 I'm working with Professor Nimela and Professor Arminio and Siri Nivasan. Today my talk is about turbulent convection in a cubic confinement and mostly we focus on a flow structure with and without roughness. To do so we perform numerical simulations and among all the available methods we use LES. Why? Because we needed to do a very long time record, we needed to do a long time simulation to find the structure of the flow during this time. So here is the filtered equations in LES, we use LES while resolving LES. By means that we directly resolve a momentum and turbulent boundary layer and for these two parameters over here, which is subgrid scale stress tensor and density flux, since we are using a complex geometry and we don't have homogeneity in our system, then we use a Lagrangian dynamic model to parametrize them. We use a very well known method proposed by Menneville and Arminio to parametrize subgrid scale eddy viscosity and thermal diffusivity in our equations. So I just quickly pass because I think everyone is familiar with this formula and these equations. How we set our domain? We choose a cubic confinement with aspect ratio one and in terms of velocity we are applying no slip condition over on all six walls, the lateral wall, the vertical walls are adiabatic and top and bottom plates are isothermal. We apply a constant density difference between the top and bottom plates. We use parameter of number 0.7 and for the main result that I will show you we use two Rayleigh number but we extend it to a wider range of Rayleigh number. The density in our equations, the density is linear function of temperature. Moreover for the grid, for low Rayleigh number we use grid number of 64, 32, 64, 32. 64 is the vertical direction in our system and x and z is in horizontal directions and for higher Rayleigh number we extend it to a finer grid mesh. We cluster the grids close to the walls using a hyperbolic tangent function and as I mentioned to properly resolve close to the momentum and thermal boundary layers. Moreover for the scaling we use the height of cube for the as a length scale. We use the free fall velocity and density difference between top and bottom. I also use a edit turn over time which is more natural in convection and here this is the time average of vertical velocity that there are eight probes distributed over the horizontal plane at the in cube and they have a vertical distance of all of them. They have a vertical distance 0.1 from the walls. This is also used in a paper of Mishra for cylindrical cell. So first what we did we examine our code and method with a published paper of Daya and Eki in 2001. This is very nice paper because he was the first they were these authors they were the first who find out thermal convection feel the shape of the geometry feel and how he figured out he set to experiment one in a cubic confinement and the other one in a cylinder. As you can see here under the same experiment all condition for example the same Rayleigh number the same working flow that he used water he measured the fluctuation the RMS fluctuation of velocity and temperature at the cell center and he found they found the the fluctuations this okay this is the figure this this is the fluctuation of temperature at the at the cell center as a function of Rayleigh number. He measured in this range of Rayleigh 10 to the 6 to 10 to the 8 and this circle over here is the measured data in cylinder and this one is the measured data in cubic in cube and he found that this the scaling of these two exponents are are different these other funds for example for Rayleigh 10 for cube the exponent the power exponent for for cube is minus 0.48. So we did the same experiment we had only cube and we extended our range of Rayleigh number from 10 to the 6 to 10 to the 8. Here the open symbols are my data and the solid line is the data of the fit to them. Here is the I'm measuring the RMS of fluctuation as a function of Rayleigh number and this is this dashed line is the data of a key and this dashed dot line is in cylinder I just put them for the comparison. We found a very good agreement with find with experiment of Daya and Eki and we also confirmed that we confirmed his finding and we found the the larger scale flow that feel the entire convection cell can can feel the shape of geometry and because this actually the title of the article is nice it is does telmar convection feel the shape of geometry and the answer is of course yes and we confirmed that. So this motivated us to move to the next part and the main part of our our work we were interested to see how is this largest scale flow that in cube because we want to see whether this large scale flow it's cube no sorry this is this does does it stay remain at its position all the time or it's orienting this is I think everyone knows that for example in cylindrical cylinder cylindrical container Nimela and Sirini was on they have a series of experiment. So yeah and they found the wind can orient can have a reversal and have a reorientation in cylinder. So we moved to our main experiment and we published it recently in physical review in March 2017 we performed an experiment with these two range of Rayleigh number with a finer with finer grid mesh compared to a previous one and we here is the number that that grid mesh are clustered close to the wall and then they are they have they have the minimum spacing close to the wall and the maximum in the in the bulk allowing y and z direction and moreover we also following the criteria by Verzico and Kamusi and also Shishkana to put to set the proper number of node within the thermal boundary layer and for example Shishkana suggested for this Rayleigh number we need to put three that the actual value I put is 12 grid mesh and then we compute the Nusselt number by this formula and we found a very good agreement with a DNS simulation of Kakzaroski and Shah who did in a cube in in a cube using DNS and here is I also wrote down the editor over time which decreases with increasing the Rayleigh number okay the next figure that I want to show you is the instantaneous iso surface of the density the figure a is for Rayleigh number 10 to the 6 and this is for 10 to the 8 the first thing that we can see with increasing Rayleigh number the flow structure the size of flow structure decreases rapidly and although for example you can see the for instant instantaneous flow structure which is upward from here left side and down from the right side in both cases but still it's nice to see how it is for a during a long period of time it is quiet well known and it is also found by other authors for example Shah or Kakzaroski and Boba Neki they found the wind this large-scale circulation is stable along a diagonal direction this is the strip lines in this figure are average over a finite time interval in which we identify that the wind is a stable in that direction the color contour denotes the magnitude of the time average vertical velocity normalized by free will freefall velocity and we also found the maximum value the maximum value of the magnitude of the vertical velocity is roughly 0.25 at the mid height somewhere at the mid height which is in good agreement with Nimela who found it in 2001 in a cylinder car container the same feature also observed for Rayleigh 10 to the 6th as you can see here for example if I can zoom maybe a black spot or here is the impingement of upward jet to the top solid solid one and then spreading out horizontally and here they are coming down cold balloon coming down and jet balloon going up and then at the at the mid height they