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16:15   Turbulent Convection 5 16:15 15 mins #132 TRANSITIONS OF REYNOLDS NUMBERS AND TEMPERATURE FLUCTUATIONS IN HORIZONTAL CONVECTION Hailong Huang, Olga Shishkina, Xiaozhou He Abstract: We report results of Reynolds numbers and local temperature fluctuations in horizontal convection (HC) for the Rayleigh numbers $1\times 10^{11}\lesssim \Ra \lesssim1.6\times 10^{12}$ and the Prandtl numbers $\Pra \simeq 5$. Two rectangular HC samples were used in the experiment, which have the same aspect ratio L:W:H = 10:1:1 with different length L = 0.5m and 1.0m. (Here W and H are, respectively, the height and width of the sample). The working fluid was heated and cooled by two squared copper plates on the bottom, which have the size of W and are placed at the two ends. Both plates were regulated at a constant mean temperature. \\ The Reynolds numbers, $\Rey_U \equiv UL/\nu$ and $\Rey_V \equiv VL/\nu$, were measured above the heating plate at (x/L = 0.005, y/W = 0.5, z/H = 0.2). Here U and V are, respectively, the mean and root-mean-squared (rms) values of the local velocity. Both velocities were obtained by applying the elliptic-approximation model on the measured temperature cross-correlation functions . In figure 1, the solid symbols represent the measured $\Rey_U$ and $\Rey_V$ as a function of Ra for $\Ra \agt 10^{11}$. The open symbols represent the $\Rey_U$ data from direct numerical simulations (DNS) for $\Ra \alt 5\times 10^{11}$. Both sets of $\Rey_U$ data are in good agreement in the overlapped $\Ra$ range. For $\Ra \alt 10^{11}$, the DNS $\Rey_U$ follows the scaling $\Rey_U \sim \Ra^{1/2}$. After undergoes wide fluctuations over the range $10^{11} \alt \Ra \alt 3\times10^{11}$, the measured $\Rey_U$ obeys the scaling $\Ra^{2/5}$. Both scalings are in agreement with the theoretical predictions for the boundary-layer dominated regimes in HC and reveal a transition from the scaling for very small Ra (regime I$^*_l$) to the Rossby scaling (regime I$_l$). \\ Figure 2 shows the real-time temperature fluctuations $\delta T(t)/\sigma_T$ in the transition range $10^{11} \alt \Ra \alt 3\times10^{11}$. The data were measured at the same locations as the Reynolds numbers. At $\Ra = 1.1\times 10^{11}$ (or below), the local temperature has a periodic oscillation. At $\Ra \simeq 2\times 10^{11}$, it starts to show period-doubling bifurcations. When $\Ra \agt 3\times 10^{11}$, $\delta T(t)/\sigma_T$ shows intermittent fluctuations and indicates a transition of the HC state from laminar to chaotic. Such a transition is consistent with that observed in the scaling of global heat transport and near-wall mean temperature profiles. 16:30 15 mins #133 Transitions of heat transfer and temperature profiles in horizontal convection Bo Yan, Olga Shishkina, Xiaozhou He Abstract: We present experimental and numerical results on heat transport and temperature profiles in horizontal convection (HC), where the fluid is heated and cooled on the same level. The convection samples are rectangular with the aspect ratio of L:W:H = 10:1:1, where L $= 0.5m$ (or $1m$) is the sample length, W and H are, respectively, the width and height of the sample. Both heating and cooling squared plates are made of copper and placed at the two ends of the bottom plate. The working fluid is room-temperature water. Our measurements cover the Rayleigh number range $2\times10^{10} \le \Ra \le 1.5 \times 10^{12}$ and the Prandtl number range $3.9 \le \Pra \le 6.5$. \vskip 6pt Figure 1 (a) shows the heat transport through the heating plate, represented by the reduced Nusselt number $Nu/\Ra^{1/5}$. Red dots are the data from the experiment and the blue triangles are the data from the direct numerical simulations \cite{SW16}. The two sets of data are in good agreement and both reveal a gradual change of the $Nu$ scaling from $Nu \sim \Ra^{1/4}$ near $\Ra = 2 \times 10^{10}$ to $Nu \sim \Ra^{1/5}$ above $\Ra \simeq 3\times 10^{11}$. With the SGL model \cite{SGL16} this result indicates a transition in laminar HC, from a very low $\Ra$ regime I$^*_l$ to a moderate $\Ra$ regime I$_l$. The latter one is also known as the Rossby regime \cite{Rossby1965}. \vskip 6pt Figure 1 (b) and (c) show the normalized mean temperature profiles $\Theta(z) \equiv \frac{T(z) - T_{wall}}{T_{ref}-T_{wall}}$ for different $\Ra$ along the central axis of the cooling and heating plates, respectively. In (b) $T_{ref}$ is the mean temperature at $z/H = 0.5$. In (c) we chose a varying $T_{ref}$ so that the $\Theta(z)$ profiles can overlap in the linear region from $z/H = 0$ up to a certain distance. It is seen that all the profiles above the cooling plate can be brought onto a single master curve, once the vertical location $z$ is normalized by the thickness $\delta_-$ of the thermal boundary layer above the cooling plate. The master curve indicates that the mean temperature profiles near the cooling plate are similar and can be described by the solution $\Theta = \int_{0}^{\xi}(1+a^{3}\eta^{3})^{-c}d\eta$ of the thermal boundary layer (BL) equation \cite{SHWC15}, for $a=\Gamma(1/3)\Gamma(c-1/3)/[3\Gamma(c)]$ and $c=1.6$. The $\Theta$ profiles above the heating plate, on the other hand, evolve in a more complex way. For $\Ra \alt 4\times10^{10}$, the profiles overlap but are different from the master profile above the cooling plate. As $\Ra$ increases, the profiles start to deviate at $z \simeq 0.4 \delta_- $ and their shapes vary with Ra. 16:45 15 mins #216 HEAT TRANSPORT IN CLASSICAL AND SYMMETRICAL HORIZONTAL CONVECTION Philipp Reiter, Mohammad Emran, Olga Shishkina Abstract: Horizontal convection (HC) is a paradigm system to study natural turbulent convection where heat is supplied and removed through a single plane. It is relevant in the ocean meridional overturning, where surface temperature gradients between the equator and pole regions, among other forces, drive a large-scale circulation and ensure a continual mixing of warm and cold water. While this circulation has a huge impact on the climate, we are yet not even close to study HC experimentally or numerically at Rayleigh numbers of order Ra = 10^20 to 10^30 of this geophysical system, but we are able to verify theoretical models, in particular the Shishkina-Grossman-Lohse (SGL) model [1] for the scaling of the Nusselt number Nu and Reynolds number Re with Ra and Prandtl number Pr. By means of direct numerical simulations (DNS) for P r = 0.1, 1 and 10 and Ra up to 10 12 , we study both classical HC [2], where heat is supplied and removed at the bottom ends of the cell (Fig. 1a) and symmetrical HC (similar to [3]), where heat is removed at the two bottom corners and supplied at the central part of the bottom plate (Fig. 1b). The latter approach bypasses the urge to isolate the end wall above the convective unstable region, which makes it interesting for ever more demanding experiments at extremely high Ra. Our DNS support the scaling regimes I_l (Rossby scaling) and I_l^∗ , according to the SGL theory, while even showing approximately equal N u and Re numbers as well as similar transition zones in both setups. However, in the symmetrical setup we observe increased volume averaged turbulent kinetic energies and in general stronger temperature and velocity fluctuations in the central part. Beside sheared Taylor-Rayleigh instabilities in the convective unstable boundary layer, the symmetry gives rise to an additional low frequency oscillatory mode around the symmetry plane. This work is supported by the DFG grants Sh405/10 and Sh405/4. We acknowledge the Leibniz Supercomputing Centre (LRZ) for providing computing resources. References [1] O. Shishkina, S. Grossmann, and D. Lohse. Heat and momentum transport scalings in horizontal convection. Geophys. Res. Lett., 43(3):1219–1225, 2016. [2] O. Shishkina and S. Wagner. Prandtl-number dependence of heat transport in laminar horizontal convection. Phys. Rev. Lett., 116:024302, 2016 [3] F. Paparella and W. R. Young. Horizontal convection is non-turbulent. J. Fluid Mech., 466:205–214, 2002. 17:00 15 mins #11 Dynamics of subsiding shells in actively growing clouds with vertical updrafts Vishnu Nair, Thijs Heus, Maarten van Reeuwijk Abstract: The dynamics of a subsiding shell at the edges of actively growing shallow cumulus clouds with updrafts is analysed using direct numerical simulation with grid sizes of up to 3072 x 1536 x 1536. The actively growing clouds have a fixed in-cloud buoyancy and velocity. Turbulent mixing and evaporative cooling at the cloud edges generate a subsiding shell which grows with time [1]. A self-similar regime is observed for first and second order moments when normalized with their respective maximum values. Internal scales derived from integral properties of the flow problem are identified [2]. Self-similarity analysis conducted by normalizing using these