Layer formation in double-diffusive convection over resting and moving heated plates

Zaussinger, Florian; Kupka, F.

doi:10.1007/s00162-019-00499-7

Cited by 13 publications

(11 citation statements)

References 56 publications

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“…Therefore, understanding the dynamical properties of how such diffusive DDC staircases can form, and (at least equally importantly) remain robust is a topic of not only fluid dynamical interest but also great climatological importance, and so we focus on such staircases here. Diffusive staircases have been observed to develop spontaneously, even in numerical simulations restricted to two dimensions both with and without shear (Noguchi & Niino 2010; Zaussinger & Kupka 2018), but their actual formation mechanism has up to now remained somewhat mysterious, as discussed by Kelley et al. (2003) and Turner (2013).…”

Section: Introductionmentioning

confidence: 99%

Layering and vertical transport in sheared double-diffusive convection in the diffusive regime

et al. 2021

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A sequence of two- and three-dimensional simulations are conducted for the double-diffusive convection (DDC) flows in the diffusive regime subjected to an imposed shear. For a wide range of control parameters, and for sufficiently strong perturbation of the conductive initial state, staircase-like structures spontaneously develop, with relatively well-mixed layers separated by sharp interfaces of enhanced scalar gradient. Such staircases appear to be robust even in the presence of strong shear over very long times, with early-time coarsening of the observed layers. For the same set of control parameters, different asymptotic layered states, with markedly different vertical scalar fluxes, can arise for different initial perturbation structures. The imposed shear significantly spatio-temporally modifies the vertical transport of the various scalars. The flux ratio $\gamma ^*$ (i.e. the ratio between the density fluxes due to the total salt flux and the total heat flux) is found, at steady state, to be essentially equal to the square root of the ratio of the salt diffusivity to the thermal diffusivity, consistent with the physical model proposed by Linden & Shirtcliffe (J. Fluid Mech., vol. 87, 1978, pp. 417–432) and the variational arguments presented by Stern (J. Fluid Mech., vol. 114, 1982, pp. 105–121) for unsheared double-diffusive convection.

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Section: Introductionmentioning

confidence: 99%

Layering and vertical transport in sheared double-diffusive convection in the diffusive regime

et al. 2021

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“…Biello [26] found that gravity waves can break near the interface and mix the composition gradient across, making the formation of secondary layers difficult to occur at low Pr. On the other hand, Zaussinger and Kupka [27] found that multiple layers can form at low Pr either by a thermal instability at the interface ahead of the main convective layer, or spontaneously develop due to double-diffusive instabilities, as the ones observed in Radko [14] and Mirouh et al [16]. We will discuss these issues in a companion paper.…”

Section: Equations (mentioning

confidence: 87%

“…5 Eq. (27) shows that the range of values of R ρ depends on the maximum value of γ. The definition of γ in eq.…”

Section: Analytic Model For the Inwards Propagation Of The Convective...mentioning

confidence: 95%

“…Secondary layers are seen in salt water experiments, but it is not known when and how they arise in time-dependent cooling at low Pr. In this regard, a few attempts have been made [26,27]. Biello [26] found that gravity waves can break near the interface and mix the composition gradient across, making the formation of secondary layers difficult to occur at low Pr.…”

Section: Equations (mentioning

confidence: 99%

“…In this work, we investigate how low Pr affects the growth of a convective layer into a composition gradient. While there has been some work done with a time-dependent background temperature profile at low Pr [26,27], it was focused on the formation and evolution of layers. Here we focus on the physics behind the growth of the convective zone.…”

Section: Introductionmentioning

confidence: 99%

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Penetration of a cooling convective layer into a stably-stratified composition gradient: entrainment at low Prandtl number

Fuentes,

Cumming

2020

Preprint

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We study the formation and inward propagation of a convective layer when a stably-stratified fluid with a composition gradient is cooled from above. We perform a series of two-dimensional simulations using the Bousinessq approximation with Prandtl number ranging from Pr = 0.1 to 7, extending previous work on salty water to low Pr. We show that the evolution of the convection zone is well-described by an entrainment prescription in which a fixed fraction of the kinetic energy of convective motions is used to mix fluid at the interface with the stable layer. We measure the entrainment efficiency and find that it grows with decreasing Prandtl number or increased applied heat flux. The kinetic energy flux that determines the entrainment rate is a small fraction of the total convective luminosity. In this time-dependent situation, the density ratio at the interface is driven to a narrow range that depends on the value of Pr, and with low enough values that advection dominates the interfacial transport. We characterize the interfacial flux ratio and how it depends on the interface stability.We present an analytic model that accounts for the growth of the convective layer with two parameters, the entrainment efficiency and the interfacial heat transport, both of which can be measured from the simulations.

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The ANTARES code: recent developments and applications

Kupka

Zaussinger²,

Fabbian³

et al. 2020

J. Phys.: Conf. Ser.

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ANTARES (A Numerical Tool for Astrophysical RESearch) is a multi-purpose numerical tool to solve different variants of the equations of hydrodynamics as they appear in problems of astrophysics, geophysics, and engineering sciences and which require the construction of detailed numerical simulation models. A presentation of the current feature set of the code with a focus on recent add-ons is given here in addition to a summary on several results from recent applications of ANTARES to solar physics, the physics of planets, and basic convection studies including the damping of pressure modes (solar oscillations) in numerical simulations of convection at the solar surface and the coupling of layers in numerical simulations of sheared and non-sheared double-diffusive convection.

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Layer formation in double-diffusive convection over resting and moving heated plates

Cited by 13 publications

References 56 publications

Layering and vertical transport in sheared double-diffusive convection in the diffusive regime

Layering and vertical transport in sheared double-diffusive convection in the diffusive regime

Penetration of a cooling convective layer into a stably-stratified composition gradient: entrainment at low Prandtl number

The ANTARES code: recent developments and applications

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