Entropy Rain: Dilution and Compression of Thermals in Stratified Domains

Anders, Evan H.; Lecoanet, Daniel; Brown, Benjamin

doi:10.3847/1538-4357/ab3644

Cited by 25 publications

(24 citation statements)

References 28 publications

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“…Goldman 2008) and departures from MLT have been found in DNS of compressible convection (e.g. Anders et al 2019). Hence, MLT predictions should be carefully compared to more turbulent DNS of convection.…”

Section: Discussionmentioning

confidence: 99%

Efficiency of tidal dissipation in slowly rotating fully convective stars or planets

Vidal

Barker

2020

Monthly Notices of the Royal Astronomical Society

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Turbulent convection is thought to act as an effective viscosity in damping equilibrium tidal flows, driving spin and orbital evolution in close convective binary systems. Compared to mixing-length predictions, this viscosity ought to be reduced when the tidal frequency |ωt| exceeds the turnover frequency ωcv of the dominant convective eddies, but the efficiency of this reduction has been disputed. We reexamine this long-standing controversy using direct numerical simulations of an idealized global model. We simulate thermal convection in a full sphere, and externally forced by the equilibrium tidal flow, to measure the effective viscosity νE acting on the tidal flow when |ωt|/ωcv ≳ 1. We demonstrate that the frequency reduction of νE is correlated with the frequency spectrum of the (unperturbed) convection. For intermediate frequencies below those in the turbulent cascade (|ωt|/ωcv ∼ 1 − 5), the frequency spectrum displays an anomalous 1/ωα power law that is responsible for the frequency-reduction νE∝1/|ωt|α, where α < 1 depends on the model parameters. We then get |νE|∝1/|ωt|δ with δ > 1 for higher frequencies, and δ = 2 is obtained for a Kolmogorov turbulent cascade. A generic |νE|∝1/|ωt|2 suppression is next found for higher frequencies within the dissipation range of the convection (but with negative values). Our results indicate that a better knowledge of the frequency spectrum of convection is necessary to accurately predict the efficiency of tidal dissipation in stars and planets resulting from this mechanism.

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Section: Discussionmentioning

confidence: 99%

Efficiency of tidal dissipation in slowly rotating fully convective stars or planets

Vidal

Barker

2020

Monthly Notices of the Royal Astronomical Society

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“…As for our Boussinesq approximation, the framework presented in this paper has already been generalized to anelastic and compressible thermals in Anders et al . (). They study thermals in the context of solar convection, and the excellent agreement between theory and simulation in their more general paradigm suggests that our framework might also be amenable to moist thermals.…”

Section: Resultsmentioning

confidence: 97%

“…m is verified to be roughly constant in Anders et al . (). The thermal is the region of fluid that moves coherently with the vortex ring and so the thermal's radius a is proportional to the vortex radius R , i.e., a = ξR . The impulse of a thermal with volume ma 3 and vertical velocity w can be written as (Akhmetov, ),

I_{z} = m a^{3} \overline{ρ} (1 + k) w,

where we parametrize virtual mass effects via a virtual mass coefficient (1+ k ) (Batchelor, ). For all ellipsoidal fluid geometries, the value of k is the same as the solid body value of the same geometry Tarshish et al .…”

Section: A New Model For Thermalsmentioning

confidence: 97%

Buoyancy‐driven entrainment in dry thermals

McKim

Jeevanjee

Lecoanet

2019

Quart J Royal Meteoro Soc

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Over 50 years ago it was proposed that dry thermals entrain because of buoyancy (via a constraint which requires an increase in the radius a). However, this runs counter to the scaling arguments commonly used to derive the entrainment rate, which rely on either the self‐similarity or a turbulent entrainment hypothesis. The assumption of turbulence‐driven entrainment has been investigated and it has been found that the entrainment efficiency e varies by less than 20% between laminar (Re=630) and turbulent (Re=6300) thermals. This motivated us to utilize the argument of buoyancy‐controlled entrainment in addition to the thermal's vertical momentum equation to build a model for thermal dynamics which does not invoke turbulence or self‐similarity. We derive simple expressions for the thermals' kinematic properties and their fractional entrainment rate ϵ and find close quantitative agreement with the values in direct numerical simulations. In particular, our expression for entrainment rate is consistent with the parametrization ϵ∼B/w2, for Archimedean buoyancy B and vertical velocity w. We also directly validate the role of buoyancy‐driven entrainment by running simulations where gravity is turned off midway through a thermal's rise. The entrainment efficiency e is observed to drop to less than one third of its original value in both the laminar and turbulent cases when g=0, affirming the central role of buoyancy in entrainment for dry thermals.

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“…These studies report the existence of deep convective plumes crossing the whole adiabatic layer. The effect of density stratification in an adiabatic region is highlighted by Anders, Lecoanet & Brown (2019) who point out its effect on descending plumes that can be sometimes compacted and accelerated downward. However, their authors also insist on the gap between the values of the stellar Rayleigh number and those actually accessible numerically.…”

Section: Effect Of Confinement and Inertiamentioning

confidence: 99%

A playground for compressible natural convection with a nearly uniform density

et al. 2022

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In the quest to understand the basic universal features of compressible convection, one would like to disentangle genuine consequences of compression from spatial variations of transport properties. For instance, one may choose to consider a fluid with uniform dynamic viscosity, but, then, compressible effects will generate a density gradient and consequently the kinematic viscosity will not be uniform. In the present work, we consider a very peculiar equation of state, whereby entropy is solely dependent on density, so that a nearly isentropic fluid domain is nearly isochoric. Within this class of equations of state, there is a thermal adiabatic gradient and a key property of compressible convection is still present, namely its capacity to viscously dissipate a large fraction of the thermal energy involved, of the order of the well-named dissipation number. In the anelastic approximation, under the assumption of an infinite Prandtl number, the number of governing parameters can be brought down to two, the Rayleigh number and the dissipation number. This framework is proposed as a playground for compressible convection, an opportunity to extend the vast corpus of theoretical analyses on the Oberbeck–Boussinesq equations regarding stability, bifurcations or the determination of upper bounds for the turbulent heat transfer. Here, in a two-dimensional geometry, we concentrate on the structure of numerical solutions. For all Rayleigh numbers, a change in the vertical temperature profile is observed in the range of dissipation number between $0$ and less than $0.4$ , associated with the weakening of ascending plumes. For larger dissipation numbers, the heat flux dependence on this number is found to be well predicted by Malkus's model of critical layers. For dissipation numbers of order unity, and large Rayleigh numbers, dissipation becomes related to the entropy heat flux at each depth, so that the vertical dissipation profile can be predicted, and so does the total ratio of dissipation to convective heat flux.

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Entropy Rain: Dilution and Compression of Thermals in Stratified Domains

Cited by 25 publications

References 28 publications

Efficiency of tidal dissipation in slowly rotating fully convective stars or planets

Efficiency of tidal dissipation in slowly rotating fully convective stars or planets

Buoyancy‐driven entrainment in dry thermals

A playground for compressible natural convection with a nearly uniform density

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