Variational formulation of the Ekman ocean
At the end of the nineteenth century during the expedition on board Fram, Fridtjof Nansen noticed that icebergs had a tendency to drift to the right of the wind direction. Vagn Walfrid Ekman was the first to mathematically assign this veering to the Coriolis effect and in 1905 presented a model for...
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| Format: | Master Thesis |
| Language: | English |
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Sveučilište u Splitu. Prirodoslovno-matematički fakultet. Odjel za fiziku.
2021
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| Online Access: | https://repozitorij.svkst.unist.hr/islandora/object/pmfst:1277 https://urn.nsk.hr/urn:nbn:hr:166:001202 https://repozitorij.svkst.unist.hr/islandora/object/pmfst:1277/datastream/PDF |
| Summary: | At the end of the nineteenth century during the expedition on board Fram, Fridtjof Nansen noticed that icebergs had a tendency to drift to the right of the wind direction. Vagn Walfrid Ekman was the first to mathematically assign this veering to the Coriolis effect and in 1905 presented a model for the vertical structure of the ocean currents induced by wind. He assumed steady wind and a uniformly rotating unbounded ocean. In his solution the surface current is deflected at a 45 degree right to the wind direction. Also, this deflection is independent of the wind direction. Existence of such a symmetry is typically associated with conservation principles. The primary objective of this paper is to formulate the Ekman problem using the variational principle, a seldom used approach during university classes on physical oceanography. Additionally, analytical and numerical formulations are explored for periodic wind forcing. Krajem devetnaestog stoljeća, tijekom ekspedicije brodom Fram, Fridtjof Nansen primjećuje da sante leda skreću udesno u odnosu na smjer vjetra. Vagn Walfrid Ekman je prvi matematički pripisao skretanje Coriolisovoj sili i 1905. prezentirao model vertikalne strukture struja uzrokovanih vjetrom. Pretpostavio je konstantni vjetar po iznosu i smjeru te uniformno rotirajući neomeđeni ocean. U njegovom rješenju površinska struja zakreće 45 stupnjeva udesno od smjera vjetra. Također, otklon struje ne ovisi o smjeru vjetra. Postojanje takve simetrije je povezano sa zakonima očuvanja. Cilj rada je formulacija Ekmanovog problema koristeći varijacijski račun. Takav klasičan pristup se rijetko koristi tijekom nastave iz oceanografije. Uz to, analitičko i numeričko rješenje se proučavaju za periodičan vjetar. |
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