Session T03: Convection and Buoyancy-Driven Flows: Turbulent Convection (8:00am - 8:45am CST)

Flow measurements in rapidly rotating Rayleigh-B\'enard convection

The problem of turbulent rotating Rayleigh-B\'enard convection has been studied for a long time due to its strong ties with the flows in geophysics and astrophysics. Its simple formulation, a layer of fluid heated from below and cooled from above rotating about an axis, makes it a good model to tackle this problem from many directions: analytical models, numerical simulations as well as experimental setups. The setup TROCONVEX is one of them. Its huge dimensions (up to 4 m tall) allow the investigation of parameters closer than ever before to the ones of astrophysical flows. In this talk we present flow measurements from this unique experimental setup using stereoscopic Particle Image Velocimetry. This technique lets us measure the 3 components of the velocity field in a full horizontal planar cross-section of our rotating cylinder. Through them we can characterize flow structures and velocity distributions of the different states of the geostrophic regime of rotating convection, a regime characterized by both strong thermal forcing and rapid rotation.   

Supergravitational turbulent thermal convection.

Thermally driven turbulent flows are ubiquitous in many natural phenomena and in industries, such as atmospheric circulations, oceanic flows, flows in the fluid core of planets, and energy generations. The key issue of turbulent thermal convection is understanding the coupling dynamics of the turbulent flow structures and global heat transfer for high Rayleigh numbers. Therefore, in recent years much attention has been paid to finding ways of increasing Rayleigh number. In this work, we present a novel approach to boost the Rayleigh number in thermal convection by exploiting centrifugal acceleration and by rapidly rotating a cylindrical annulus to reach an effective gravity of 60 times Earth's gravity. We show that in the regime where the Coriolis effect is strong, the scaling exponent \begin{figure}[htbp] \centerline{\includegraphics[width=0.10in,height=0.21in]{020820201.eps}} \label{fig1} \end{figure} of the Nusselt number with the Rayleigh number exceeds 1/3 once the Rayleigh number is large enough. Remarkably, the convective rolls revolve in prograde direction, signifying the emergence of zonal flow. The present findings open a new avenue on the exploration of high Rayleigh number turbulent thermal convection, and will improve the understanding of the flow dynamics and heat transfer processes in geophysical and astrophysical flows, and other strongly rotating systems.   

Thermal Convection over Fractal Surfaces

We use well resolved numerical simulations with the Lattice Boltzmann Method to study Rayleigh-B\'enard convection in cells with a fractal boundary in two dimensions for $Pr = 1$ and $Ra \in \left[10^7, 10^{10}\right]$. The fractal boundaries are functions characterized by power spectral densities $S(k)$ that decay with wavenumber, $k$, as $S(k) \sim k^{p}$ ($p < 0$). The degree of roughness is quantified by the exponent $p$ with $p < -3$ for smooth (differentiable) surfaces and $-3 \le p < -1$ for rough surfaces with Hausdorff dimension $D_f=\frac{1}{2}(p+5)$. By computing the exponent $\beta$ in power law fits $Nu \sim Ra^{\beta}$, where $Nu$ and $Ra$ are the Nusselt and the Rayleigh numbers for $Ra \in \left[10^8, 10^{10}\right]$, we observe that heat transport scaling increases with roughness over the top two decades of $Ra \in \left[10^8, 10^{10}\right]$. For $p$ $= -3.0$, $-2.0$ and $-1.5$ we find $\beta = 0.288 \pm 0.005, 0.329 \pm 0.006$ and $0.352 \pm 0.011$, respectively. We also observe that the Reynolds number, $Re$, scales as $Re \sim Ra^{\xi}$, where $\xi \approx 0.57$ over $Ra \in \left[10^7, 10^{10}\right]$, for all $p$ used in the study. For a given value of $p$, the averaged $Nu$ and $Re$ are insensitive to the specific realization of the roughness.   

Reduced flow reversals in turbulent convection in the absence of corner vortices

We report a comparative experimental study of the reversal of the large-scale circulation (LSC) in turbulent Rayleigh-B{\'e}nard convection in a quasi-two dimensional (2D) corner-less cell where the corner vortices are absent and in a quasi-2D normal cell where the corner vortices are present. It is found that in the corner-less cell the reversal frequency exhibits a slow decrease followed by a fast decrease with increasing Rayleigh number $Ra$, separated by a transitional $Ra$ ($Ra_{t,r}$). The transition is similar to that in the normal cell, and $Ra_{t,r}$ is almost the same for both cells. Despite the similarities, the reversal frequency is greatly reduced in the corner-less cell. The reduction of the reversal frequency is more significant, in terms of both the amplitude and the scaling exponent, in the high Ra regime. In addition, we classified the reversals into main-vortex-led (MVL) and corner-vortex-led (CVL), and found that both types exist in the normal cell while only the former exists in the corner-less cell. The frequency of MVL reversal in normal cell is found in excellent agreement with the frequency of reversals in corner-less cell. Our results reveal for the first time the quantitative role of the corner vortices in the occurrence of the reversals of the LSC.   