converge and then in flowing inward to the cell okay as I mentioned before the RM is to provide accurate characterization of the time evolution of the large-scale flow over a very long period of time so we extended our simulation for a longer time and we found although the the convection is statistically stationary but but this large-scale flow does not remain at the same position all the time we found overall we found four distinct stable state for the large-scale flow it is also nice to look at the structure when the when the wind is moving from one corner to the other as as I mentioned for example in cylindrical cell they found sometimes wind stop and then start in another random direction that we did not find it in cubic cell we did not find cessation we didn't see the flow slow down and start in another direction this is transient state when the when the wind for example moving from this corner to the other it stopped for a little short period of time along the wall here is the top panel and as you can see instead of spot we have an extended line this this is the when the this large-scale flow contact the top the top panel it can create this line over here moreover we did not find we did we found we found something else uh the switching uh rate uh yeah the the switching uh no okay let's let's say it in this way the time that uh structure this flow structure large-scale circulation stay at each position is not constant for for instance this one is the time average over 70 edit over time and this one is over 100 uh edit turn over time and for example for transient uh state is about 10 edit uh 10 edit over time so if I can show you uh in a movie maybe it's clear okay I'm showing you a three horizontal plane close to the bottom close to the bottom wall mid-plane and close to the top the vectors are uh 3d uh velocity and the contour the color contour is the density in in this case as you can see the wind first is oriented in this direction uh from this point to this point and for example the top panel as you as you can see is oriented in that direction and after a little while after a short while the go the the wind is moving to another direction and now you can see this transient state how it should be stable from this corner to the other as you can see if this is this coming down and then this is going up this is the vector showing upward here is downward like uh laboratory experiment we also perform uh numerical we perform um numerical experiment uh by means by means of uh putting a huge number of probes in cubic confinement to measure the velocity but what I'm showing you right now only eight of them here is the horizontal plane at the mid height so we put uh eight probes distributed as you mutally uh over this horizontal plane and I named them for example from prob uh one has a zero angle and so on I show you at the moment the for for for for right now uh the um velocity of probes which are placed diagonally for example probe number six and two four and eight more details are published in my paper if you look at these uh time series of the vertical velocity for probes four and eight for example which is uh they are placed here uh for for instance you you can see there are uh many uh uh instances that going on during this time there sometimes probe for example four is positive sometimes is uh positive sometimes is negative and sometimes there is like fluctuation but overall what you can see is the mean mean velocity is uh sometimes is they have the same magnitude but in opposite sign and sometimes they have the the mean magnitude of the velocity is zero with huge amount of fluctuation what is happening here is this is exactly the signature of the large scale flow for example let's look at this isolated box here this probes number eight is showing probes number eight over here is showing upward uh uh positive velocity and the other one showing downwards so you you expect to see flow directed in this diagonal and at the same time the other the other probe showing the mean velocity is zero with huge amount of fluctuation this is exactly what we already saw in this figure if the mean wind is for example oriented in that direction here is showing the upward plus and here is at the middle showing downward and here is the place of do these two counter rotating vertices this is the huge amount of fluctuation happening at this point so this is this is one example for example remember this time at this time over here the angle of the mean wind is 135 that also by Fourier transform we confirm this observation i choose the same formula as tione and i calculated the the phase and the strength of the wind and as you can see here at this for example at at the same time time 200 the the direction of the mean wind is 135 and during all this time that we recorded in our long time simulation we did not observe reverse by means of for example there is no you cannot find the angle that the difference of between two angles is 180 so now i will show you the main result we put also two different type of roughness we put a groove which is two dimension and they split in two dimension and also pyramids if you look at for example here is the zoom of pyramid at the corner which is three dimension i call them three dimension and we choose three different height for this groove the maximum one is the i i call hydrodynamic alirof which is close to the experiment of tongue and stringana and versico who they did it in a cylindrical cell and what we found for the case of for for this low height of the groove in case of groove which is for example the height is quarter of the this value the maximum value i call it smooth hydrodynamically smooth we found the same thing no surprise the wind is oriented along the diagonal direction and everything is fine so what will happen if we treat with rough surface for in case of groove we have seen the wind is locked along the along the wall and it as you can see it with also probes and Fourier transport we have seen it oscillate at its position the angle is like 180 it stay at angle of 180 and it goes on their oscillation between two adjacent corners here is i'm showing you the for example the velocity at two probes at the at the mid height and as you can see overall it's one of the prop probes is positive and the other one is negative and the Fourier the Fourier transform also showing the fluctuation around the angle of 180 and interestingly we remove the alignment what we have here we have we are aligning the plumes that erupts from the tip of the the groove and in case of pyramid when we remove this alignment we go back to the when to the case when the wind is oriented along the diagonal direction okay the main conclusion of my study is we observe non-switching non-periodic switching of the mean wind from one diagonal plane to the other and the simultaneous appearance of the counter rotating cell in the in the in the other in our simulations unlike cylindrical cell orientation switching a cure through rotation we haven't seen sensation with pyramidal structure on the rough condition the wind a cure in the diagonal planes as it would without roughness element with hydrodynamically groove surface the wind is forced along direction of groove alignment but it is unstable oscillating periodically between adjacent diagonal planes where where we would otherwise expect it the difference from the pyramidal case is due to the direction uh directional concentration of plume emission along the groove from which the wind is generated this also can be done by tilting the cylinder you can lock the mean wind at its its position thank you