Large-scale mean patterns in turbulent convection

Emran, Mohammad S.; Schumacher, Jörg

doi:10.1017/jfm.2015.316

Cited by 61 publications

(59 citation statements)

References 31 publications

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“…In Rayleigh-Bénard convection, patterns can be identified (Bodenschatz et al 2000;Weiß et al 2012;Emran & Schumacher 2015). In a star, the gradients of temperature and density are generally non-uniform and vary non-linearly over the full stellar radius.…”

Section: Introductionmentioning

confidence: 99%

Spherical-shell boundaries for two-dimensional compressible convection in a star

Pratt

Baraffe

Goffrey

et al. 2016

A&A

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Context. Studies of stellar convection typically use a spherical shell geometry. The radial extent of the shell and the boundary conditions applied are based on the model of the star investigated. We study the impact of different two-dimensional spherical shells on compressible convection. Realistic profiles for density and temperature from an established one-dimensional stellar evolution code are used to produce a model of a large stellar convection zone representative of a young low-mass star, such as our sun at 10 6 years of age. Aims. We analyze how the radial extent of the spherical shell changes the convective dynamics that result in the deep interior of the young sun model, far from the surface. In the near-surface layers, simple smaller-scale convection develops from the profiles of temperature and density. A central radiative zone below the convection zone provides a lower boundary on the convection zone. The inclusion of either of these physically distinct layers in the spherical shell can potentially affect the characteristics of deep convection. Methods. We perform hydrodynamic implicit large-eddy simulations of compressible convection using the MUltidimensional Stellar Implicit Code (MUSIC). Because MUSIC has been designed to use realistic stellar models produced from one-dimensional stellar evolution calculations, MUSIC simulations are capable of seamlessly modeling a whole star. Simulations in two-dimensional spherical shells that have different radial extents are performed over tens or even hundreds of convective turnover times, permitting the collection of well-converged statistics. Results. To measure the impact of the spherical shell geometry and our treatment of boundaries, we evaluate basic statistics of the convective turnover time, the convective velocity, and the overshooting layer. These quantities are selected for their relevance to one-dimensional stellar evolution calculations, so that our results are focused toward studies exploiting the so-called 321D link. We find that the inclusion in the spherical shell of the boundary between the radiative and convection zones decreases the amplitude of convective velocities in the convection zone. The inclusion of near-surface layers in the spherical shell can increase the amplitude of convective velocities, although the radial structure of the velocity profile established by deep convection is unchanged. The impact from including the near-surface layers depends on the speed and structure of small-scale convection in the near-surface layers. Larger convective velocities in the convection zone result in a commensurate increase in the overshooting layer width and decrease in the convective turnover time. These results provide support for non-local aspects of convection.

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Section: Introductionmentioning

confidence: 99%

Spherical-shell boundaries for two-dimensional compressible convection in a star

Pratt

Baraffe

Goffrey

et al. 2016

A&A

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“…As the Rayleigh number is increased, the patterns, which are present at the onset, vanish due to increasing turbulent fluctuations in the temperature and velocity fields. The time-averaged fields, however, reveal patterns which are similar to those present at lower Ra near the onset [13]. These time-averaged structures in thermal convection are termed turbulent superstructures of RBC.…”

Section: Introductionmentioning

confidence: 81%

“…These time-averaged structures in thermal convection are termed turbulent superstructures of RBC. They were for example studied in a Γ = 50 cylindrical cell for P r between 0.7 and 10 and Ra up to 5 × 10 5 [13]. While the instantaneous temperature and velocity fields looked different when comparing Ra = 5 × 10 3 and Ra = 5 × 10 5 , the time-averaged fields for Ra = 5 × 10 5 appear to be very similar to those for Ra = 5 × 10 3 [13].…”

Section: Introductionmentioning

confidence: 99%

Turbulent superstructures in Rayleigh‐Bénard convection for varying Prandtl numbers

Pandey

Schumacher

2017

Proc Appl Math and Mech

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Using direct numerical simulations, we study the properties of turbulent superstructures in thermal convection in a large aspect ratio square cell. We estimate the characteristic length scale of superstructures using spatial auto-correlation functions and two-dimensional power spectra, and observe that the typical length scale increases weakly with increasing Prandtl number. We also find that the Prandtl number dependence of heat and momentum transport are similar to those observed in small aspect ratio systems.

