Resolving eddies by local mesh refinement |
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| Institution: | 1. Alfred Wegener Institute, Helmholtz Centre for Polar and Marine Research, Bremerhaven 27515, Germany;2. A. M. Obukhov Institute of Atmospheric Physics RAS, Moscow, Russia;1. Jailoo SRL, seamod.ro, Valea Iepii nr. 1, Com. Salatrucu, Jud. Arges, Romania;2. GeoHydrodynamics and Environment Research, University of Liege, Belgium;1. British Antarctic Survey, High Cross, Madingley Road, Cambridge CB3 0ET, UK;2. Atmospheric, Oceanic and Planetary Physics, Department of Physics, University of Oxford, Oxford OX1 3PU, UK;3. Centre for Ocean and Atmospheric Sciences, School of Environmental Sciences, University of East Anglia, Norwich, UK;4. School of Marine Science, Nanjing University of Information Science and Technology, Nanjing, China;1. Institute for Coastal Research, HZG Geesthacht, Max-Planck-Straße 1, 21502 Geesthacht, Germany;2. Department of Atmospheric Sciences, Sun Yat-Sen University, 135 Xingang Xi Road, Guangzhou 510275, PR China;1. College of Harbor, Coastal and Offshore Engineering, Hohai University, Nanjing 210098, China;2. Center for Applied Coastal Research, Department of Civil and Environmental Engineering, University of Delaware, Newark, DE 19716, USA;3. Department of Civil and Environmental Engineering, Old Dominion University, Norfolk, VA 23529, USA;4. College of Engineering, Ocean University of China, Qingdao 266100, China;1. Interdisciplinary Programme in Climate Studies, Indian Institute of Technology, Bombay, India;2. Department of Civil Engineering, Indian Institute of Technology, Bombay, India;3. ESSIC, University of Maryland, College Park, Maryland, USA |
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| Abstract: | Nesting in large-scale ocean modeling is used for local refinement to resolve eddy dynamics that would not be accessible otherwise. Unstructured meshes offer this functionality too by adjusting their resolution according to some goal function. However, by locally refining the mesh one does not necessarily achieve the goal resolution, because the eddy dynamics, in particular the ability of eddies to release the available potential energy, also depend on the dynamics on the upstream coarse mesh. It is shown through a suite of experiments with a zonally re-entrant channel that baroclinic turbulence can be out from equilibrium in wide (compared to a typical eddy size) zones downstream into the refined area. This effect depends on whether or not the coarse part is eddy resolving, being much stronger if it is not. Biharmonic viscosity scaled with the cube of grid spacing is generally sufficient to control the smoothness of solutions on the variable mesh. However, noise in the vertical velocity field may be present at locations where the mesh is varied if momentum advection is implemented in the vector invariant form. Smoothness of vertical velocity is recovered if the flux form of momentum advection is used, suggesting that the noise originates from a variant of the Hollingsworth instability. |
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