scales reveal that contrary to classical self similar flows, the Turbulent Kinetic Energy (TKE) budget terms and the velocity moments scale according to the buoyancy and not with the mean velocity. The shell thickness is observed to increase linearly with time. The shell buoyancy scale remains constant as it thickens and is set by the initial thermodynamics of the cloud and environment. The shell accelerates ballistically with a magnitude defined by the saturation value of the buoyancy of the cloud-environment mixture. In this regime, the shell is buoyancy driven and independent of the in-cloud velocity. The shell thickness and the velocity continue to grow indefinitely and could possibly be limited only by the lifetime of the cloud or thermal. Relations are obtained for predicting the shell thickness and minimum velocities by linking the internal scales with external flow parameters. The values of shell thickness and velocities calculated using these derived relations are consistent with the values of a typical shallow cumulus cloud [3]. The entrainment coefficient, which is predicted by studying the rate of growth of the shell thickness, is observed to be a function only of the initial state of the cloud and the environment. This coefficient is linked to the fractional entrainment rate used in cumulus parameterization schemes for large scale models and is shown to be of the same order of magnitude [4]. References: [1] Heus, T., and H. Jonker, 2008: Subsiding shells around shallow cumulus clouds. Journal of the Atmospheric Sciences, 65, 1003–1018, doi:10.1175/2007JAS2322.1. [2] Craske, J., and M. van Reeuwijk, 2015: Energy dispersion in turbulent jets. part 1. Direct simulation of steady and unsteady jets. Journal of Fluid Mechanics, 763, 500537, doi:10.1017/jfm.2014.640. [3] Rodts, S., P. Duynkerke, and H. Jonker, 2003: Size distributions and dynamical properties of shallow cumulus clouds from aircraft observations and satellite data. Journal of the Atmospheric Sciences, 60,1895–1912. [4] Romps, D., 2010: A direct measure of entrainment. Journal of the Atmospheric Sciences, 67, 1908–1927, doi:10.1175/2010JAS3371.1. 17:15 15 mins #276 DNS OF A TEMPORALLY EVOLVING VERTICAL NATURAL CONVECTION BOUNDARY LAYER Junhao Ke, Nicholas Williamson, Steven Armfield Abstract: The present study concerns a temporally evolving natural convection boundary layer (Pr = 0.71) adjacent to an isothermally heated vertical plate with infinite extent in the streamwise and spanwise directions. It is demonstrated that the integral boundary layer thickness does not increase monotonically through transition of the temporally evolving boundary layer due to the roll-up and ejection of the convective rolls, which differs from the spatially evolving boundary layer. In the turbulent regime, the mean flow statistics behave similarly to the spatially developing natural convection boundary layers. In the near wall region, the mean temperature profile follows the linear relationship that is commonly found in the viscous sublayer. However, such near-wall linear relationship does not exist for the mean velocity profile. In the present study, it can be found that the mean velocity profile is shifting to the linear relationship when the Grashof number increases. It is presumed that the viscous sublayer, in which region the linear relationship holds, is able to become visible, as long as the Grashof number reaches a sufficiently large value. 17:30 15 mins #323 SUPPRESSION OF RAYLEIGH-TAYLOR TURBULENCE BY TIME-PERIODIC ACCELERATION Marta Magnani, Stefano Musacchio, Guido Boffetta Abstract: The dynamics of Rayleigh-Taylor turbulent convection [1] in presence of an alternating, time periodic acceleration is studied by means of extensive, high resolution, direct numerical simulations of the Boussinesq equations. It is well known that it is possible to stabilize an unstable fixed point of a mechanical system by a periodic modulation of the forces, e.g. a famous example is the Kapitza inverted pendulum. The Rayleigh-Taylor instability is a perfect system to investigate the same effect in the framework of fluid dynamics. We consider a single phase system, composed by an upper heavier (colder, of density ρc) layer and a lower lighter (warmer, of density ρw) layer of the same fluid, initially separated by an horizontal interface. We study the case of periodic inversion of the gravity field by using a square and a sinusoidal wave of