@phdthesis{Littmann2024,
  author    = {Littmann, Daniela-Christin},
  title     = {Large eddy simulations of the Arctic boundary layer around the MOSAiC drift track},
  doi       = {10.25932/publishup-62437},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-624374},
  school      = {Universit{\"a}t Potsdam},
  pages     = {xii, 110},
  year      = {2024},
  abstract  = {The icosahedral non-hydrostatic large eddy model (ICON-LEM) was applied around the drift track of the Multidisciplinary Observatory Study of the Arctic (MOSAiC) in 2019 and 2020. The model was set up with horizontal grid-scales between 100m and 800m on areas with radii of 17.5km and 140 km. At its lateral boundaries, the model was driven by analysis data from the German Weather Service (DWD), downscaled by ICON in limited area mode (ICON-LAM) with horizontal grid-scale of 3 km. The aim of this thesis was the investigation of the atmospheric boundary layer near the surface in the central Arctic during polar winter with a high-resolution mesoscale model. The default settings in ICON-LEM prevent the model from representing the exchange processes in the Arctic boundary layer in accordance to the MOSAiC observations. The implemented sea-ice scheme in ICON does not include a snow layer on sea-ice, which causes a too slow response of the sea-ice surface temperature to atmospheric changes. To allow the sea-ice surface to respond faster to changes in the atmosphere, the implemented sea-ice parameterization in ICON was extended with an adapted heat capacity term. The adapted sea-ice parameterization resulted in better agreement with the MOSAiC observations. However, the sea-ice surface temperature in the model is generally lower than observed due to biases in the downwelling long-wave radiation and the lack of complex surface structures, like leads. The large eddy resolving turbulence closure yielded a better representation of the lower boundary layer under strongly stable stratification than the non-eddy-resolving turbulence closure. Furthermore, the integration of leads into the sea-ice surface reduced the overestimation of the sensible heat flux for different weather conditions. The results of this work help to better understand boundary layer processes in the central Arctic during the polar night. High-resolving mesoscale simulations are able to represent temporally and spatially small interactions and help to further develop parameterizations also for the application in regional and global models.},
  language  = {en}
}
@phdthesis{Branding2012,
  author    = {Branding, Volker},
  title     = {The evolution equations for Dirac-harmonic Maps},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-64204},
  school      = {Universit{\"a}t Potsdam},
  year      = {2012},
  abstract  = {This thesis investigates the gradient flow of Dirac-harmonic maps. Dirac-harmonic maps are critical points of an energy functional that is motivated from supersymmetric field theories. The critical points of this energy functional couple the equation for harmonic maps with spinor fields. At present, many analytical properties of Dirac-harmonic maps are known, but a general existence result is still missing. In this thesis the existence question is studied using the evolution equations for a regularized version of Dirac-harmonic maps. Since the energy functional for Dirac-harmonic maps is unbounded from below the method of the gradient flow cannot be applied directly. Thus, we first of all consider a regularization prescription for Dirac-harmonic maps and then study the gradient flow. Chapter 1 gives some background material on harmonic maps/harmonic spinors and summarizes the current known results about Dirac-harmonic maps. Chapter 2 introduces the notion of Dirac-harmonic maps in detail and presents a regularization prescription for Dirac-harmonic maps. In Chapter 3 the evolution equations for regularized Dirac-harmonic maps are introduced. In addition, the evolution of certain energies is discussed. Moreover, the existence of a short-time solution to the evolution equations is established. Chapter 4 analyzes the evolution equations in the case that the domain manifold is a closed curve. Here, the existence of a smooth long-time solution is proven. Moreover, for the regularization being large enough, it is shown that the evolution equations converge to a regularized Dirac-harmonic map. Finally, it is discussed in which sense the regularization can be removed. In Chapter 5 the evolution equations are studied when the domain manifold is a closed Riemmannian spin surface. For the regularization being large enough, the existence of a global weak solution, which is smooth away from finitely many singularities is proven. It is shown that the evolution equations converge weakly to a regularized Dirac-harmonic map. In addition, it is discussed if the regularization can be removed in this case.},
  language  = {en}
}