Scaling in concentration driven convection boundary layers with transpiration

Concentration-driven natural convection boundary layers (NBL) on horizontal surfaces, subjected to a weak uniform blowing velocity ($V_i$), are studied for the dimensionless blowing parameter range $10^{-8} < J = Re^3/Gr < 10^{-5}$. Here, $Re$ and $Gr$ are the Reynolds number based on $V_i$ and horizontal location $x$, and Grashoff number based on $x$ and concentration difference across the boundary layer. Integral boundary layer equations are deduced under the assumption that the concentration does not drop within the species boundary layer, which is valid for weak blowing into thin species boundary layers that occur at high Schmidt numbers $(Sc \sim 600)$. Numerical solution of the equations reveal that the species and velocity boundary layer thicknesses scale as, $\delta_d = 1.6x(Re/Gr)^{1/4}$ and $\delta_v = \delta_d Sc^{1/5}$. Also, the horizontally averaged dimensionless concentration profile across the boundary layer shows a $Gr_y^{2/3}$ scaling, where $Gr_y$ is the Grashoff number based on the vertical location $y$. The profile matches well with the experimentally observed mean concentration within the NBL that form on a horizontal permeable membrane, when a weak flow is gravitationally forced from below the horizontal membrane that has brine above it and water below it.   

Temperature-dependent thermal diffusivity in turbulent convection in an extended domain

In solar convection molecular properties of the fluid depend strongly on the temperature $T$; for example, the thermal diffusivity varies roughly as $\kappa\sim T^3$. We simulate the effects of such a strongly temperature-dependent thermal diffusivity in the simplified setting of Rayleigh-B\'enard (RB) convection in a horizontally-extended domain. The thermal diffusivity is set to decrease from the bottom to the top in a similar way as in the Sun. This variation causes the governing parameters — the Rayleigh and Prandtl numbers — to decrease with the increasing depth. As a result, we find that the top-down symmetry of statistical moments, which is exactly satisfied in the standard RB case, is broken. While the diffusive and convective heat fluxes remain essentially symmetric about the midplane, the thermal structures develop ever finer granules with increasing height. Furthermore, the turbulent eddy viscosity and diffusivity, and thus the turbulent Prandtl number, vary with height. These behaviors are compared with those of reference RB with parameters corresponding to the top and bottom conditions.   

Thermal wind and convection simulated in the generalized quasilinear approximation

We probe the connections between shear flows, vortices and convective turbulence, in 3D simulations of a rotating flow with a thermal wind basic state plus Boussinesq perturbations. The model occupies a horizontally periodic Cartesian slab, with fixed temperatures above and below, generalizing the Rayleigh-Benard system. We vary the basic state’s meridional temperature gradient ($T_y$ which also controls the strength of the thermal wind), strength of convection (via Rayleigh number Ra), and rotation (via Taylor number Ta). Nonlinear (NL) runs provide benchmarks for assessing the effectiveness of the generalized quasilinear (GQL) approximation. GQL decomposes each variable (say $u$) in horizontal Fourier space, with a `low' part ($u_L$) at $|k_x|, |k_y|\leq\Lambda$, and a `high' ($u_H$) remainder. Varying the GQL cutoff ($\Lambda=\infty,10,5,1,0$) alters the kinetic energy and other statistics in the final quasi-steady state. As a controlled barrier to inter-modal exchanges, $\Lambda$ impairs specific $k$-dependent processes, apparent in mean spectra and transfer functions. Morphologically, high-$\Lambda$ simulations resemble the NL benchmark (with blurring), but low-$\Lambda$ can artificially sustain features such as giant vortices that would otherwise dissolve.   

Heat Transfer in turbulent convection described by Lagrangian Statistics

In direct numerical simulations of turbulent flows driven by convection, there is considerable variation in the contributions to the Nusselt number, both because of the local spatial variations of plumes and because of convective variation in time. We present a new exit-distance statistic, constructed from Lagrangian tracer particles, that we have developed to more completely describe the structure of heat transfer. We call this the Lagrangian heat structure. In a comparison between direct numerical simulations of homogeneous turbulence driven by Boussinesq convection, the Lagrangian heat structure reveals significant non-Gaussian character, as well as clear trends with Prandtl number and Rayleigh number. For large temperature differences, the Lagrangian heat structure produces converging results; this is encouraging for simulations that focus on large scales, such as large eddy simulations of natural systems including Earth’s atmosphere and oceans, as well as planetary and stellar dynamos.   

Effect of Reynolds Number on the Buoyant Jet Puffing Instability

Buoyant plumes display a global instability near the jet exit in which coherent vortical structures are regularly shed due to buoyancy accelerating the lighter fluid, creating a "puffing" phenomenon. These flow structures are commonly found in nature or as a result of combustion processes; the instability is also important in providing oxygen in buoyancy-driven reacting flows. In this work, we study axisymmetric helium plumes using high-fidelity three-dimensional numerical simulations with adaptive mesh refinement. We investigate, in particular, the effects of Reynolds number on the structure and dynamics of the puffing motion for different Richardson numbers. As the flow transitions to fully turbulent with increasing Reynolds number, we find that: (i) secondary vortices form along and normal to the shear layer, ejecting helium to create "finger-like" structures; and (ii) the puffing dynamics become increasingly complex from both spatial and temporal perspectives. We quantify the dependence of the puffing frequency on the Reynolds number and connect the present results with prior computational and experimental studies of puffing in buoyancy driven flows.