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Application of a dynamic turbulence parametrization in a circulation model

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thank you very much there welcome to my talk I want to show you the application of all recently developed at number 2 in standardization in or at
most McMullen the gold was to obtain the privatization of the it
allows us to investigate also small smallest scale it's always it's the smallest use of skits in all model that means that we don't want to use some sort of high diffusion which condemns everything all some of the ideas that's even this was years of scarce shoulder there's some Ristic gravity reflectivity like it's as pictured here and also the spectral off the kinetic energy the energy looks reasonable as it has shown here I presented some this model in detail in the last time at whose MMSE and so I want to make only year the shorter its respective of all condescends to win standardization then on that occasion to move the atmosphere relies heavily on stratified students and thus I want to say some words about the basic properties of his stratified jubilance in the atmosphere and finally I want to give some resides in the 1st application in all models so the I like this picture planted
it's the last and here sketched though part of the kinetic energy in the atmosphere we started to large-scale synoptic states with different heating and which is converts into burgling base and then they can anti cascades down from the scales up to the schools scales letters dissipated by Mollica friction this is as it happens in nature but in the global circulation although we have a finer resolution scale and if we had no 4 of our parametrization that's happens so that it in eyes up close to the resolution scale and finally the model is unstable so many models the set of say circuit we just need some in type of viscosity and this is often done by some the high-order hyper diffusion and works quite well for the notch their parts but with a price that's the lower certain scale we can call it if it DIFF resolutions game every emotional there is reused strongly dams and we cannot regard this any longer as something with this has to do with reality and so however who we are and half for the some limited the capacities and be interested it is possible to extend the is the realistic part of the spectrum close to a resolution scale therefore we decided through the use of a of a sophisticated so most here apparent isation relying on the physical properties and therefore we designed this dinner the Nymex migrants the laws and generalization of food at another time is It's
based on the mixing approach that means we have the diffusion of and this makes length and we can connect this mixing length with this with scalar waivers memories become meter and the dynamic approach is read we define a test scale will move is assumed here are some to Minsky it's and within this re- soft 3 you the collectors members who permanent and transferred to the honors of states but for some reasons of consistency be developed and the July rise version relevance ties in depend reserve and scale and this is the basic approach of it we also and the use of some
constraints from scale invariance be below 1 can derive some scale-invariant information for the basic like creation and 1 property is important for parametrization and I want to motivated also with some the robots and at 1st if we introduce some scaling here room with his exponentials and I call this vectors and exponentiates the scaling factors off time low on the length scales and so on and when we can show that for all the vertical diffusion of all of the momentum equation this is smaller so this term is scary around all you under certain constraints but is that makes thing always this specific scale ratio and it's still something special because it's the Vatican makes length scanning depends on the vertical scaling and on the results of scaling which is not the case for example of if you take a little horizontal mixing length however then the primitive equations which we use in atmospheric the we can specify this is Whittaker's scaling factor and thus the mixing it's that is also not deter mined and here comes the idea of stratified students into play because in this study a tremendous a prison publish made in talk there's an aspect ratio of horizontal and vertical scales z and x rays it depends also on this in ICT G. dissipation rate and for brands with the frequency for like it's did you always assume that constant and for measles gets we can also assume that these is a constant and once we have this from this aspect ratio of their the relation the Whittaker scaling factor is 1 3rd of can effect on we can apply this when in 2 ways either we can apply this directly into the service constraint for over 2 commits then it that has all that this scaling factor is 0 and this is the current to the case but the vertical mixing is a constant so the lexicon of for the vertical diffusion at Sussex whether it's model is also physical consistent all we can apply this ratio directly follow mixing angles and conformant from this dynamic approach for this what makes a link where it is dependent on the but extent is proportional to the cupric of flaws on mixing so this idea rest on this street had trouble answering and so I want to explain this in more detail and as I think it's the most of you are not so familiar of a fit FIL positive jubilance we need basically 2 requirements 1st was strong on as a triply and of course there's some to blend motion and want to discuss 1st the anisotropy and because this if you look closer into that mistake equations finds that's feed non damage unless it's so called few model food number which is very loan a very small in comparison to 1 there which is given by there are some typical Hosoda velocity was on specific assume some horror stated further by was shown the summoned 15 years ago that's if we look at for poetic those the returns all of that is the accompanied by the ratio of typical values which is similar to the solvent of room number well we have a vertical length scale in and it is as though and quality went through number but there was a fire in we're only looking at its 3 cannot argue wolfach magnitude this if about they the of us also performance can analysis which is some for what similar to this scale the crash in those criteria I mentioned before and they found that there exists a transformation group for the former variables but here's scarce vertical velocity is when was the frequency and density we which are connected and have a scaling factors the have this equalities and their deduced from it but this radical length scale is proportional to the 1 over this frequency the however I fear look performer dimension the proportion of factory i which is missing you must be a velocity and we have the main basically to possibilities of horizontal velocity on the way to commence at but there is a scaling is is the does not allow all this 2nd approach so we have this only this choice for obvious what to collect and if we want this to Verdi me condition of his batting for numbered sounds too but for the transitory in this it was nice of proximation the Vedic afford number is more or less equal to 0 0 to 1 the 2nd part we use this that's we have some 2 went velocity hands this is you the can be expressed by the dissipation rate and length scale with this when on the pituitary lobe of his the cube root dependence and then this was added to the idea of in talks to combine these 2 together for sort of federal men's by eliminating this horizontal velocity here and so we obtain this aspect ratio for the stratified