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Area M: Mathematics, new concepts and methods

Area M represents the foundation of our project. The scientists in that area work on new mathematical concepts and numerical methods to be tested in the other project areas. Thus, it forms the basis for future work.

Interdisciplinary approach

Applied mathematicians and experts from geo sciences are working together in area M, to foster an exchange with the other research areas and to transfer knowledge between the different disciplines. By working on consistent model formulation, new and consistent parameterisations and numerics for both atmosphere and ocean, the mathematicians can help climate scientists improve their models and thus enhance climate projections.

Specific research questions in Research Area M are:

  • What is a mathematically and physically consistent model formulation for the different dynamical regimes and their interaction?
  • Can we formulate better and physically consistent sub-grid scale parameterisations for the interaction between different dynamical regimes?
  • Can we develop better numerical schemes?

  • Fofonova, V., Kärnä, T., Klingbeil, K., Danilov, S., Burchard, H. et al. (2021). Plume spreading test case for coastal ocean models. Geosci. Model Dev. 14(11), doi: https://doi.org/10.5194/gmd-14-6945-2021.

  • Scholz, P., Sidorenko, D., Danilov, S., Wang, Q., Koldunov, N., Sein, D., & Jung, T. (2022). Assessment of the Finite-VolumE Sea ice–Ocean Model (FESOM2.0) – Part 2: Partial bottom cells, embedded sea ice and vertical mixing library CVMix. Geosci. Model Dev. 15(2), 335–363, doi: https://doi.org/10.5194/gmd-15-335-2022.

  • Prugger, A., Rademacher, J. D. M., & Yang, J. (2022). Geophysical fluid models with simple energy backscatter: explicit flows and unbounded exponential growth, Geophysical & Astrophysical Fluid Dynamics 116(5-6), doi: https://doi.org/10.1080/03091929.2021.2011269.

  • Nobili, C. (2023). The role of boundary conditions in scaling laws for turbulent heat transport[J]. Math. Eng. 5(1), 1-41, doi: https://doi.org/10.3934/mine.2023013. 

  • Ovsyannikov, I. & Ruan, H. (2022). Classification of Codimension-1 Singular Bifurcations in Low-Dimensional DAEs. Front. Appl. Math. Stat. 8:756699, doi: https://doi.org/10.3389/fams.2022.756699.

  • Noethen, F. (2022). Well-Separating Common Complements for Sequences of Subspaces of the Same Codimension are Generic in Hilbert Spaces. Anal. Math., doi: https://doi.org/10.1007/s10476-022-0124-z.

  • Ovsyannikov, I. (2022). On the Birth of Discrete Lorenz Attractors Under Bifurcations of 3D Maps with Nontransversal Heteroclinic Cycles. Regul. Chaot. Dyn. 27, 217–231, doi: https://doi.org/10.1134/S156035472202006X.

  • Darbenas, Z., van der Hout, R. & Oliver, M. (2022). Long-time asymptotics of solutions to the Keller–Rubinow model for Liesegang rings in the fast reaction limit. Ann. Inst. H. Poincaré Anal. Non Linéaire 39(6), 1413–1458, doi: https://doi.org/10.4171/AIHPC/34.

  • Drivas, T.D., Nguyen, H.Q. & Nobili, C. (2022). Bounds on heat flux for Rayleigh–Bénard convection between Navier-slip fixed-temperature boundaries. Phil. Trans. R. Soc. A. 380(2225), doi: https://doi.org/10.1098/rsta.2021.0025. 

  • Li, X., Lorenz M., Klingbeil, K., Chrysagi, E., Gräwe, U., Wu, J. & Burchard, H. (2022). Salinity Mixing and Diahaline Exchange Flow in A Large Multi-outlet Estuary with Islands. J. Phys. Oceanogr., doi: https://doi.org/10.1175/JPO-D-21-0292.1.