10:45
Rotating Flows 1
10:45
15 mins
#49
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SUBCRITICAL TURBULENT CONDENSATE IN ROTATING RAYLEIGH-BÉNARD CONVECTION
Benjamin Favier, Céline Guervilly, Edgar Knobloch
Abstract: The possibility of subcritical behaviour in the geostrophic turbulence regime of rapidly rotating thermally driven convection is explored. In this regime a non-local inverse energy transfer may compete with the more traditional and local direct cascade. We show that, even for control parameters for which no inverse cascade has previously been observed, a subcritical transition towards a large-scale vortex state can occur when the system is initialized with a vortex dipole of finite amplitude. The positive feedback between the large-scale vortex and the small-scale turbulent fluctuations is shown to be at the origin of the subcritical behaviour. This new example of bistability in a turbulent flow, which may not be specific to rotating convection, opens up new avenues for studying energy transfer in strongly anisotropic three-dimensional flows such as atmospheric and oceanic circulations.
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11:00
15 mins
#81
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GEOSTROPHIC TURBULENT REGIME OF ROTATING RAYLEIGH-BÉNARD CONVECTION AT DIFFERENT PRANDTL NUMBERS
Andrés J. Aguirre-Guzmán, Matteo Madonia, Jonathan S. Cheng, Rodolfo Ostilla-Mónico, Herman J.H. Clercx, Rudie P.J. Kunnen
Abstract: In the rotating Rayleigh-Bénard (RRB) configuration different regimes of turbulent rotating convection can be reached depending on the strength of the buoyant forcing (Rayleigh number, Ra), the strength of rotation (Ekman number, Ek) and the fluid properties (Prandtl number, Pr) [1,2]. In particular, we investigate the rotation-dominated regime of geostrophic turbulence as it is relevant to numerous geo- and astrophysical flows. For instance, in the Earth’s outer core, the convective currents of conducting materials that are source of the Earth’s magnetic field fall into this regime. We study the flow morphology and characterize it via mean temperature distribution, boundary layer thicknesses and heat transport efficiency. We also investigate the boundaries of this regime, especially with the rotation-affected regime. In geostrophic turbulence, the flow shows quasi-two-dimensional turbulent behavior [3], while in the rotation-affected regime the flow is rather three-dimensional [4].
We directly simulate the RRB flow for a wide range of (Ra,Ek) values to cover the transition between geostrophic turbulence and the rotation-affected regime at different Prandtl numbers. We include cases at Pr=0.1, ~5 and 100 that are relevant to liquid metals, oceanic processes and geophysical flows, respectively. We consider a horizontally periodic domain with no-slip condition at the top/bottom of the RRB cell. To properly resolve the turbulent flow down to the smallest dissipation scales, we use resolutions up to 1408x1408x1280 grid points for the Pr=0.1 case. For higher-Pr cases, we use a multiple-resolution strategy where temperature is resolved in a finer mesh than that for velocity. The most demanding case is Pr=100, where we use resolutions up to 512x512x768 grid points for the flow and 1536x1536x1960 for temperature, which makes it one of the largest simulations of turbulent rotating thermal convection.
Figure 1 (see PDF version) shows single-time snapshots of the horizontal kinetic energy at the different values of Pr. We highlight the presence of a large-scale vortex in the geostrophic turbulent regime at the lowest Pr case (Figure 1a). It is the first time a structure of this kind has been observed for no-slip boundary conditions. At higher Prandtl numbers, the flow is dominated by small-scale structures (Figures 1b,c). In the presentation we will further show how the flow morphology and heat transfer in geostrophic turbulent convection depend on Pr, as does the transition point to rotation-affected convection.
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11:15
15 mins
#37
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Global flow structures in rotating Rayleigh--B\'enard convection in pressured SF$_6$
Xuan Zhang, Olga Shishkina
Abstract: Effects of rotation on flow structures in a Prandtl number Pr=0.8 flow (pressurized sulfur hexafluoride SF$_6$) are analyzed using our finite-volume code Goldfish \cite{bib:Kooij2018}.
A cylindrical rotating Rayleigh--B\'enard convection (RBC) cell of diameter-to-height aspect ratio 0.5 is considered.
