17 research outputs found

    Stability of the selfsimilar dynamics of a vortex filament

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    In this paper we continue our investigation about selfsimilar solutions of the vortex filament equation, also known as the binormal flow (BF) or the localized induction equation (LIE). Our main result is the stability of the selfsimilar dynamics of small pertubations of a given selfsimilar solution. The proof relies on finding precise asymptotics in space and time for the tangent and the normal vectors of the perturbations. A main ingredient in the proof is the control of the evolution of weighted norms for a cubic 1-D Schr\"odinger equation, connected to the binormal flow by Hasimoto's transform.Comment: revised version, 36 page

    Multi-dimensional Limiting Process on Triangular and Tetrahedral Meshes

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    The present paper deals with the continuous work of extending multi-dimensional limiting process (MLP), which has been quite successfully proposed on two- and three-dimensional structured meshes, onto the unstructured meshes. The basic idea of the present limiting strategy is to control the distribution of both cell-centered and cell-vertex physical properties to mimic a multi-dimensional nature of flow physics, which can be formulated as so called the MLP condition. The MLP condition can guarantee a high order spatial accuracy without yielding spurious oscillations. Starting from the MUSCL-type reconstruction on unstructured meshes followed by the efficient implementation of the MLP condition, MLP slope limiters on unstructured meshes are proposed. Through various numerical analyses and extensive computations, it is observed that the proposed limiters are quite effective in controlling numerical oscillations and very accurate in capturing both discontinuous and continuous multi-dimensional flow features on 2-D triangular meshes and 3-D tetrahedral meshes.The authors appreciate the financial supports provided by the second stage of the Brain Korea 21 Project for Mechanical and Aerospace Engineering Research at Seoul National University, the KARI under KHP Dual-Use Component Development Program funded by the MKE, and by Agency for Defense Development

    Multi-Dimensional Limiting Process on Triangular and Tetrahedral Meshes

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    A modelling study of the atmospheric chemistry of DMS using the global model STOCHEM-CRI

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    The tropospheric chemistry of dimethylsulfide (DMS) is investigated using a global three-dimensional chemical transport model, STOCHEM with the CRIv2-R5 chemistry scheme. The tropospheric distribution of DMS and its removal at the surface by OH abstraction, OH addition, NO3 oxidation, and BrO oxidation is modelled. The study shows that the lifetime and global burden of DMS is ca. 1.2 days and 98 Gg S, respectively. Inclusion of BrO oxidation resulted in a reduction of the lifetime (1.0 day) and global burden (83 Gg S) of DMS showing that this reaction is important in the DMS budget. The percentage contribution of BrO oxidation to the total removal of DMS is found to be only 7.9% that is considered a lower limit because the study does not include an inorganic source of bromine from sea-salt. BrO oxidation contributed significantly in the high latitudes of the southern hemisphere (SH). Inclusion of DMS removal by Cl2 showed that potentially a large amount of DMS is removed via this reaction specifically in the remote SH oceans, depending on the flux of Cl2 from the Southern Ocean. Model DMS levels are evaluated against measurement data from six different sites around the globe. The model predicted the correct seasonal cycle for DMS at all locations and correlated well with measurement data for most of the periods
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