The Fluid Dynamics of Cumulus Clouds by Roddam Narasimha

thank you very much um you hear me and it's sort of looking at club stuff about the 20 years but the philosophy has me which step-by-step each type take one one additional effect and see what one can learn from it before we put more parameters into it you have a large number of parameters so easy you're not certain about and of course you're not quite sure exactly what computation to say so that will be thinking so I want to do is this some of the people here will have heard me speak about earlier work on clouds but still in order to see where we are may be good to see what the tech near work said because some of the major conclusions came from the Tahlia work and I want to tell you what they are or I go ahead to what we're doing so the first place close are really in by my grand challenge problem in atmospheric sciences today you're talking about climate change we are talking about the monsoons clouds are the weakest point and that International Panel on Climate Change has said that many many tight it's appeared as a peaceful physicist start looking at clouds II for a long time there have been efforts to what are these clouds and a brief summary from a fluid dynamical point of you appeared in others very well-known book we will see if exits thunder himself light some very experiments realize of course that buoyancy is an important factor and when he made Table Topics with bubbles in each one but none of them really looked like a cloud here for example is one where he had that bubble kind of experiments and you see you can is growing linearly just like a standard standard blue conventional grows linearly it height you see the experimental points they line up exactly where a classical to does and at that time well big cookie resolutions are still not very common and the attempt was made to describe it in terms of similarity theory self similarity of such reservation as some turbulence people like to call it the basic assumption is that the beam flow as well as it in our census scale the same way the same length and velocity states well that didn't get very far and I show you why and I'll conclude it and at present there is alternative model there are lots of cloud types but the ones that we are most interested in is cumulus that's what really that's a great deal of things in the tropics the cumulus is the real flow club it's a fluid dynamicists cloud so to speak some of those other clothes no it's not for terribly important they seem to be the right one to try and tackle and started trying by trying to see how shapes like this for example do typical cloud you can see how quickly disease you know fluffy balls this is like a tower both of them are cumulus shapes what goes on with Mannix with sweet image why is this or why is that and is there anything that we can understand even one major problem is entrainment how much of the dry air gets into and first choice for making those assumptions we will go back against two Turner was to say um hypothesis made by Taylor the entrainment velocity into the plume or into the cloud is proportional to a mean velocity characteristic in the cloud flow or the means you so you take the centerline velocity and you take this it's proportional to that often folks the problems that Turner handle it doesn't work well in clothes at all and in fact in the 1990s which is the support assignment we were starting of a work evangelist said an old similarity proof model is totally discredited didn't tell us much about clothes so it can be very different shallow deep off a smooth boiling waters chaotic order etc flow close and that's what makes the most interesting so you'll have the first three models that were try not give anything looking like a cloud he started looking at what heating does to a plume heating is the the proxy for the leads of latent heat the phase change occurs and the main difference was we said well heat release is only over a certain region what happens to the flow and a cold is not a city cloud in fact if you look at flower lifetimes that actually not very long median of 10 minutes ago look at the old movies for some of them can be much longer rise the mail much longer lies so really the kind of flow that we set up was what I call a transient diabetic blue the first thing that we found was that if I wanted to put it in our is one of those pigeonholes fluid dynamicists I would wear this for fixing I would say a cloud flow will put in the transient diabetic model I want to show you why see the overall picture we have of what we are doing in terms of the club is of course a cloud is a very complex flow couple system micro physics thermodynamics droplets particles and so on yes transitions italy's and then the cloud word the macro dynamics I would like to call it what you can handle the danger Stokes listen is clever this of course a car fix although this is a pro cycle but I only look going to look at this green mean here by our dodge this is doing it because at that time it seemed to me that that's where you seem to understand the least here are the equations there are more or less the standard equations for the boussinesq approximation as we know then see changes are taken to be so small that the fluid is le Crump incompressible can be treated as incompressible as far as activities goes but when you commits to momentum balance change in density does not affect the inertia terms but it does affect e we will see term so it is converted the density change is converted to temperature through the coefficient of expansion G is the acceleration due to gravity G is so high compared to these accelerations the small temperature differential is enough to make this term large and it is the energy equation this