Bulletin of the American Physical Society
75th Annual Meeting of the Division of Fluid Dynamics
Volume 67, Number 19
Sunday–Tuesday, November 20–22, 2022; Indiana Convention Center, Indianapolis, Indiana.
Session J23: Convection and Buoyancy-Driven Flows: Turbulent Convection |
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Chair: Herman Clercx, Eindhoven University of Technology Room: 231 |
Sunday, November 20, 2022 4:35PM - 4:48PM |
J23.00001: Theoretical results on wall-normal heat flux and wall shear stress in turbulent vertical convection between two differentially heated plates Emily S.C. Ching Turbulent vertical convection in a fluid between two differentially heated vertical plates is ubiquitous in nature and in engineering applications. It is also a common model system for studying buoyancy-driven turbulent flows. We report our theoretical study of turbulent vertical convection between two infinite vertical plates with constant temperature difference. The mean vertical velocity and temperature are governed by the mean momentum balance equation and the mean thermal energy balance equation in terms of the wall-normal turbulent heat flux and the Reynolds shear stress. By solving the mean momentum balance equation, we show that mean wall shear stress at the plate is equal to the buoyancy force per unit area in the velocity boundary layer and, as a result, obtain a relation between the shear Reynolds number Reτ and the Nusselt number Nu in terms of the Rayleigh (Ra) and Prandtl numbers (Pr). By analysing the mean thermal energy balance equation, we estimate a relation between Nu, Pr and Reτ. These two results lead to scaling laws for Nu and Reτ in terms of Ra and Pr. |
Sunday, November 20, 2022 4:48PM - 5:01PM |
J23.00002: Discontinuous Transitions Towards Vortex Condensates in Rotating Rayleigh-Bénard Turbulence Herman Clercx, Xander de Wit, Andrés Aguirre Guzmán, Rudie Kunnen We explore the transitions between turbulent states from a 3D flow state towards a quasi-2D condensate known as the large-scale vortex (LSV). Using direct numerical simulations of rotating Rayleigh-Bénard convection, we vary the Rayleigh number Ra as control parameter and study the system response (strength of the LSV) in terms of order parameters assessing the energetic content in the flow and the upscale energy flux. By sensitively probing the boundaries of the domain of existence of the LSV, we find discontinuous transitions and we identify the presence of a hysteresis loop as well as nucleation-and-growth type of dynamics, manifesting striking correspondence with first-order phase transitions in equilibrium statistical mechanics. We show furthermore that the creation of the condensate state coincides with a discontinuous transition of the energy transport into the largest mode of the system. |
Sunday, November 20, 2022 5:01PM - 5:14PM |
J23.00003: Flow measurements of turbulent rotating Rayleigh-Bénard convection in the geostrophic regime Rudie Kunnen, Matteo Madonia, Jonathan S Cheng, Andrés J Aguirre Guzmán, Herman Clercx Rotating turbulent convection can be used as a simple model that captures principal properties of many large-scale geophysical and astrophysical flows. In particular the rotation-dominated geostrophic regime is relevant here. It is named after the so-called geostrophic force balance of pressure gradient and Coriolis forces, which dictates the flow dynamics in this regime to lowest order. Dedicated experiments and numerical simulations have recently been able to enter this regime. Here we present a suite of flow measurements in geostrophic convection. Stereoscopic particle image velocimetry is applied to measure three-component velocity fields in a horizontal planar cross-section of a large-scale cylindrical convection experiment. We consider the magnitude of velocity and vorticity fluctuations at different Rayleigh numbers (strength of thermal forcing) under constant, rapid rotation and interpret them according to scaling predictions based on theoretical force balances. Energy spectra and flow animations reveal the development of a quadrupolar vortex structure that fills the entire cross-section. |
Sunday, November 20, 2022 5:14PM - 5:27PM |
J23.00004: Dynamics of large-scale flow states in turbulent Rayleigh-Bénard convection in a cubic container: A low-dimensional transition manifold approach Priyanka Maity, Andreas Bittracher, P\'eter Koltai, Joerg Schumacher We investigated the transitions between large-scale circulations (LSC) in a closed cubic Rayleigh-Bénard cell, with no-slip velocity boundaries. The simulations were performed at a fluid of Prandtl number Pr = 0.7 and Rayleigh numbers Ra = 106 and 107, assuming thermally insulated sidewalls. We observed that the system bounces between four long-lived LSC (LL-LSC) state aligned along the diagonals, via short-lived LSC (SL-LSC) state aligned along the edges, and the decoherent state. The transitions between the states are induced by the destabilizing action of intense vortices, which are found on both sides of the LSC. The frequency of transitions is higher for the lower Ra due to larger values of vorticity fluctuations in the system. We, thereafter, applied time lagged independent coordinate analysis technique (TICA) for dimensionality reduction of the data aiming for a more energy and time efficient analysis. The TICA analysis confirmed the presence of four prominent clusters corresponding to the four LL-LSC states. Further application of low-dimensional transition manifold analysis, faithfully captures the transition pathways between the states. |
Sunday, November 20, 2022 5:27PM - 5:40PM |
