey Danilov (Alfred Wegener Institute for Polar and Marine Research), Dr. Janin Jäger (Catholic University of Eichstätt-Ingolstadt), Prof. Stephan Juricke (GEOMAR Helmholtz Centre for Ocean Research Kiel), Prof. Marcel Oliver (Catholic University of Eichstätt-Ingolstadt)

Computational models of atmosphere and ocean can only resolve a limited range of scales. Dynamical processes on scales smaller than the grid scale are parameterized or simply truncated.

When the grid scale lies within one of the classical turbulent inertial ranges, the use of viscous closures is well-understood, but in practice, simulations tend to be over-dissipative because of insufficient scale separation between numerical dissipation and the forcing scale. This problem is particularly severe when forcing occurs near the grid scale, for example through the process of baroclinic instability which converts available potential energy into kinetic energy in eddy-permitting or barely eddy-resolving simulations of the ocean. In general, momentum closures, as well as momentum advection, must aim at being minimally dissipative, which may require active reinjection of energy into the resolved kinetic energy range, a process termed in the context of oceanic momentum closures as kinetic energy backscatter.

This project will evaluate existing closure and advection schemes and develop new ones with a particular focus on (i) properly analysing their precise discrete behaviour, especially the energy budget near the resolution scale and the propagation of linear waves on unstructured meshes, (ii) developing closures that work on unstructured and variable grids (the B-grid in FESOM, the hexagonal and triangular C-grids in ICON-IAP and ICON-o), (iii) gaining physical understanding of numerically induced processes, and (iv) developing and assessing stochastic closures.

We will, first, continue the development of ocean kinetic energy backscatter which, as we demonstrated in the first project phase, is an effective means of improving energy consistency of eddy-permitting or barely eddy-resolving ocean simulations. Second, we will investigate the behaviour of models near the grid scale (i) top-down, by analysing the effective resolution of different choices of grids, discrete operators, and momentum closures empirically in the context of realistic model runs, and (ii) bottom-up, by building physical and mathematical understanding of the explicit as well as implicit choices of momentum closures. The combination of these methods and the application to the two different main models of the TRR181 – i.e., FESOM and ICON – will ensure a holistic approach to the development of efficient, energetically consistent and optimal discretizations of the momentum equations.

Next phase outlook:

➢ Spurious interfacial waves on unstructured meshes

➢ Further development and adjustment of kinetic energy backscatter schemes in global ocean models

➢ Investigation of effective resolution of general circulation models on various grids

The union of different grids (B) and the local inclusions of refined mesh areas (C) imply the appearance of a new type of waves, namely guided waves propagating at the interface, and local waves. These types of waves, sometimes called Rayleigh-Stoneley waves, considered to be "spurious" in the current context and should be muffled, since there are no such waves in the original uniform grid (A) reflecting the homogeneity of real models.

Report - HYEL 2026 Conference in Trondheim, Norway by Mansi Singh

Mansi Singh, Postdoc at Catholic University Eichstätt-Ingolstadt , attended the 10th International Conference on Hydroelasticity in Marine Technology (HYEL 2026) in Trondheim, Norway from 16–18 June 2026. Here she shares her experiences.

I had the opportunity to participate in the 10th International Conference on Hydroelasticity in Marine Technology (HYEL 2026), held from 16–18 June 2026 in Trondheim, Norway. The conference brought together researchers, engineers, and industry experts from around the world working on hydroelasticity, fluid–structure interaction, offshore renewable energy, floating structures, wave energy, marine membranes, floating wind turbines, ship hydrodynamics, and ice–water interactions. The conference venues themselves were memorable and reflected the unique character of Trondheim. The first two days were hosted at the Sverresborg Trøndelag Folk Museum, and the final day was held at NTNU’s Professor Mørch’s House. I was particularly impressed by the building’s striking architectural design, especially its elegant spiral staircase, whose sweeping geometry and openness created a visually stunning space. The contrast between the historic museum setting and the contemporary university architecture made the conference experience even more unique and memorable.

As part of the conference programme, I delivered an oral presentation entitled: “Comparative Study of Energy Dissipation under Capillary–Gravity Wave Scattering by Submerged Porous, Poroelastic, and Porous Piezoelectric Plates.”

My presentation focused on a mathematical and physical comparison of different flexible porous structures and their ability to dissipate water wave energy. The work generated interesting discussions regarding the potential use of porous and piezoelectric structures for wave-energy applications and coastal protection systems. Presenting the work to an international audience provided valuable feedback and opened possibilities for future collaborations.

