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?

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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. 
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WeierstraßInstitut für Angewandte Analysis und Stochastik (WIAS), LeibnizInstitut für Atmosphärenphysik (IAP)

Release Date 
2019

Language 
English

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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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00:00
they're very detailed that introduction to what I want to discuss and this seconds around think
00:08
because my it's given ions of one's most of the issues I want to discuss because I don't want to give a talk
00:19
about late results but the what's to issues in this the solving this the genomics and risky model and as Boston said so did anemic numerous
00:33
listeners there there we assume all you want to discuss it the mixing of length approach and but in order to have a nice picture in my talk which would be the last 1 had here some the idea few matching efforts in all future hidden known the the event mixing things would be if the food processor formula to rule and in the course of interface it's gets mixed and when there's limit since the of the bill finally this length scale is smallest the mixing length and stood there and the Smolinski approach this is constant and this anemic the procedure must should we k collected from a resolved scales hence
01:26
there to do it's winter the we introduce some filtering as busses sets and for example and that's that's all there is fireworks there from the spectrum on the fitting this very easy when recalculating of gridbased and quantities the cut off of food in figure skater just over reasons and S. sparse and I use the convention that the result the quantities are denoted by and the other ones with a and to the fit of 1 of the 2 Cook sense there
02:11
as the issues I want to address how mathematical issues synopsis of the physical on most them by FAO have missed migrants is derived in my view we saw that this and I use a simplified but in this case the constant the entity because the what's happening there is the the and this this not depend on whether the density is constant or not in principle case so the advection terms around cannot be candidate fits the former is a flow but it is the parameter of we need at this tall and as we saw that last and this difference between the the honors of product and productive result the quantities and this emergency approaches is parametrized with this length scale what makes length and missed who interference and move for the cake relation of Fresnel monitor the was here and now the all the deviant or a part of his tens of it means that to trace often attends lace 0 but is white he is a star this is lifted trays the funny was he it's 0 and here these theorists also tried in office then there really they could compute the wonderful according to the creation and in I use cases constant there is sufficient to have a constant whistling but this is surely not the case in atmosphere and soul René model it's a promise of states
04:06
and Espersen sets we introduce us this filtering and there we can provides again this tens of this the federal for products and food for a public official but velocities and this is also parameterized again the 1st moment approach which I
04:33
would the call C 1 at 1st because this will be 1 issue the 1 with late on the talk then we have this too the attempt was and with the knowledge defined reticulata and and here's the difference between this the intends lied for the federal state and for fitrat of resources the obtained this but differences which consists of 1 it a velocity recently loss it is but on the 1st part is the product is fed to and the 2nd part is really in the middle the it is offered as and then this is the other part is that the the replace both tensile Silvis according Slowinski parameterizations and we assume that's this permits are the same and then finally gets all of densely creation of genomics forwards mode he 1 problem also the former former it off learning ballpoint the this should expand from both close and the codes of brackets and this is also the case on on on us lights whenever of you see this codes red heads this filtering and should be for the whole product and so that is the creation is usually written in literature in this the formation and as was instead vested with months the stress solution is a positive definite and this mediates some problems and but this is not the the from I want address the von problem the 1st problem I wanted this this this this the creation real there indeed very creation the should solve and
06:41
and if you do it only from the momentum occasions there it is not the case the because as I write it down again this momentum occasioned of his theories of fun and it also meant the template denotes wanted to know the word on interested in is the CIA and the this is similar to Boston I consider the momentum equation also there can fit scarce business non but then how can we obtain all of the tensile accretion then but it was my perspective is that it's a flux both recreations both food creations then we here this as I J and hear the difference of the tells us which we can be parameterized and then 1 could say that this is so creation we have to solve to Optane dinner Fitzmorris parameter with this divergence operator in front of it and this in the Commission is also them for the famine gnomic creation when the look of the heat fluxes this is all not to 10 those but connect us that is the inverse of the noted also the flat and so what are the
08:13
consequences of this it then the solution to this equation would look like this that's say we have also tens of geez in addition on this what change the value of this moment the promotor because if you the the described this then shorter and and as as agents with a hat when we could reuse this summit approach to solve this the Call attendance monster her mentor and then the canon against but up this and of course this is only 0 if G is 0 and this some in some the greedy incidents the only constraint for G is but the this conference must be fulfilled or in the case of and have creation this G vector this divergent free the and so here I maybe I think best because of their fears he constraints so we knew right there's there's the creation from the from constraint that's at the end of from energycreation maybe in in this the derivation we can do that again to the conclusion that his G maybe 0 I don't know all but have to think of it but I was a velvet before so what's other consequences if we would have to fulfill the secretion maybe and we have to also specify this is tens of product of G. I. H. J and no no of this is problem 1 issue had I have no answer to it there is a first one in a 2nd 2nd the problem is that's what
10:26
something was was already this up elsewhere and what is this so experiment of inverse filtering approach usually this sector from filtering and this is strictly true only if is a constant that's this contradicts the assumption would you want have a locally variable so as a parameter 1 of 4 some effort is to boss provided also in the nineties but he assumed but really move that seconds for when was that living this filtering approach and the thing that it is already known and then you solve this the creation and only follow with the smugglers at him later at the the right of the case on but you know we have to pay a price that's this all get some information was on the interstate eyes and free prose is discussed to use a value from the previous time step or use it it's a relation scheme all some iterative scheme however the in the later on this idea was them all but I did not find many papers which used such an approach every thing to used assumption some mention it but it is a threat its might be key some a response most just but the us that it is often a comment recently I
12:14
found a different solution which is from the right of his lesson difference definition of and there I haven't there it has it's also and in our stated is somewhat of a sophisticated introduce based approach to the sort of a dynamic from missing women but at least in the spectra 1 that is Morris simply applying a 2nd time this test photo but again I repeats the 2 momentum equations for book the fitted on resource and critics want immigration and then of a play at 2nd Stivers Theater and in respect to model the 2 times referred to as a the same as the what I'm afraid what why should we do it if the then knowledge the the form the difference of these 2 equations then we have his filtering 1 filtering above both components there the differences and then by this property of this spectral models we can absorb this filtering into food food ring and here again and so the have this the the different the fitting the very 1st product has no intrinsic flew fiddling again and the wrist look leads to such a a creation by them all in are also uses this altered his divergent but I kept it for there to be consistent with the 1st problem and he claim that this is sort of the amount identity and for the we see that he is also more filtering about this Tao tends and so it is very easy to that there's no problem to extracted from and the only assumption is that at the this is the same in the 2 scales 1 issue is it's is not the more the of the motion of a fitted few but the Adleman has problems and so
14:46
of the question how tool can be solve this the creation relative to voters the the vote the narrow it says just just look if inverse filtering and solve it and other of his through this with the and so but S is would you know filtering but I think this is we then is also mistake here to ignore this filtering at in this the creation of all we assume that's this s a all longterm variations in such a solution would be possible to all men in excess of ideas and to summary both issues in in brief the first one is should be soft rather this equation that of these I don't know when they're and we would have this constraint is this gene it ever of gene on the 2nd issue is what is usually done surface flows has asserted from official this is great this is questionable and I formed this 2 equations now this 2 solutions to it if you have some ideas hold to comply with its I would be grateful so our crystal common state
16:18
so at the root of the problem and have to so as the sum of
16:27
to some degree to to the caps is the branch on elicit because I will consist of isomerism