On the validity of two-dimensional numerical approaches to time-dependent thermal convection

Schmalzl, J.; Breuer, M.; Hansen, Ulrich

doi:10.1209/epl/i2003-10298-4

Cited by 96 publications

(111 citation statements)

References 23 publications

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“…For this reason, we ran a series of tests to compare both the qualitative behavior and the quantitative estimates of the fluxes (and other system diagnostics) in 2D and 3D. Simulations in 2D and 3D often lead to very different types of dynamics, especially at low Pr (Schmalzl et al 2004;van der Poel et al 2013;Garaud & Brummell 2015). Fortunately, however, as we see from is very similar to that of the 3D simulation analyzed in the previous section.…”

Section: D Simulationsmentioning

confidence: 54%

A New Model for Mixing by Double-Diffusive Convection (Semi-Convection). Iii. Thermal and Compositional Transport Through Non-Layered Oddc

Moll

Garaud

Stellmach

2016

ApJ

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Oscillatory double-diffusive convection (ODDC; also known as semi-convection) refers to a type of doublediffusive instability that occurs in regions of planetary and stellar interiors that have a destabilizing thermal stratification and a stabilizing mean molecular weight stratification. In this series of papers, we use an extensive suite of three-dimensional (3D) numerical simulations to quantify the transport of heat and chemical species by ODDC. Rosenblum et al. first showed that ODDC can either spontaneously form layers that significantly enhance the transport of heat and chemical species compared to microscopic transport or remain in a state dominated by large-scale gravity waves, in which there is a more modest enhancement of the turbulent transport rates. Subsequent studies in this series focused on identifying under what conditions layers form and quantifying transport through layered systems. Here we proceed to characterize transport through systems that are unstable to ODDC, but do not undergo spontaneous layer formation. We measure the thermal and compositional fluxes in nonlayered ODDC from both two-dimensional (2D) and 3D numerical simulations, and show that 3D simulations are well approximated by similar simulations in a 2D domain. We find that the turbulent mixing rate in this regime is weak and can, to a first-level approximation, be neglected. We conclude by summarizing the findings of papers I through III into a single prescription for transport systems unstable to ODDC.

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Section: D Simulationsmentioning

confidence: 54%

A New Model for Mixing by Double-Diffusive Convection (Semi-Convection). Iii. Thermal and Compositional Transport Through Non-Layered Oddc

Moll

Garaud

Stellmach

2016

ApJ

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“…Good consistency between 2D and 3D runs have also been found for thermal convection when Pr . 1 (Schmalzl et al 2004). Whether this condition also applies to diffusive convection is, however, not known.…”

Section: Heat Flux Scaling a Results From Dnsmentioning

confidence: 99%

Energy and Variance Budgets of a Diffusive Staircase with Implications for Heat Flux Scaling

Hieronymus

Carpenter

2016

Journal of Physical Oceanography

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The steady-state energy and thermal variance budgets form the basis for most current methods for evaluating turbulent fluxes of buoyancy, heat, and salinity. This study derives these budgets for a double-diffusive staircase and quantifies them using direct numerical simulations; 10 runs with different Rayleigh numbers are considered. The energy budget is found to be well approximated by a simple three-term balance, while the thermal variance budget consists of only two terms. The two budgets are also combined to give an expression for the ratio of the heat and salt fluxes. The heat flux scaling is also studied and found to agree well with earlier estimates based on laboratory experiments and numerical simulations at high Rayleigh numbers. At low Rayleigh numbers, however, the authors find large deviations from earlier scaling laws. Last, the scaling theory of Grossman and Lohse, which was developed for Rayleigh-Bénard convection and is based on the partitioning of the kinetic energy and tracer variance dissipation, is adapted to the diffusive regime of doublediffusive convection. The predicted heat flux scalings are compared to the results from the numerical simulations and earlier estimates.

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“…Two-dimensional simulations are used to aid visualization and identification of plume emission locations. Even though two-dimensional (2D) RB differs from three-dimensional (3D) RB in terms of integral quantities for finite Pr [24,32], the theoretical arguments for logarithmic profiles are not specific to 3D RB. Furthermore, the two-dimensional domain is more suitable to study the horizontal dependence of the boundary layer profile than the three-dimensional domain.…”

Section: Impactingmentioning

confidence: 99%

Logarithmic Mean Temperature Profiles and Their Connection to Plume Emissions in Turbulent Rayleigh-Bénard Convection

et al. 2015

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Two-dimensional simulations of Rayleigh-Bénard convection at Ra = 5 × 10 10 show that vertical logarithmic mean temperature profiles can be observed in regions of the boundary layer where thermal plumes are emitted. The profile is logarithmic only in these regions and not in the rest of the boundary layer where it is sheared by the large scale wind and impacted by plumes. In addition, the logarithmic behavior is not visible in the horizontal average. The findings reveal that the temperature profiles are strongly connected to thermal plume emission and support a perception that parts of the boundary layer can be turbulent, while others are not. The transition to the ultimate regime, in which the boundary layers are considered to be fully turbulent, can therefore be understood as a gradual increases in fraction of the plume-emitting ('turbulent') regions of the boundary layer.

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On the validity of two-dimensional numerical approaches to time-dependent thermal convection

Cited by 96 publications

References 23 publications

A New Model for Mixing by Double-Diffusive Convection (Semi-Convection). Iii. Thermal and Compositional Transport Through Non-Layered Oddc

A New Model for Mixing by Double-Diffusive Convection (Semi-Convection). Iii. Thermal and Compositional Transport Through Non-Layered Oddc

Energy and Variance Budgets of a Diffusive Staircase with Implications for Heat Flux Scaling

Logarithmic Mean Temperature Profiles and Their Connection to Plume Emissions in Turbulent Rayleigh-Bénard Convection

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