Energy spectrum of buoyancy-driven turbulence

Kumar, Abhishek; Chatterjee, Avik P.; Verma, Mahendra K.

doi:10.1103/physreve.90.023016

Cited by 113 publications

(157 citation statements)

References 36 publications

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“…Interestingly, in turbulent RBC, the buoyancy term is nearly cancelled by the viscous term. This feature of RBC could be the reason for the Kolmogorov's spectrum in RBC, as reported by Kumar et al [41]. The aforementioned wall effects should also be present in other bounded flows such as in channels, pipes, rotating convection, spheres, and cylinders.…”

Section: Discussionmentioning

confidence: 52%

Dynamics of large-scale quantities in Rayleigh-Bénard convection

et al. 2016

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In this paper we estimate the relative strengths of various terms of the Rayleigh-Bénard equations. Based on these estimates and scaling analysis, we derive a general formula for the large-scale velocity, U , or the Péclet number that is applicable for arbitrary Rayleigh number Ra and Prandtl number Pr. Our formula fits reasonably well with the earlier simulation and experimental results. Our analysis also shows that the wall-bounded convection has enhanced viscous force compared to free turbulence. We also demonstrate how correlations deviate the Nusselt number scaling from the theoretical prediction of Ra 1/2 to the experimentally observed scaling of nearly Ra 0.3 .

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Section: Discussionmentioning

confidence: 52%

Dynamics of large-scale quantities in Rayleigh-Bénard convection

et al. 2016

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“…2.2.3). More generally, we point out that the isotropic BO59 scaling laws are not observed either in simulations of Rayleigh-Bénard convection with order-unity vertical to horizontal aspect ratio (Rincon 2006(Rincon , 2007Kumar et al 2014). While the conclusions of these previous studies apply to the regime kH > 1 (where k is an isotropic wave number), they do not appear to be directly applicable to the strongly anisotropic regime k h H 1 characteristic of the astrophysical problem investigated in the present paper.…”

Section: Theoretical Considerationsmentioning

confidence: 87%

“…However, this scaling theory is only applicable for λ h λ r . As λ h becomes of the order of λ r ∼ H ρ , there should be a crossover to either the standard isotropic Bolgiano regime δu ∼ λ 3/5 , δθ ∼ λ 1/5 , or directly to the Kolmogorov regime δu ∼ λ 1/3 , δθ ∼ λ 1/3 (Kumar et al 2014). In both cases, the cascade proceeds in both horizontal and vertical directions, with F c ∼ λ 4/5 for BO59 or F c ∼ λ 2/3 for K41, that is, the convective flux decreases with decreasing scale λ.…”

Section: Spectral Amplitudes Vs Theoretical Estimatesmentioning

confidence: 99%

Supergranulation and multiscale flows in the solar photosphere

Rincon

Roudier

Schekochihin

et al. 2017

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The Sun provides us with the only spatially well-resolved astrophysical example of turbulent thermal convection. While various aspects of solar photospheric turbulence, such as granulation (one-Megameter horizontal scale), are well understood, the questions of the physical origin and dynamical organization of larger-scale flows, such as the 30-Megameters supergranulation and flows deep in the solar convection zone, remain largely open in spite of their importance for solar dynamics and magnetism. Here, we present a new critical global observational characterization of multiscale photospheric flows and subsequently formulate an anisotropic extension of the Bolgiano-Obukhov theory of hydrodynamic stratified turbulence that may explain several of their distinctive dynamical properties. Our combined analysis suggests that photospheric flows in the horizontal range of scales between supergranulation and granulation have a typical vertical correlation scale of 2.5 to 4 Megameters and operate in a strongly anisotropic, self-similar, nonlinear, buoyant dynamical regime. While the theory remains speculative at this stage, it lends itself to quantitative comparisons with future highresolution acoustic tomography of subsurface layers and advanced numerical models. Such a validation exercise may also lead to new insights into the asymptotic dynamical regimes in which other, unresolved turbulent anisotropic astrophysical fluid systems supporting waves or instabilities operate.

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“…A recent three-dimensional DNS analysis of Rayleigh-Bénard convection shows such a scaling as well [62]. BO scaling has been associated with a bi-dimensionalization of the flow due to stratification and the growth of the mixing layer leading to a confined dynamics [63,64].…”

Section: Spectral Behavior a Evidence For A Large-scale Bolgianomentioning

confidence: 93%

Evidence for Bolgiano-Obukhov scaling in rotating stratified turbulence using high-resolution direct numerical simulations

et al. 2015

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We report results on rotating stratified turbulence in the absence of forcing, with large-scale isotropic initial conditions, using direct numerical simulations computed on grids of up to 4096 3 points. The Reynolds and Froude numbers are respectively equal to Re = 5.4×10 4 and F r = 0.0242. The ratio of the Brunt-Väisälä to the inertial wave frequency, N/f , is taken to be equal to 4.95, a choice appropriate to model the dynamics of the southern abyssal ocean at mid latitudes. This gives a global buoyancy Reynolds number RB = ReF r 2 = 32, a value sufficient for some isotropy to be recovered in the small scales beyond the Ozmidov scale, but still moderate enough that the intermediate scales where waves are prevalent are well resolved. We concentrate on the largescale dynamics, for which we find a spectrum compatible with the Bolgiano-Obukhov scaling, and confirm that the Froude number based on a typical vertical length scale is of order unity, with strong gradients in the vertical. Two characteristic scales emerge from this computation, and are identified from sharp variations in the spectral distribution of either total energy or helicity. A spectral break is also observed at a scale at which the partition of energy between the kinetic and potential modes changes abruptly, and beyond which a Kolmogorov-like spectrum recovers. Large slanted layers are ubiquitous in the flow in the velocity and temperature fields, with local overturning events indicated by small Richardson numbers, and a small large-scale enhancement of energy directly attributable to the effect of rotation is also observed.

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Energy spectrum of buoyancy-driven turbulence

Cited by 113 publications

References 36 publications

Dynamics of large-scale quantities in Rayleigh-Bénard convection

Dynamics of large-scale quantities in Rayleigh-Bénard convection

Supergranulation and multiscale flows in the solar photosphere

Evidence for Bolgiano-Obukhov scaling in rotating stratified turbulence using high-resolution direct numerical simulations

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