is the temperature differential incidentally standard plus a term due to the amount of heat you're looking in that can be a function of X and T what is it a equation now I don't know what is in the equation you are now because what happens to the vorticity is very interesting and sometimes we an expected I think therefore an understanding the vorticity field might contribute to our understanding what happened are we make a non-dimensional parameter or the amount of heat which you are putting in is a total of us that's the total amount of heat which are putting into the flow acceleration due to gravity coefficient of expansion density Sikhi V is the length scale U is a velocity scale best when they are looking at clouds on the cloud base infuse it well Aman teaching you also make a local number so our model as a plume which starts from a hot spot on the ground this is a classical pool and then session heat release now I try to do this with steam and hair and so on for six months and then experiment it work out very well so it turned out that it would work best in what are going cook so funny to make clocks with water so really we made an experimental apparatus this looks like this it's about 1 meter square box what one-and-a-half meters high and you can think of this as the flow equivalent to the growl we make a plume here is the plume chamber hot bit of food loses out to this tank of water you have a case here of electrodes the tool fluid coming in is electrically conducting that's my cell or something I serve it is electrically non-conducting it's ji hyo's water so this is really a conductor inside a insulator and by applying voltages across these grids you can put it eat ohmic loss and you can control that we have done it in such a way now that you wanted to repeat it eating is free push a button and you can get that same piously again and again it's a transient flow if I want to repeat it again and again if you have ranges and you can also make some certification otherwise this is neutrally stable and you can make that scale analysis from the heat leads in the cloud fluid is of the order 1 1 meter it turns out that if you do it in water that says it's a very manageable one kilowatt the way you put it about a one kilowatt heat water a fistful of water ready producing the condition so set it up it's a standard starting clue we can that's Tennessee lead for example this is the same sort of plume Heelys here and you can see is already significantly you must forget the part below this that part of a club with you will never see yet this way becomes visible only after condensation so in factory can produce several different kinds of cumulus clouds at least three and I want to compare quickly there are clouds here are the pictures are the ones which you bared in the lab see how many we could reproduce what kind according to this is a congestus so it's a pretty dense as you can see several kinds of consistency comes here is a mediocracy when the mediocracy is really not releasing getting heat no condensation taking place it is as the name suggests it sort of dying cloud it's not it's not a very active Club you can make that I like laying out with the amount of heating you're doing it's not other one there's a factors as you can see it's as if somebody is really pulling it out to pieces you can take that as well practice things hanging wrong now but this needs some certification at the top in other words what I am trying to say is it what we learnt from those pictures that you can make cold like force the lab the optimist it's just a few control variable sorry eating some stratification and against it require but very importantly but non-dimensional Italy is above us we the same as of the problem then also it is not the same but the heat reason about must mean see hatred is number right and these four things that are mentioned here we can get a wide variety it was shade so what happens if you excite me measurements will be divided by the diffusion term okay that is the diffusion here there are not suppose a pretty long mm so the diffusion is a small but not negligible certainly not realistic they're not somebody here not realistic she said one other thing that this is showing they're not somebody is not as important as you think there are circle problems for which there are somebody's important output mixing and even there I personally feel do not have to learn how to do this I realize they're not simple I think great deal can be learned it will get smaller there are symbols provided we have beyond what is called the mixing transition I come to that literal well this is we first started three flows and you can see what happens immediately that's the diameter of the blue see - what is the height you heat eject here slide is what the conventional floaters without heating and as you start putting in the heating these values of the heat sleeper you can see that the width actually shrinks I think seems to sort of become constant in other words cloud doesn't grow like a regular jet of it actually is a modern more coming towards most of us which you saw was like Sally shakes the beam velocity at the center light increases that's a reciprocal of the centerline velocity so that's what it would be in a regular jet heat this comes down so the velocity actually goes up so it accelerates as you might expect the turbulence intensity is also go up in absolute value that scaling there does it vary with X or you could actually have visited Bob tells you why if you have a bumpy ride in a graphic and here is a entrainment coefficient you can actually measure the mass flux and compute the internment coefficient this is the way that discrete of like ship was happy that M is the mass flux the rate of X is a bus he's the