Bulletin of the American Physical Society
69th Annual Meeting of the APS Division of Fluid Dynamics
Volume 61, Number 20
Sunday–Tuesday, November 20–22, 2016; Portland, Oregon
Session L10: Convection and Buoyancy Driven Flows: Theory II 
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Sponsoring Units: DFD GPC Chair: Charles Doering, University of Michigan Room: B118119 
Monday, November 21, 2016 4:30PM  4:43PM 
L10.00001: New variational bounds on convective transport. I. Formulation and analysis Ian Tobasco , Andre N. Souza , Charles R. Doering We study the maximal rate of scalar transport between parallel walls separated by distance $h$, by an incompressible fluid with scalar diffusion coefficient $\kappa$. Given velocity vector field ${\bf u}$ with intensity measured by the P\'eclet number $Pe = h^2 \langle  \nabla {\bf u} ^2 \rangle^{1/2}/\kappa$ (where $\langle\cdot\rangle$ is spacetime average) the challenge is to determine the largest enhancement of walltowall scalar flux over purely diffusive transport, i.e., the Nusselt number $Nu$. Variational formulations of the problem are presented and it is determined that $Nu \le c Pe^{2/3}$, where $c$ is an absolute constant, as $Pe \rightarrow \infty$. Moreover, this scaling for optimal transportpossibly modulo logarithmic correctionsis asymptotically sharp: admissible steady flows with $Nu \ge c' Pe^{2/3}/[\log{Pe}]^2$ are constructed. The structure of (nearly) maximally transporting flow fields is discussed. [Preview Abstract] 
Monday, November 21, 2016 4:43PM  4:56PM 
L10.00002: New variational bounds on convective transport. II. Computations and implications Andre Souza , Ian Tobasco , Charles R. Doering We study the maximal rate of scalar transport between parallel walls separated by distance $h$, by an incompressible fluid with scalar diffusion coefficient $\kappa$. Given velocity vector field ${\bf u}$ with intensity measured by the P\'eclet number $Pe = h^2 \langle  \nabla {\bf u} ^2 \rangle^{1/2}/\kappa$ (where $\langle\cdot\rangle$ is spacetime average) the challenge is to determine the largest enhancement of walltowall scalar flux over purely diffusive transport, i.e., the Nusselt number $Nu$. Variational formulations of the problem are studied numerically and optimizing flow fields are computed over a range of $Pe$. Implications of this optimal walltowall transport problem for the classical problem of RayleighB\'enard convection are discussed: the maximal scaling $Nu \sim Pe^{2/3}$ corresponds, via the identity $Pe^2 = Ra(Nu1)$ where $Ra$ is the usual Rayleigh number, to $Nu \sim Ra^{1/2}$ as $Ra \rightarrow \infty$. [Preview Abstract] 
Monday, November 21, 2016 4:56PM  5:09PM 
L10.00003: Global heat transport scaling in plumecontrolled regime in turbulent RayleighB\'enard convection$^1$ Kai Leong Chong , ShiDi Huang , KeQing Xia Previous study by Chong et al.$^2$ has introduced a normalized aspectratio $\Gamma/\Gamma_{opt}$ ($\Gamma_{opt}=29.37Ra^{0.31}$) where the plume coverage at fixed $\Gamma/\Gamma_{opt}$ is invariant with respect to $Ra$ in the socalled plumecontrolled regime in RayleighBĂ©nard convection. We have studied the global heat transport scaling (expressed as Nusselt number $Nu$) at fixed $\Gamma/\Gamma_{opt}$ with the Rayleigh number $Ra$ between $10^7$ and $10^{10}$ at fixed Prandtl number $Pr=4.38$ by direct numerical simulations. It is found that at $\Gamma/\Gamma_{opt}=1$ where the thermal plume becomes highly coherent and systemsized, $Nu$ exhibits the scaling $Nu1 \sim Ra^{0.327\pm0.001}$ over three decades of $Ra$. This scaling is different from that found at $\Gamma=1$ for which $Nu1 \sim Ra^{0.308\pm0.001}$, and this difference in scaling can be shown evidently in the compensated plots. 1. This work was supported by RGC of HKSAR (No. CUHK404513), CUHK Direct Grant (No. 3132740) and through a HKPhD Fellowship. 2. Chong, K. L., Huang, S.D., Kaczorowski, M. \& Xia, K.Q. 2015 Condensation of coherent structures in turbulent flows. Phys. Rev. Lett. 115, 264503. [Preview Abstract] 
Monday, November 21, 2016 5:09PM  5:22PM 
L10.00004: Universality of energy spectrum in turbulent RayleighBenard convection Kunlun Bai , Judith Hoeller , Eric Brown We present study of energy spectrum in turbulent RayleighBenard convection, in both cylindrical and cubic containers, tilting and nontilting conditions, and with Rayleigh number ranging from $0.5 \times 10^9$ to $1 \times 10^{10}$. For these different conditions of geometry, tilt, and Rayleigh number, the temperature spectra measured on the system side walls are significantly different from each other. Even for the same condition, the spectrum varies depending on whether the sensors locate in the path of largescale circulations. However, quite interestingly, once the signals of largescale circulations are subtracted from the raw temperature, all spectra display a universal shape, regardless of system geometry, tilt, Rayleigh number, and location of sensors. It suggests that one could model the largescale circulations and smallscale fluctuations separately in turbulent RayleighBenard convection. [Preview Abstract] 
Monday, November 21, 2016 5:22PM  5:35PM 