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“…Therefore the underlying assumption is that a description in terms of an order parameter field, superposed by fluctuations, remains valid in the turbulent case. As we will see in the following, such a simple model suffices to conceptually explain recent observations on turbulent superstructures [12,[16][17][18]. Suitably nondimensionalized, the SH equation with random advection takes the form…”

mentioning

confidence: 97%

“…Both experiments and, in particular, numerical simulations have provided insights into these complex flow regimes [1][2][3]. Remarkably, coherent large-scale flow patterns, so-called turbulent superstructures, have been reported in the presence of small-scale turbulence [12][13][14][15][16][17][18]. Using suitable averaging techniques, the topology and dynamics of the superstructures have been extracted from the turbulent flow fields, demonstrating, e.g.,large-scale dynamics reminiscent of spiraldefect chaos [16].…”

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confidence: 97%

Large-Scale Pattern Formation in the Presence of Small-Scale Random Advection

2019

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Despite the presence of strong fluctuations, many turbulent systems such as Rayleigh-Bénard convection and Taylor-Couette flow display self-organized large-scale flow patterns. How do small-scale turbulent fluctuations impact the emergence and stability of such large-scale flow patterns? Here, we approach this question conceptually by investigating a class of pattern forming systems in the presence of random advection by a Kraichnan-Kazantsev velocity field. Combining tools from pattern formation with statistical theory and simulations, we show that random advection shifts the onset and the wave number of emergent patterns. As a simple model for pattern formation in convection, the effects are demonstrated with a generalized Swift-Hohenberg equation including random advection. We also discuss the implications of our results for the large-scale flow of turbulent Rayleigh-Bénard convection.Many turbulent systems show a remarkable degree of large-scale coherence, despite the presence of strong fluctuations. Large-scale convection patterns in the atmosphere and in the oceans are among the most fascinating examples. Rayleigh-Bénard convection (RBC) [1][2][3][4], the flow between two plates heated from below and cooled from above, is a prototypical model for such flows and displays a range of phenomena-the emergence of laminar large-scale rolls close to the onset of convection, transitions to increasingly complex flow patterns as the temperature difference is increased, and finally, the emergence of turbulence. Close to onset, techniques like linear stability analysis as well as amplitude and phase equations explain the emergence and stability of convection patterns [5][6][7][8][9][10][11]. Further away from the onset of convection, the flow becomes increasingly difficult to describe, especially when it becomes turbulent. Both experiments and, in particular, numerical simulations have provided insights into these complex flow regimes [1][2][3]. Remarkably, coherent large-scale flow patterns, so-called turbulent superstructures, have been reported in the presence of small-scale turbulence [12][13][14][15][16][17][18]. Using suitable averaging techniques, the topology and dynamics of the superstructures have been extracted from the turbulent flow fields, demonstrating, e.g.,large-scale dynamics reminiscent of spiraldefect chaos [16]. Extensive experimental and numerical investigations revealed that the length scale of the emerging patterns increases as a function of Rayleigh and Prandtl numbers as the flow becomes increasingly unsteady [19][20][21] and, finally, turbulent [14,18]. Investigations of RBC close to onset suggest that there is no universal scale selection mechanism, see, e.g., [22,23] for an overview. As soon as turbulence sets in, the issue is even more delicate: so far there is no conclusive explanation for the increased wavelength of turbulent superstructures. Interestingly, similar issues remain in explaining turbulent Taylor Couette flow [24], i.e. the flow between two rotating cylinders. Also here, the ...

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Large-scale mean patterns in turbulent convection

Cited by 61 publications

References 31 publications

Spherical-shell boundaries for two-dimensional compressible convection in a star

Spherical-shell boundaries for two-dimensional compressible convection in a star

Turbulent superstructures in Rayleigh‐Bénard convection for varying Prandtl numbers

Large-Scale Pattern Formation in the Presence of Small-Scale Random Advection

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