amplitude g0 in which the sign of g(t) is reversed every half period T/2. Thus, we discover a new mechanism of relaminarization of turbulence. The alternating acceleration, which initially produces a quadratic growth of the turbulent mixing layer (similar to the standard Rayleigh-Taylor dynamics), at longer times suppresses turbulent fluctuation and drives the system toward an asymptotic stationary configuration where the mixing layer no longer spreads. Dimensional arguments and linear stability theory for a diffused temperature profile [2] are used to predicts the width of the mixing layer in the asymptotic state as a function of the period of acceleration (see Fig.1). Our results provide an example of simple control and suppression of turbulent convection with many potential applications from confined nuclear fusion, to plasma physics, and laser matter interactions. 17:45 15 mins #72 DIRECT NUMERICAL SIMULATION OF SHOCK-DRIVEN TURBULENT MIXING Tao Wang, Bing Wang, Jianyu Lin, Jingsong Bai, Ping Li, Gang Tao Abstract: The Richtmyer-Meshkov instability (RMI) is a complex phenomenon happening at a perturbed interface between two different fluids, when the interface is driven by a shock wave. The mechanism of RMI is baroclinic vorticity deposition owing to the misalignment of the pressure gradient of across the shock front and the local density gradient at the interface. At late times the RMI can induce the turbulent mixing. It is very important in a variety of applications ranging from man-made to natural phenomena, and has gained much attention all long. Based on the operator splitting and dimension-splitting PPM scheme, we developed a direct numerical simulation code MVFT (multi-viscous-flow and turbulence) which solves the compressible multicomponent Navier-Stokes (NS) equations. It uses PPM-based contact discontinuity steepening to capture shock. In this paper, a three-dimensional multi-mode Richtmyer-Meshkov instability and induced turbulent mixing in air/SF6 configuration are directly numerically simulated by using MVFT code. The complex structures of turbulent mixing zone (TMZ) are obtained, seen in Fig. 1. The TMZ width grows as a power law in time before reshock; after reshock and first rarefaction wave action, the TMZ width grows as negative exponential laws in time but with different growth factors; at late time, the TMZ width grows approximately in a linear way, seen in Fig. 2. The integral statistics in the TMZ decay with time in the similar way, that is to say the evolution of TMZ has a statistics similarity behavior. At the same time, the TMZ evolves and materials mixes asymmetrically across the TMZ, illustrated in Fig. 3. The turbulent mixing behaves anisotropy all along, which can be demonstrated by no occurrence of power law in the energy spectra. Figure 1. Structures of turbulent mixing. Figure 2. TMZ width vs. time. Figure 3. Spatio-temporal distribution of enstrophy. References [1] R. D. Richtmyer. Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Math. 13(2): 297-319, 1960. [2] E. E. Meshkov. Instability of the interface of two gases accelerated by a shock wave. Sov. Fluid Dyn. 4(5): 101-104, 1969. [3] J. S. Bai, J. H. Liu, T. Wang, et al. Investigation of the Richtmyer-Meshkov instability with double perturbation interface in nonuniform flows. Physical Review E, 81(2): 056302, 2010. [4] T. Wang, J. S. Bai, P. Li, et al. Large-eddy simulations of the Richtmyer-Meshkov instability of rectangular interface accelerated by shock waves. Sci China Ser G, 53(5): 905-914, 2010. 18:00 15 mins #172 Local heat transport in turbulent Rayleigh-Bénard convection at high aspect ratio Ronald du Puits, Anna Hertlein Abstract: We study the heat transport in turbulent Rayleigh-Bénard (RB) convection focusing on high aspect ratios equal or larger than eight. Using particular heat flux sensors embedded into the heating and the cooling plates of the RB experiment, we measure the heat flux between the horizontal walls and the fluid layer in between time-resolved and at various places along their surfaces. In our talk, we will discuss as well the spatial and time-dependent distribution of the wall heat flux under these specific conditions, as we will analyze the statistics of the fluctuations. The application of multiple sensors at both plates also enables us to identify spatio-temporal correlations between the sensors at a single plate, but also between the two opposite plates.