The scientific programme was exceptionally diverse, featuring keynote lectures and technical sessions on hydroelasticity, aquaculture structures, floating bridges, offshore wind turbines, wave-energy systems, bio-inspired marine technologies, and ice–water interactions. These presentations provided valuable insights into current developments in marine technology and offshore engineering, particularly in flexible wave-energy converters, floating wind platforms, and advanced modelling techniques combining potential-flow theory, finite-element methods, and computational fluid dynamics. I was especially fascinated by talks on bio-inspired marine systems, where the motion and flexibility of fish were modelled through fluid–structure interaction frameworks and translated into the design of robotic fish and flexible underwater vehicles for environmental monitoring, underwater inspection, and marine exploration. As a mathematician working on fluid–structure interaction problems, it was exciting to see how fundamental theoretical models can directly contribute to innovative engineering solutions inspired by nature. Equally valuable were the opportunities for informal discussions during coffee breaks, lunches, and conference events, gaining insights into ongoing research worldwide, identifying emerging challenges in the field, and initiating discussions that may lead to future collaborations. For me as an early-career researcher, these exchanges were invaluable for expanding my scientific network and broadening my research perspective.

The conference venue itself contributed significantly to the experience. Much of the event was held at the Sverresborg Trøndelag FolkMuseum, an open-air museum that showcases Norwegian cultural heritage. During a guided tour, we visited the remarkable Haltdalen Stave Church, dating from the 1170s and considered one of the oldest surviving stave churches in the world. We also learned about the history of King Sverre’s Castle, whose ruins overlook Trondheim and played an important role in medieval Norwegian history. These visits provided a fascinating perspective on Norway’s cultural and architectural heritage.

Outside the conference programme, Trondheim offered many memorable experiences. Walking through the city, I was particularly impressed by the historic wooden buildings built on stilts located in the Brygge district along the flanks of the Nidelva River, which are among Trondheim’s most iconic landmarks. Another highlight was visiting the magnificent Nidaros Cathedral, one of Scandinavia’s most important medieval cathedrals. The combination of historic architecture, scenic waterways, and surrounding natural landscapes made Trondheim a truly unique destination.

A particularly memorable experience was witnessing Norway’s long summer daylight. Even late at night, the sky never became completely dark. As someone who had often heard during childhood that “the sun never sets” in the far north during summer, it was fascinating to experience this phenomenon firsthand. The extended daylight created a unique atmosphere and allowed us to enjoy the city well into the evening. Nature was another striking aspect of the visit. During our stay, it was common to encounter wildlife such as deers, rabbits, and sheeps in areas close to roads and residential neighbourhoods. This close coexistence of urban life and nature left a lasting impression and highlighted Norway’s strong connection with its natural environment.

Overall, participation in HYEL 2026 was an extremely rewarding scientific and cultural experience. The conference allowed me to present my research to an international audience, gain exposure to cutting-edge developments in hydroelasticity and marine technology, establish new professional connections, and explore the rich history and natural beauty of Norway. The knowledge gained and collaborations initiated during this visit will undoubtedly contribute to my future research activities within the framework of the TRR and beyond.

 

Report - EGU General Assembly in Vienna by Hao Liang (May 26)

I travelled together with colleagues from MIDS (Mathematical Institute for Machine Learning and Data Science) from Catholic University Eichstätt-Ingolstadt and arrived in Vienna on a sunny Sunday afternoon. Even before the conference officially began, the city already felt connected to EGU. Around metro stations, cafés, and the conference venue, it was easy to spot participants wearing name badges or carrying poster tubes. Vienna itself provided a beautiful setting for the week, with its grand historical buildings, churches, parks, and opera houses creating a calm yet lively atmosphere.

The scale of the conference was impressive. Oral sessions, poster presentations, short courses, and networking events ran throughout the day. What impressed me most, however, was how much effort people put into presenting and discussing their work. Researchers from very different backgrounds were all eager to exchange ideas and explain their research in detail.
During the week, I mainly attended sessions related to ocean dynamics, turbulence, numerical modelling, and machine learning applications in geoscience, especially the OS1.11 and NP6.4 sessions organised by members of the TRR 181 project. The talks covered a wide range of topics, from physical ocean processes to modern computational and data-driven methods, and the discussions were often lively and inspiring. Researchers from the TRR 181 project also contributed several excellent talks and poster presentations throughout the week, and unexpectedly meeting familiar faces across different sessions added another enjoyable part to the conference experience.

