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14:00   Turbulent Convection 6 14:00 15 mins #362 Large-scale coherence of turbulent superstructures in Rayleigh-Bénard convection Dominik Krug, Roberto Verzicco, Detlef Lohse, Richard Stevens Abstract: Many relevant application cases of the Rayleigh-B\'{e}nard problem, e.g. the atmospheric convection, are unbounded laterally. This fact has motivated researchers to go beyond the widely studied cases with $\Gamma \sim 1$ and to consider domains with large aspect ratios $\Gamma = W/L$ \cite{Fitzjarrald1976,Hartlep2003,stevens2018,Pandey2018}, where $W$ and $L$ are the width and height of the cell, respectively. Such investigations are experimentally cumbersome and require expensive simulations. Only recently, \cite{stevens2018,Pandey2018} were able to provide evidence of the existence of so-called `superstructures', i.e. very large scale and long living flow structures, over a wide range of Prandtl numbers $Pr$ and Rayleigh numbers up to $Ra = 10^9$. An example of the superstructure organization in the temperature ($\theta$) field is shown in figure 1a. The remarkable observation that will be subject of this paper is that the corresponding wall-normal velocity ($w$) field (see figure 1b) displays a significantly finer structure. Such differences where found for $Ra > 10^6$ and are surprising since the buoyancy driving naively suggests a high correlation between $\theta$ and $w$. Here, we address this issue via a spectral analysis. We find that very large scale organisation also exists in the $w$ field and that those large scales are indeed highly correlated between $w$ and $\theta$. We further quantify the spatial coherence of the structures and demonstrate that our findings hold over a range of $Ra$ and $Pr$. Finally, it is found that the bulk of the buoyant production of $w$ fluctuations happens at intermediate or small scales, explaining the different appearances of $w$ and $\theta$ in figure 1. 14:15 15 mins #389 Resolved energy budget of superstructures in Rayleigh-Bénard convection Gerrit Green, Dimitar Vlaykov, Juan-Pedro Mellado, Michael Wilczek Abstract: Please see attached pdf. 14:30 15 mins #123 POD ANALYSIS AND MODELLING OF LARGE-SCALE REORIENTATIONS IN A CUBIC RAYLEIGH-BÉNARD CELL Berengere Podvin, Laurent Soucasse, Philippe Riviere, Anouar Soufiani Abstract: Direct numerical simulation of Rayleigh Bénard convection in a cubic cell is performed for air at a Rayleigh number of Ra = 10 7 . Proper Orthogonal Decomposition (POD) is applied to the joint velocity and temperature fields of an enriched database which captures the statistical symmetries of the flow. The dominant spatial modes correspond to a large-scale circulation aligned with the diagonals of the cube, so that four quasi-stable states are possible. The flow spends most of the time near one of these states, with occasional, brief reorientations, during which the circulation becomes parallel with one of the vertical sides of the cell. The symmetries of the different POD modes are discussed, as well as the possible physical mechanisms they are related to. A description of the reorientation process in terms of POD modes is provided and a comparison with other approaches such as [1] is carried out. Galerkin projection is then used to build a low-dimensional model. Unresolved modes are accounted for in the model by an extra dissipation term and the addition of noise. A seven-mode model is able to reproduce the dynamics of the large scales in the cube, such as the intermittent reorientations of the diagonal circulation on a slow time scale, along with permanent oscillatory motion on a faster time scale (see figure 1). The model suggests that the reorientation process crucially depends on the diagonal corner flows. 14:45 15 mins #147 Vortex formation during spin-up of thermal convection Daisuke Noto, Yuji Tasaka, Takatoshi Yanagisawa, Yuichi Murai Abstract: Columnar vortex formation during spin-up of non-rotating thermal convection is experimentally investigated with using optical visualization techniques. Centrifugal and Kelvin-Helmholtz instabilities evoke to columnar vortices in a initial state of rotating thermal convection. The mechanism will be discussed in detail through parametric studies on different Rayleigh and Ekman numbers. 