L10.00005: Study of global heat transport and plume morphology in severelyconfined RayleighB\'enard convection$^1$ KeQing Xia , Kai Leong Chong We study systematically how severe geometrical confinement influences the global heat transport (expressed as Nusselt number $Nu$) and the plume morphology in RayleighB\'enard convection (RBC) by means of direct numerical simulations. Broad ranges of widthtoheight aspectratio ($1/128 \le \Gamma \le 1$) and Rayleigh number ($3\times10^4 \le Ra \le 10^{11}$) at fixed Prandtl number $Pr=4.38$ are considered in present study. It is found that $Nu$ exhibits the scaling $Nu1 \sim Ra^{0.61}$ over three decades of $Ra$ at $\Gamma=1/128$ and the flow is dominated by fingerlike, longlived plume columns for such severelyconfined situation. The $Nu$ scaling and the flow structures contrast sharply to that found at $\Gamma=1$ for which $Nu$ exhibits the scaling $Nu1 \sim Ra^{0.31}$ and the flow is dominated by mushroomlike, fragmented thermal plumes. Analogy is made between the severelyconfined RBC and strongly rotating RBC. 1. This work was supported by RGC of HKSAR (No. CUHK404513), CUHK Direct Grant (No. 3132740) and through a HKPhD Fellowship. [Preview Abstract] 
Monday, November 21, 2016 5:35PM  5:48PM 
L10.00006: Superstructures in RayleighBenard convection Richard Stevens , Roberto Verzicco , Detlef Lohse We study the heat transfer and the flow structures in RayleighB\'enard convection as function of the Rayleigh number $Ra$ and the aspect ratio. We consider threedimensional direct numerical simulations (DNS) in a laterally periodic geometry with aspect ratios up to $\Gamma=L_x / L_z=L_y/ L_z=64$ at $Ra=10^8$, where $L_x$ and $L_y$ indicate the horizontal domain sizes and $L_z$ the height. We find that the heat transport convergences relatively quickly with increasing aspect ratio. In contrast, we find that the large scale flow structures change significantly with increasing aspect ratio due to the formation of superstructures. For example, at $Ra=10^8$ we find the formation of basically only one large scale circulation roll in boxes with an aspect ratio up to $8$. For larger boxes we find the formation of multiple of these extremely large convection rolls. We illustrate this by movies of horizontal crosssection of the bulk and the boundary layer and analyze them by using spectra in the boundary layer and the bulk. In addition, we study the effect of the large scale flow structures on the mean and higher order temperature and velocity statistics in the boundary layer and the bulk by comparing the simulation results obtained in different aspect ratio boxes. [Preview Abstract] 

L10.00007: ABSTRACT WITHDRAWN 
Monday, November 21, 2016 6:01PM  6:14PM 
L10.00008: Roughness as a Route to the Kraichnan Regime in Thermal Convection Srikanth Toppaladoddi , Sauro Succi , John Wettlaufer We use highly resolved numerical simulations to study turbulent RayleighB\'enard convection in a cell with sinusoidally rough upper and lower walls in two dimensions. By varying the wavelength at a fixed amplitude, we find an optimal wavelength for which the NusseltRayleigh scaling relation is $\left(Nu1 \propto Ra^{0.482}\right)$. This is consistent with (i) the upper bound of Goluskin and Doering (2016) who prove that $Nu$ can grow no faster than ${\cal O} (Ra^{1/2})$ as $Ra \rightarrow \infty$, and thus (ii) the concept that roughness facilitates the attainment of the socalled ultimate regime of Kraichnan (1962). In the limits of very small and very large wavelengths we recover the planar case results, demonstrating how controlling the wall geometry manipulates the interaction between the boundary layers and the core flow. [Preview Abstract] 
Monday, November 21, 2016 6:14PM  6:27PM 
L10.00009: The parameter space of windy convection David Goluskin In horizontally periodic RayleighB\'enard convection at large Rayleigh numbers (Ra), wavenumberzero horizontal winds can arise spontaneously and dramatically alter the flow. The resulting ``windy convection" has been observed in 2D domains and horizontally anisotropic 3D domains. As Ra is raised, the fraction of total kinetic energy contained in the wind approaches 100\%. Vertical heat transport is greatly depressed by the wind and grows very slowly (if at all) as Ra is raised. Two different types of windy convection have been observed at different Prandtl numbers (Pr). At smaller Pr, heat is vertically convected almost exclusively during discrete bursts that are separated by long quiescent phases. At larger Pr, convective transport remains significant at all times. Convection can thus be identified as either windy or nonwindy, and windy states can be either bursting or nonbursting. The regions of the RaPr parameter plane in which each type of convection can occur remain poorly understood, as do transitions between these regions. This talk will summarize the phenomenon of windy convection in 2D and 3D and present a preliminary exploration of the RaPr plane in the 2D case. [Preview Abstract] 
Monday, November 21, 2016 6:27PM  6:40PM 
L10.00010: Modeling of the thermal boundary layer in turbulent RayleighB{\'e}nard convection. Mohammad Emran , Olga Shishkina We report modeling of the thermal boundary layer in turbulent RayleighB{\'e}nard convection (RBC), which incorporates the effect of turbulent fluctuations. The study is based on the thermal boundary layer equation from Shishkina et al., Phys. Rev. Lett. 114, 114302 (2015) and new Direct Numerical Simulations (DNS) of RBC in a cylindrical cell of the aspect ratio 1, for the Prandtl number variation of several orders of magnitude. Our modeled temperature profiles are found to agree with the DNS much better than those obtained with the classical PrandtlBlasius or FalknerSkan approaches. [Preview Abstract] 
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