to we can rewrite is also slice the tool gets long the formulation I presented in all iteration but this that is gets a proportional to with few few offer horizontal length scales but this was not the only thing which was shown by the book he also looked for the energy spectra and so full of every referee and waving arguments the if we could say that some more a suspect as the something like in this graph of velocity times length scale and he stays OK but I assume that horizontal energy spectra is depends only on horizontal links skates and a spectrum metal fits and if the user then this to glance velocity hearing find this is proportional to to the specters proportional to move this thing of Pfeiffer at all if the approach but it is too with Nobel Rivest minus 5 foot law always if the the in this or look for all that the energy spectrum the if you're body length scale and then we can apply this fruit lumbar and then if behavior that this spectrum is proportional to the the mind says mine's free of Vatican wave number FIL it is possible to show that for the stratified blends also a frequency spectrum can be he arrived this proportion to only get to minus 2 which is important for the the little there final comment on this certified Joelynn's ends the this and the other loses from ensure losses that we can also calculate the magnitude of kinetic and potential energy and hence alter but then the kinetic energy is 1 plus horizontal budget from muskrat times the spread of of horizontal velocity and put into energy as on any of his the ready different number and so we can neglect is in 1st order intensive exists is for to was sort of a tree partition of committing potential energy which is similar as for gravity waves in women of mid-frequency so this is the sort of dominance then
I return on 2 or 1 of the and so I want to show that it's really provides the the correct with of that's just what we wanted it to do for example here's a snapshot of horizontal divergence we see that as much as the missiles get activity but it is well connected to some the break to off the thing was received you can see you some the worst we wave and is rather some American the context which was claimed by his had for beginning by some of a people who revolted high the diffusion give only numeric artifacts we can also show that is Hollis
Maritz a primate is closely related to the other 2 Wilentz in all model as a proxy for 2 Tillman's we have the the kinetic energy and contours for with muss they're not of a 90 all model has a with number resolution of freedom and the 30 I should and b c that's of asthma it's apparently this Morris of similar structure as the mental and so this is something on which we really appreciate the look at the it's and the rest from this 1st parameter and it has all obviously person the shape of the wing and you can note that the variation of mixing the encounters too much lower but this understandable because preface Q. crossed dependence and lists you can present also of the diffusion in all model of vowel and the diffusion of wasn't momentum and you see that the ri ability of its its a controlled by virtue of his moments support meter this is not the case for the classics Marinsky because they're there we have a constant mixing link and for is only given by this wasn't a major and of this
the final result so I want to show his that's the energy spectrum the on very them of in our opinion very reliable the SynOptics gets of month efforts love and transition most 5 thought around their calculated for of 500 to 50 and unaffected poster which is the middle troubles the upper torso and lower stratosphere the BEC bots here is the modern version where I used a constant but the mixing length the US in the assuming the other approach I mentioned before I have a similar and so they're in we can say it's it's from the perspective of the in the modeling and say this game and so we can use 1 of these 2 approaches then we can also compare always spectral before for example M W F and losers as shown here of some some years ago and use the same color scheme in my if you have a C and you see that we have in a scarce up to approximately with was the same features for example here the trouble sphere and a higher part of the reason not to expect from some of things and in the stratosphere is this slower Greek difference between the 2 others this is that difference the notion strong dissipation due to some hyper diffusion in all model we have frequent annotation to over and of a spectral inductive resources gave us we argue that's even though small waste the solitaire my 1st picture which the sort of flesh never from 200 inch Fred yours of like that power can be regarded as something which is right all closed 1 is close to the nature the I presented resides enough for for over tuple sensors loss hurdles fear
main region of interest of Institute is the it's a lot of the up to 100 and 10 kilometers than to you want to move the apply our this anemic position or in version of all model which range is to is heights this is of particle interest for us because the developments and chains of exam a much stronger than in the troposphere if you have no trouble sphere sum over some period of time some there the development of all comma decimal 1 all points to a curve in the same period of time in vet from image regional it can be 1 or 2 heaven and so this this this is why we are very interested in this furthermore the gravity race which emerges in the energy region have higher wavelength when they're in the troposphere so we can cover the bigger part of food gritty they spectra nominal and so and we assume that it's the Goretti rates which are all in the UN only generated by the break of primary gravity waves and with our students is in the star HOSIC sense and this precipice positional feasible ways more less visible or a most as sort of had 2 wins and this is that this is not a very the strange the idea is to confirm by some make them into a radio data of from last year but a strong that's in the energy region at 84 to 88 polluters the spec shuffle Montebello's it is indeed showed with this behavior of omega to minus 2 shown you is so we assume that's the energy reaches governed by strict effects do men's and all our 2 bends her division is fewer corrects for use for polarization formal to study this region in detail so I
will come to my Ltd as I said before we want in this case if it is ready respected and the region with respect to start effect still lands we want to compel is also the measurements and the and we want to apply they're all model also for the temperature and also in of our UGC and so the 1st we can say it for free is sets resides a printed will be published in a paper which was just accepted and school we plan to woo and extended apply or optimization through them achieve this the comparison the experiments there is also a on the goods the past exists set up of which MIDI or output and area the inaudible Institute started it started in 2 flows and flooding is still know but it's it's examined and we as as a lost tool to compute want to measure the horizontal wind fuse in this energy region however we received last month the approval for another project which is this time four-line us and this this will allows losses also tool look at the horizontal waves on loan to the or those structures by a light as it is region and finally the of application to of the variables or other models will be given by the to po starts though positions within this transfer lead you project images France has an atmosphere and ocean and so then I of
Tobin's I thank you for your attention
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Formale Metadaten

