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How Consistent Can We Solve the Tensor Equations of the Dynamic Smagorinsky Model?
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Title  How Consistent Can We Solve the Tensor Equations of the Dynamic Smagorinsky Model? 
Title of Series  Leibniz MMS Days 2019 
Author 
SchaeferRolffs, Urs

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CC Attribution 3.0 Germany: You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. 
DOI  10.5446/40500 
Publisher  WeierstraßInstitut für Angewandte Analysis und Stochastik (WIAS), LeibnizInstitut für Atmosphärenphysik (IAP) 
Release Date  2019 
Language  English 
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Subject Area  Mathematics 
Abstract  The basic idea of the Dynamic Smagorinsky Model (DSM) is the tensor equation that relates the resolved stress terms with the respective Smagorinsky parametrizations. Although there exist for almost 30 years approaches to solve it, they include common practices which are, in my opinion, applied too uncritically. For instance, a stringent derivation of the tensor equation results in an ambiguous formulation involving a divergence operator. A second problem that may cause inconsistencies is the frequentlyused extraction of the Smagorinsky parameter from the test filtering. In my presentation, I want to point out some of these issues to obtain a better understanding of the DSM. This may also lead to a reduction of mathematical inconsistencies regarding its solution. 
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