Direct numerical simulations (DNS) are performed at Rayleigh number $10^7$ to $10^{10}$ and Rossby number 0.02 to 50.
Effects of rotation on the temporal and mean flow structures are investigated in terms of local historical temperature signals, instantaneous and time-averaged distribution of the temperature, vorticity and velocity fields.
For lower rotation rates, a cyclonic flow is observed in the core part of the domain, due to the presence of a large-scale circulation.
For higher rotation rates, in accordance with the Taylor--Proudman theorem, an anti-cyclonic flow develops in the entire domain apart from a thin region near the vertical wall, the thickness of which scales with Ekman number as $\sim$ Ek$^{0.6}$ (differently from the Stewartson scaling).
\begin{figure}[h]
\setlength{\unitlength}{1cm}
\begin{center}
\includegraphics[width=16cm]{meanflow.pdf}
\end{center}
\caption{Mean flow structures (at the mid-plane contoured by u$_{\phi}$) at different rotation rates, Pr=0.8, Ra=$10^9$.}
\label{fig1}
\end{figure}
\begin{thebibliography}{1}
\bibitem{bib:Kooij2018}
G. L. Kooij, M. A. Botchev, E. M. Frederix, B. J. Geurts, S. Horn, D. Lohse, E. P. van der Poel, O. Shishkina, R. J. Stevens and R. Verzicco. Comparison of computational codes for direct numerical simulations of turbulent Rayleigh--B\'enard convection. \textit{Computers \& Fluids} \textbf{166}: 1--8, 2018.
\end{thebibliography}
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11:30
15 mins
#131
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Rotating homogeneous Rayleigh-Benard convection
Francesco Toselli
Abstract: Turbulent convection is a conceptual challenge which involves the coupling between a turbulent flow and an active transported temperature field. A typical case of study for turbulent convection system is the one referred to a flow where the fluid, confined to a box, is heated from below and cooled from above: this setup is called Rayleigh-Bénard (RB) convection.
Several internal and external factors can modify the dynamical and statistical properties of turbulent convection: among the latters, rotation along the vertical axis (the one of gravity) is known to affect dramatically the efficiency of turbulent
transport of heat.
Here we show results from direct numerical simulation of homogeneous Rayleigh-Bénard turbulence (i.e. Rayleigh-Bénard turbulence with temperature field forced by a mean unstable gradient γ and periodic boundary conditions in all directions) in presence of rotation. This system models the bulk of turbulence only, verifying the Pr and Ra scaling laws of the Reynolds and the Nusselt number (Re, Nu) for the so called ’ultimate regime of thermal convection’ according to the theory by Kraichnan. In particular the temperature fluctuations and the Nu number dependency on different rotation intensities are studied. Moreover, the role of rotation acting on the flow, is investigated in terms of identification of strong convective events, bidimensionalization of the system and finally by computing the vertical correlation function of velocities and temperature fields.
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11:45
15 mins
#356
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Rotating turbulent Rayleigh-Bénard convection at very large Rayleigh numbers
Marcel Wedi, Dennis van Gils, Guenter Ahlers, Eberhard Bodenschatz, Stephan Weiss
Abstract: Thermal convection is of major importance in various astro- and geophysical systems, exemplary are buoyancy driven flows in the atmosphere or in the stellar interior. Due to the rotation of the hosting celestial bodies the convection is both, highly turbulent and strongly influenced by Coriolis forces. An idealized model system to study thermal convection is Rayleigh-Bénard convection (RBC), which consists of a horizontal fluid layer heated at the bottom and cooled at the top [1]. Within the Oberbeck-Boussinesq approximation this system is controlled by two parameters only, the thermal driving, expressed dimension-less in the Rayleigh number Ra and the Prandtl number Pr that relates the momentum and thermal diffusivities of the fluid. The applied rotation is expressed in a dimensionless form by the inverse Rossby number 1/Ro. With an experimental RBC realization we aim to study the influence of rotation on the heat transport and the temperature field at very large Ra in the High Pressure Convection Facility (HPCF) in Göttingen. The facility consists of a cylindrical cell of 1.10 m diameter and 2.20 m height that is filled with pressurized sulfur hexafluoride (SF6) at up to 19 bar. The height of the cell and the large density of SF 6 enable us to reach Ra as high as 2 × 10^15. The cell has been used previously for studies without rotation [2].