types of the law that allows velocity see as you go up that is the heat injection so if the behavior at most of these is roughly like this starts out takes a little while and reaches a peak that comes down was that does it happen at this particular floor and this particular flow I think was a lot different what we had this other experiment made it it also shows this big decrease under D key but it goes negative is raising again partly I think because the heating was very much higher at a retention number of large one but incidentally it also shows that there is no universal curve and quite a bit of it may depend how much heat you get how do you put it in what is the distribution native other parameters so what is happening to the flow to cut out entrainment as you cite there as you move on incidentally that that picture shows that the self-similarity model does it work working or alpha he should have it Const clearly doesn't work why doesn't it work when you get a cook take a cross-section is taken with basically div you take a cross-section we flow blue and is no heating look like this that's a dye concentration basically wavelet analysis on this a 2d wave recognized and at some wavelets cage well although that what seems like a mess is a pretty ordered structure fossil in other words this mess of the flow is actually hiding at a certain scale relatively well-organized or I will rotate instance and we know that from other measurements that I think like this this is part of the core et cetera flow the turbulent flow shear flows are not as disordered as a spot greatest exit there but if you add heat that's what happens to the flow you can see how qualitatively differently dramatically different and our own structure as superior and here is part of the flow which is unmixed incidentally like the protected code that we child is talk about these clogs but of course we said absolutely don't which don't mix much of the mixing of outside search phenomenon is debated here we can in fact therefore see what is happening there series quite not going to the city Technic towards type just a compiler with certain other kind of calculation shows measurements of the calculation so you come to the conclusion that it's a good hypothesis to make you less cloud for special example of a trench aerobatic all these all these things are important so we nominate a DNS X out in a box suggesting temporal simulation and that's the box the fluid expands this way that of the pool and we put in heat in time is the denial denial about attention up including space thank you and the jet expands this way I'm here to solve the same equation I'm not going to but what I want to show you this is a needed flow there is that co-editor this is that toroidal vortex structure that we talked about monocle now you put heat into it that's what happens it see that this is incidentally the vorticity has a boot on you can see the dramatic it's huge what the city field goes up enormously and in fact you want to find out how much you can compare this with usual jet and it starts off also there is the first few diameters every the jet starts transition to turbulent flow each of this peak and then slowly decays but you can treat it this is what happens this is instead of an hour and a logarithmic scale the artnet you can see how extraordinarily is rafi increases it's an order of magnitude more than a factor of 10 so you had a y or tissa T of walk declining the artery J you now have something like 10 times that increasing sit with the display the end of that flow velocity therefore is dramatically increased in fact you exaggerate things a little bit vorticity which you see the cloud what they suggest Elia comes from heating exactly started in approve almost irrelevant because of the barometric thought I had an equation for the vorticity there wherever the term because they probably come back so which Rivera plating for now this is our third generation TNS quote we tried to compute an actual transient diabetic pro it is numbers here so first of all usually what do you get I have what we computed here yeah watching observe here these are the parameters as I told you there are some it is not very high doesn't matter for mixing but in other cases it doesn't seem to matter a Grady so you can see that flaws are very similar and it comes from we wear a clinic talk many of the things you'll be understood from bara claret talk if you look at what's happening across this flow the temperature is is intubated so the buoyancy force is largest in the building you go toward the edges which is smaller so there is a barrel electric operating gear this way on this side this way on the other side that vertical Indic talk increases the velocity in the centerline and diminishes it the edges that's really what accelerates the flow and it has a variety of but there is not only a mean binocular clock that instantaneous particular car and this is a CDU you split the flow it said cylindrical almost our clouds a sabbatical in clockwise raise up the flow the lots of fluctuating baroclinic talks operating here following the temperature gradients of course radially velocity compare across and that almost increases vorticity how did that happen especially last yeah yeah then I think I forgot to point out one thing I did have a spectrum live interesting thing either the high frequency were missing and it's larger increase that lower frequency obesity see that I must have skipped that I figure anyway if I take a balance what is happy to be its trophy that starts with the Navy Association play or heating actually being more tricity offer a steady flow and these are the various terms which contribute to the mean words this is the turbulent transport of turbulent electricity so this what