My own poster presentation took place towards the end of the conference. It was my first time presenting a poster at such a large international meeting, and I really enjoyed the experience. Compared with oral presentations, the poster session allowed for more direct and relaxed discussions. I had several interesting conversations about possible applications of the method, which gave me useful ideas for future research.

Outside the sessions themselves, the conference had a very lively atmosphere. During breaks, many participants gathered outside in the sunshine, sitting on the grass and continuing scientific discussions. Others explored the exhibition area, where journals, scientific companies, and research organisations presented new projects, software, and publications. There were also quiet working areas filled with researchers preparing talks, answering emails, or making last-minute changes to posters.
Vienna itself also became an important part of the experience. After the conference sessions ended, colleagues and I often spent the evenings walking through the city centre while continuing discussions from the day. The architecture constantly changed from one street to another: monumental buildings, quiet courtyards, churches, statues, and elegant parks appeared almost everywhere.

After the conference, I stayed an extra day in Vienna and visited the Kunsthistorisches Museum. The museum’s collections span thousands of years of history, from Egyptian and Classical antiquities to Renaissance paintings and sculptures. One highlight for me was seeing Pieter Bruegel’s The Tower of Babel in person, part of the museum’s remarkable Bruegel collection.
Overall, EGU 2026 was a highly valuable experience for me. Beyond presenting my own work, the conference provided many opportunities for discussion, inspiration, and new perspectives on interdisciplinary research. At the same time, Vienna itself added a unique atmosphere to the week, combining science, history, art, and music in a memorable way.

At the beginning of May, I travelled to Vienna to participate in the EGU General Assembly 2026. The meeting brought together around 20,000 scientists from all over the world working across many areas of geoscience. Coming from a mathematical background and working on spectral recovery from sparse observations, it was exciting to experience such a large and interdisciplinary conference environment.

I travelled together with colleagues from MIDS (Mathematical Institute for Machine Learning and Data Science) from Catholic University Eichstätt-Ingolstadt and arrived in Vienna on a sunny Sunday afternoon. Even before the conference officially began, the city already felt connected to EGU. Around metro stations, cafés, and the conference venue, it was easy to spot participants wearing name badges or carrying poster tubes. Vienna itself provided a beautiful setting for the week, with its grand historical buildings, churches, parks, and opera houses creating a calm yet lively atmosphere.

The scale of the conference was impressive. Oral sessions, poster presentations, short courses, and networking events ran throughout the day. What impressed me most, however, was how much effort people put into presenting and discussing their work. Researchers from very different backgrounds were all eager to exchange ideas and explain their research in detail.

During the week, I mainly attended sessions related to ocean dynamics, turbulence, numerical modelling, and machine learning applications in geoscience, especially the OS1.11 and NP6.4 sessions organised by members of the TRR 181 project. The talks covered a wide range of topics, from physical ocean processes to modern computational and data-driven methods, and the discussions were often lively and inspiring. Researchers from the TRR 181 project also contributed several excellent talks and poster presentations throughout the week, and unexpectedly meeting familiar faces across different sessions added another enjoyable part to the conference experience.

My own poster presentation took place towards the end of the conference. It was my first time presenting a poster at such a large international meeting, and I really enjoyed the experience. Compared with oral presentations, the poster session allowed for more direct and relaxed discussions. I had several interesting conversations about possible applications of the method, which gave me useful ideas for future research.

Outside the sessions themselves, the conference had a very lively atmosphere. During breaks, many participants gathered outside in the sunshine, sitting on the grass and continuing scientific discussions. Others explored the exhibition area, where journals, scientific companies, and research organisations presented new projects, software, and publications. There were also quiet working areas filled with researchers preparing talks, answering emails, or making last-minute changes to posters.

Vienna itself also became an important part of the experience. After the conference sessions ended, colleagues and I often spent the evenings walking through the city centre while continuing discussions from the day. The architecture constantly changed from one street to another: monumental buildings, quiet courtyards, churches, statues, and elegant parks appeared almost everywhere.

After the conference, I stayed an extra day in Vienna and visited the Kunsthistorisches Museum. The museum’s collections span thousands of years of history, from Egyptian and Classical antiquities to Renaissance paintings and sculptures. One highlight for me was seeing Pieter Bruegel’s The Tower of Babel in person, part of the museum’s remarkable Bruegel collection.

Overall, EGU 2026 was a highly valuable experience for me. Beyond presenting my own work, the conference provided many opportunities for discussion, inspiration, and new perspectives on interdisciplinary research. At the same time, Vienna itself added a unique atmosphere to the week, combining science, history, art, and music in a memorable way.