The cell is mounted on a rotating table and connected to the non-rotating world via water feed-throughs and slip rings. With these, the signals of more than 100 thermistors close to the sidewalls are collected. With this setup we reach Ek down to 10^-8, possibly entering the geostrophic regime. At very high rotation rates the Froude number increases and centrifugal forces become important. We study the effects of rotation on the heat transport and the temperature distribution inside the cell for 5 × 10^9 < Ra < 10^15 and 0.74 < Pr < 0.96. While studies at larger Pr found an increase in heat transport at slow rotation [3], no increase was found in our investigation. The observed decrease in the heat transport is accompanied with a change in the temperature distribution close to the sidewall. With increasing rotation rate the temperature distribution clearly shows two distinct maxima that are thermal signatures of localized up- and down-draft regions inside vertical columns. In our talk, we discuss these behaviors of the flow as well as the heat transport in RBC for a large range in the Ra-Ek parameter space.
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12:00
15 mins
#628
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Tilted Rotating Rayleigh-Bénard Convection
Lyuba Novi, Jost von Hardenberg, Antonello Provenzale
Abstract: We explore numerically Rayleigh-Bénard convection at high Rayleigh number when the system is rapidly rotating about a distant axis that is tilted with respect to the gravity vector. The tilt angle between the rotation axis and the horizontal plane is varied and can be seen as a proxy for planetary latitude for convective dynamics in a rotating fluid shell. The domain has an aspect ratio of 2pi, it is periodic and free-slip boundary conditions are used at the top and bottom plates.
As the tilt angle is increased from the horizontal (perpendicular to the gravity vector) to the vertical (aligned with the gravity vector), our results indicate the appearance of three regimes: 1) when the rotation axis is horizontal we find sheared, intermittent large-scale winds in the direction perpendicular to the plane defined by the gravity and rotation vectors (studied in [1]); 2) at the other extreme when the rotation axis is almost vertical (between 45◦ and 90◦) a large-scale cyclonic vortex tilted along the rotation axis appears (see also [2]); 3) at intermediate angles (up to about 60◦) we find also an intermediate regime characterized by vertically sheared large-scale winds perpendicular to both gravity and rotation, organized in bands that are tilted along the rotation axis, with unit horizontal wavenumber in the plane defined by gravity and rotation. This intermediate solution, presented for the first time here [3], is characterized by weaker vertical heat transport than the cases with large-scale vortices and we verified that at intermediate tilt angles (between about 45◦ and 60◦) it coexists with the large-scale vortex solution, with different initial conditions leading to one or the other dynamical behavior. Additional recent experiments extending the domain size will be discussed, exploring the dependence of the wavenumber of the intermediate banded solution and of vertical heat transport on the aspect ratio (up to 6pi).
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12:15
15 mins
#121
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Explaining sharp transitions in turbulent rotating Rayleigh-Bénard convection with Lagrangian statistics
Rudie Kunnen, Kim Alards, Richard Stevens, Detlef Lohse, Federico Toschi, Herman Clercx
Abstract: Rotating Rayleigh-Bénard convection is a popular system to study the interaction of rotation and buoyancy-driven turbulence. In the typical upright-cylinder geometry, used in both experiments and numerical simulations, the heat transfer displays a sharp transition: below a critical rotation rate rotation is too weak to affect the convective heat flux (expressed in dimensionless form as the Nusselt number Nu); stronger rotation leads to a gradual increase of Nu with rotation for fluids with Prandtl number Pr>1. The reported critical rotation rate is Ro_c~=2.3-2.9, where Ro is the convective Rossby number comparing the strength of buoyancy and Coriolis acceleration (Ro is inversely proportional to the rotation rate). Ro_c is primarily determined by the diameter-to-height aspect ratio Gamma of the cylinder.
The leading explanation of the sharp transition in Nu points at the change in the dominant flow structure. At Ro>Ro_c (slow rotation) the well-known large-scale circulation (LSC) is found: a single domain-filling convection roll made up of many individual thermal plumes. At RoRo_c) and Ekman layers (for Ro
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