15:00 15 mins #208 Slip length effect on heat transfer and temperature profiles in turbulent Rayleigh-B\'{e}nard convection maojing huang, Yin Wang, Yun Bao, xiaozhou He Abstract: We report a numerical study of heat transport and temperature profiles in turbulent Rayleigh-B\'{e}nard convection (RBC) with slip boundary condition (BC). We conducted direct numerical simulations (DNS) in both two-dimensional (2D) rectangular and three-dimensional (3D) cuboid confinements. With the slip BC on the horizontal plates, the velocity on their surface is set to $\boldsymbol{u}_s=b/L(\partial{\boldsymbol{u}}/\partial{\boldsymbol{n}})|_s$\cite{Hodes2017}. Here $b$ is the slip length and $L$ is the height of RBC sample. The no-slip BC still holds on the walls parallel to gravity. In our DNS, we can systematically change the slip length from no-slip($b/L=0$) to free-slip$(b/L\rightarrow\infty)$, and the Rayleigh number range is $10^{7} \alt \Ra \alt 10^{10}$ with a fixed Prandtl number $\Pra = 4.3$. \\ Figure 1 (a) shows the numerically calculated Nusselt number $Nu$ for global heat transport, as a function of $b/L$ at $\Ra = 10^9$. The $Nu$ data with different $b/L$ are scaled by the $Nu_0$ for $b/L = 0$ (no-slip BC). It is found that with an increase of b/L the $Nu/Nu_0$ increases, and its functional form follows the equation $Nu/Nu_0 = 0.8\times tanh(100\times b/L) + 1$. When $b/L$ approaches to $\infty$, the heat transport $Nu$ for free-slip BC is $\sim 80\%$ higher than $Nu_0$ for no-slip BC. \\ Figure 1 (b) shows normalized mean temperature profiles $\Theta(z/\delta) \equiv (T_{b}-\langle T(z) \rangle)/((T_b-T_t)/2)$ as a function of $z/\delta$ with various $b/L$ at $\Ra = 10^9$, where $\delta$ is thermal boundary layer thickness, ${T_b}$ and $T_{t}$ are the temperature of the bottom and top plates, respectively. For $b/L = 0$, we conduct DNS in a cuboid sample with the aspect ratio being $L:H:W = 4:4:1$ (Here $H$ and $W$ are, respectively, the length, and width of the cuboid). The numerical data agree well with the solution $\Theta=\int_0^{\xi}(1+a^3\eta^3)^{-c}d\eta$ for the mean temperature profile in a fluctuating thermal boundary layer \cite{Shishkina2015}, with $a=\frac{\Gamma(1+1/3)\Gamma(c-1/3)}{\Gamma(c)}$ and $c=1.4$. The result also agrees with that in a cylindrical sample \cite{Wang2016}. The data for $b/L > 0$ are from 2D simulations in a squared sample. Following the same spirit as in Ref.\cite{Shishkina2015}, we derived a general solution $\Theta=\int_0^{\xi}[1+m^x\eta^x]^{-n}d\eta$ ($2 \leq x \leq 3$) with $m=\frac{\Gamma(1+1/x)\Gamma(n-1/x)}{\Gamma(n)}$ for slip BC. The fits to the data are shown in figure 1 (b). When $b/L$ increases from 0 to $\infty$, $x$ decreases from $3$ to $2$, indicating that the near-wall temperature has stronger fluctuations. As a result, the global heat transport is enhanced. 15:15 15 mins #286 Solitary turbulent plumes in steadily-heated flow of 2D Boussinesq model Yoshiki Hiruta, Sadayoshi Toh Abstract: We numerically investigate the (modified) Boussinesq model on two-dimensional periodic domain. Subcritical turbulence transition is observed that mediated by plume-like localized structures embedded in the trivial solution. We will also talk about parameter dependence of flow state and the stability of the trivial solution. 15:30 15 mins #271 Development of turbulent cellular structures in Rayleigh-Benard convection in a finite liquid metal layer Yuji Tasaka, Megumi Akashi, Takatoshi Yanagisawa, Tobias Vogt, Sven Eckert Abstract: Development of large-scale coherent structures of Rayleigh-Benard convection in a fluid container filled with liquid metal was examined experimentally. Ultrasonic velocity profile measurements elucidated that there are structure transition from oscillatory four-roll to turbulent cellular structures via intermediate thee-roll structure with increase of Rayleigh number. Scalling law derived from relations of typical flow velocity and oscillation time scale of the structures provided good representation of the size variation of structures. The scalling law also indicated that the structure development is originated from two-dimentional steady rolls formed at the onset of convection.