is it aprox on top we draw 230 trances in stretching rate overland flow such a turbulent water sitting here viscous diffusion you write an equation for the travel intense low fee there are a large number of terms actually ah the generation by the mean velocity gradient here capital Omega turbulent transport doctor one derivative searching by bead slain sitting by turbulent strain this goes diffusion the viscous dissipation well I don't think that lychee I won't go through a detail the order of magnitude analysis of this equation interesting the only terms which wife that order making order of magnitude analysis V to cease to stay quiet or we'll explain discuss dissipation now that is for the regular but if you don't do it with heating and a long story short you see the equation for the intro contains three terms one from the fluctuating water snakes and other dissipation due to the fluctuating work city they should be primed here and a third one source but applicable now why I wanted to make here one thing to remember is that okay okay I continue for a few minutes and one thing you have to remember here is that if you have a flow with a certain vorticity you do something to it you change the what you see as you are doing with heating I do it without heating vorticity large-scale the same way the velocity as it lends itself to Zurich solutions you should do I compared to large-scale vorticity let's say the turbulent shear flow vorticity increases like the square root over a hot stone because very last weight seven if in addition you have heating it it because absolutely huge actually what see this term therefore is it really grow China ideas well that's the continuation of e so you can see that here this is a the vorticity surfaces in the regular flu what city surfaces a cloud like see how much it has changed and you can also achieve the you change the specter of visually because a lot of small scale motions we just scroll the whole floor it is the mass flow if you take the mass flow as you normally do with a lab experiment on turbulent shear flow you would integrate it across the floor and is the outer curve here the black curve this is DNS so you can actually go to the edge of the flow vorticity write what the axial increases the path of the turbulent flow is that's always a little less it does depend a little bit of the threshold you use especially in this part but bioglass is a part of the flow is not turbulent it is black right so this is one more reason why I now feel that the old I wanted to call it entrainment coefficient LSD fish I don't think it is relevant it does it remain constant depends on what is happening and in any case what really matters is the turbulent flow which gets in and that's not the same so here the velocity scale H of one actually here the sentient flow you have a variation in height I'm saying of our situation it goes up as it did in the earlier case and I think that I just want to show something like a movie let's see this is one of the data solutions for the transit diabetic view is the vorticity consult contours inside that's the scale so reddish is very high Louise let me go see verticity is actually out there at the top it's a bit earlier just above the dejection so you would get a factor of 10 they're the biggest to look like it's loud I have a similar movie or have mental cross-sections so the last thing and how does increase mint occur love a big debate going on about how a treatment occurs every now and then it looks as if it to having every nominee debate orientation how do you propose this big B this is what standard picture what happens we're coming in like that parallel flow huh I was convoluted edge fractal edge for the dead who goes in but what happens is more like it is it's not at all parallel a lot of fluid coming in from outside I think in only at certain places very high values so there a finite lifetime these pictures show that entrainment is really episodic not start continuous it's not that fluid is coming in from outside in fact the outside flow is also organized which people have missed my dogma is flow it works on the world sees inside coherent vortices this is actually that's a vortex ring you saw that vortex seeing this part of the vortex thing is like well that's another big they conclude so latent Italy's what's really important to the dynamics the Chancellor diabetic group is a good exposure dynamical model what happened folks wide variations in the internment coefficient directly they talk rise the flow engine and the vorticity is very important as a description Lasseter thank you very much sorry exceeded by type what if if you include the radiative cooling on top of the - like what like in a real flat vessel usually we didn't lay in the real estate economist out there is a ready tequila reckoning on top yes that's always lean otherwise but we haven't had time to do it these were of this suggest something else but I think there are ways of doing it this is one the idea we toyed with was that you had a very thin quiet scary a very poor fluid is it roughly look you can't cool it if you want I'm asking which what will happen if you include that ah ok that will of course safely in stiffie if it's cold gets heavy therefore the fluid will spread out you know it will actually become more or less like laminar flow right I've seen clouds evenings for example right the screw out if there is a diversion the temperature is increasing and oh yeah let's say this is all this assumes that the atmosphere is at rest just to make the problem simple yes of course being slowly looking

Channel: International Centre for Theoretical Sciences

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Length: 32min 37sec (1957 seconds)

Published: Thu Jun 29 2017