Titel Application of a dynamic turbulence parametrization in a circulation model
Serientitel The Leibniz "Mathematical Modeling and Simulation" (MMS) Days 2018
Autor Schaefer-Rolffs, Urs
Mitwirkende Leibniz-Institut für Oberflächenmodifizierung e.V. (IOP)
Leibniz-Institut für Troposphärenforschung (TROPOS)
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DOI 10.5446/35365
Herausgeber Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS), Technische Informationsbibliothek (TIB)
Erscheinungsjahr 2018
Sprache Englisch
Produktionsort Leipzig

Inhaltliche Metadaten

Fachgebiet Informatik, Mathematik
Abstract Preliminary results from the application of our recently developed extension of the Dynamic Smagorinsky model (DSM) are presented. The DSM serves as a parameterization for subgrid-scale momentum diffusion in a general circulation model (GCM) that allows for stable simulations even without a hyperdiffusion. Due to gravity, the horizontal and vertical scales have to be treated differently. Our extension includes a test filter for the Smagorinsky parameter that is separated from the resolution scale, and a dynamic approach for the vertical diffusion based on the ideas of stratified turbulence. The aim of our investigations is to extend our model into the MLT for a study of GW spectra with respect to the scaling ratio of stratified macro-turbulence. Therefore, we show the performance of the DSM up to the lower stratosphere and discuss the implications from the scale-invariance criterion for LES parameterizations on the approach for dynamic vertical diffusion.

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