J23.00005: Turbulent transition in Rayleigh-Bénard convection with rough and smooth boudaries. Lucas Méthivier, Lyse Brichet, Romane Braun, Francesca Chillà, Julien Salort Density gradients occur naturally in the oceans, the atmosphere or the interior of stars. When they are stable, they support internal gravity waves. When they are unstable, they are at the origin of coherent structures called plumes. The development and the interaction of the plumes give birth to large scale turbulent motions. These phenomena are not well understood but are mandatory in the modelling of mixing and energy transport in geophysical flows. |
Sunday, November 20, 2022 5:40PM - 5:53PM Author not Attending |
J23.00006: Geostrophic turbulence heat transfer scalings in experimental rotating convection Vincent Bouillaut, Benjamin Miquel, Keith A Julien, Gabriel Hadjerci, Sébastien Aumaître, Basile O Gallet The buoyancy-driven turbulent flows and the associated heat transfers in planetary and stellar interiors are strongly affected by the rapid rotation of these astrophysical bodies. Asymptotic theories have predicted that in the limit of rapid rotation, characterized by vanishingly small Ekman numbers $E$, the flow should enter a "geostrophic turbulence regime". In this regime, the heat flux (measured by the Nusselt number $Nu$) and the temperature difference (measured by the Rayleigh number $Ra$) obey the scaling law $Nu \sim Ra^{3/2} E^{2}$. This scaling can be obtained with simple theoretical arguments: (i) molecular diffusivities should not play a role and (ii) the heat flux if a function of the ratio of Ra over its threshold value. We present a rotating convection experiment where dyed water is heated from below by means of a powerful spotlight shining through the transparent bottom of the rotating tank. When rotation is increased from zero, temperature measurements indicate that the system transitions from the non-rotating diffusivity-free heat-transfer scaling to the geostrophic turbulence regime of rapidly rotating convection. |
Sunday, November 20, 2022 5:53PM - 6:06PM |
J23.00007: Turbulent convection in confined and extended domains Ambrish Pandey, Dmitry Krasnov, Joerg Schumacher, Ravi Samtaney, Katepalli R Sreenivasan To understand turbulent convection at very high Rayleigh numbers, direct numerical simulations in slender cells are an option. However, the effects of horizontal confinement on the flow properties need to be assessed. We explore the properties of the flow in a slender cylindrical cell of aspect ratio 0.1 for a wide range of Prandtl numbers and compare them with those in an apparatus of aspect ratio 25. We observe similarities in many flow properties — such as the root mean square fluctuations of temperature and velocity, probability distributions of the temperature fluctuation and the kinetic energy dissipation rate — between the confined and extended convection domains. In addition, we estimate the turbulent Prandtl number and find that it varies very similarly with the molecular Prandtl number in both domains. |
Sunday, November 20, 2022 6:06PM - 6:19PM |
J23.00008: Beyond the anealstic approximation: Compressibility effects in turbulent convection John Panickacheril John, Joerg Schumacher We systematically study the compressibility effects on Rayleigh-B\'{e}rnard turbulent convection for an ideal gas using DNS of fully compressible Navier-Stokes equations. Compressibility effects in convection are parametrized by the dissipation number, $D= gd/c_{p}T_{B} $ and superadiabaticity, $\epsilon= \Delta T / T_{B}$ where $T_{B}$ and $\Delta T$ correspond to the bottom plate temperature and superadiabatic temperature difference across the plates respectively. Our simulations encompass the Oberbeck-Boussinesq (OB) limit $\left( D, \epsilon \rightarrow 0 \right)$ to regimes going beyond the anelastic approximations $\left( D, \epsilon ~ \approx O(1) \right)$ starting from a Rayliegh number, $Ra \approx 10^{6}$ and fixed Prandtl number, $Pr= 0.72$. We show the symmetry breaking of the mean superadiabatic temperature with strong stratification of density. Asymmetry is also observed for compressibility parameters: the turbulent Mach number, $M_{t}= u_{rms}/ \langle c \rangle$ and dilatation, $\theta = \partial u_{i} / \partial x_{i}$. We separate compressible mechanisms responsible for symmetry breaking from incompressible non-OB ones. Analyses include the bulk statistics and scaling of Nusselt number with different compressible parameters and Rayleigh numbers. |
Sunday, November 20, 2022 6:19PM - 6:32PM |
J23.00009: Mesoscale convection at Prandtl numbers as low as 0.001 Joerg Schumacher, Ambrish Pandey, Dmitry Krasnov, Katepalli R Sreenivasan Many natural convection flows possess regular patterns at an intermediate range of scales, the mesoscale range. A prominent example is granulation and supergranulation on the surface of the Sun. Here, we study mesoscale convection in the simpler Rayleigh-Bénard setup. Our direct numerical simulation studies are taken to Prandtl numbers as low as 0.001, which is beyond the capabilities of controlled laboratory experiments. We study several properties of the flow. The data show, for example, that the turbulence in the bulk of the convection layer is close to the classical homogeneous and istropic turbulence. |
Sunday, November 20, 2022 6:32PM - 6:45PM Author not Attending |
J23.00010: Experimental calibration of thermal particles to study natural and mixed convective flow fields Jesus O Rodriguez-Garcia, Babak Ranjbaran, Bahadir Turkyilmaz, Ármann Gylfason Turbulence plays a primary role in many naturally occurring processes, such as atmospheric and oceanic currents. It is also present in the vast majority of industrial processes, including industrial mixers. In these systems, in addition to mechanically forced turbulence, a difference in temperature is instrumental in their evolution. This fact provokes research on mixed convective flows. |
Sunday, November 20, 2022 6:45PM - 6:58PM |
J23.00011: The Cooling Box Problem: Accounting for the Dynamic Surface Temperature Jason Olsthoorn Rayleigh-Benard convection is often modelled with a constant surface temperature. How- |
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