The Magnitude of Viscous Dissipation in Strongly Stratified Two-dimensional Convection

Currie, Laura K.; Browning, Matthew K.

doi:10.3847/2041-8213/aa8301

Cited by 15 publications

(18 citation statements)

References 23 publications

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“…Different results were obtained in Currie & Browning (2017), where a larger dissipation than our limit (7.25) is obtained. There are actually several differences in the configuration they have studied: (i) they use an EoS of an ideal gas, (ii) they model conduction using the gradient of entropy, (iii) they use a boundary condition of a fixed flux (bottom), (iv) they consider inertia (Pr = 1 or 10), (v) they have a square domain and (vi) they have non-penetrative conditions on lateral walls.…”

Section: Effect Of Confinement and Inertiacontrasting

confidence: 83%

“…In our work, this state is obtained in the limit of large superadiabatic Rayleigh numbers, although that limit might be difficult to reach for small dissipation numbers. A second state, observed by Currie & Browning (2017), can be seen when inertia is introduced and when vertical walls are present. Convection is large-scale, descending plumes are stuck to a wall (the left wall in the particular snapshot in figure 17) and viscous dissipation is enhanced compared to the first state.…”

Section: Effect Of Confinement and Inertiamentioning

confidence: 94%

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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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Section: Effect Of Confinement and Inertiacontrasting

confidence: 83%

Section: Effect Of Confinement and Inertiamentioning

confidence: 94%

A playground for compressible natural convection with a nearly uniform density

et al. 2022

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“…By adopting the Boussinesq approximation, we have neglected the effects of compressibility and imposed a symmetry between upflows and downflows that does not exist in the full system, which may well have implications for the stratification that is established (e.g., Korre et al 2017;Käpylä et al 2017a). Moreover, in strongly stratified systems, dissipative heating can be large resulting in convective fluxes that greatly exceed the luminosity (see e.g., Currie & Browning 2017). Furthermore, when stratification is present, the convective velocities will also generally vary with depth, so the influence of rotation on the dynamics may be depth-dependent as well (see, e.g., discussions in Ireland & Browning 2018).…”

Section: Discussionmentioning

confidence: 99%

Convection with misaligned gravity and rotation: simulations and rotating mixing length theory

Currie

Barker

Lithwick

et al. 2020

Monthly Notices of the Royal Astronomical Society

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We present numerical simulations, using two complementary setups, of rotating Boussinesq thermal convection in a three-dimensional Cartesian geometry with misaligned gravity and rotation vectors. This model represents a small region at a non-polar latitude in the convection zone of a star or planet. We investigate the effects of rotation on the bulk properties of convection at different latitudes, focusing on determining the relation between the heat flux and temperature gradient. We show that our results may be interpreted using rotating mixing length theory (RMLT). The simplest version of RMLT (due to Stevenson) considers the single mode that transports the most heat. This works reasonably well in explaining our results, but there is a systematic departure from these predictions (up to approximately 30% in the temperature gradient) at mid-latitudes. We develop a more detailed treatment of RMLT that includes the transport afforded by multiple modes, and we show that this accounts for most of the systematic differences. We also show that convectively-generated zonal flows and meridional circulations are produced in our simulations, and that their properties depend strongly on the dimensions of the box. These flows also affect the heat transport, contributing to departures from RMLT at some latitudes. However, we find the theoretical predictions of the multi-mode theory for the mid-layer temperature gradient, the root-mean-square (RMS) vertical velocity, the RMS temperature fluctuation, and the spatial spectrum of the heat transport at different latitudes, are all in reasonably good agreement with our numerical results when zonal flows are small.

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“…In general, we anticipate from the results of e.g., Currie & Browning (2017) that f is closer to 1 than 0, but its precise value must be measured from simulations. Indeed, we find that f 0 but f < 1 in our simulations (see e.g., Fig.…”

Section: Kinetic Energy and The Dissipation-flux Linkmentioning

confidence: 99%

Stellar convective penetration: parameterized theory and dynamical simulations

Anders,

Jermyn,

Lecoanet

et al. 2021

Preprint

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Most stars host convection zones in which heat is transported directly by fluid motion. Parameterizations like mixing length theory adequately describe convective flows in the bulk of these regions, but the behavior of convective boundaries is not well understood. Here we present 3D numerical simulations which exhibit penetration zones: regions where the entire luminosity could be carried by radiation, but where the temperature gradient is approximately adiabatic and convection is present. To parameterize this effect, we define the "penetration parameter" P which compares how far the radiative gradient deviates from the adiabatic gradient on either side of the Schwarzschild convective boundary. Following Roxburgh (1989) and Zahn (1991), we construct an energy-based theoretical model in which the extent of penetration is controlled by P. We test this theory using 3D numerical simulations which employ a simplified Boussinesq model of stellar convection. We find significant convective penetration in all simulations. Our simple theory describes the simulations well. Penetration zones can take thousands of overturn times to develop, so long simulations or accelerated evolutionary techniques are required. In stellar contexts, we expect P ≈ 1 and in this regime our results suggest that convection zones may extend beyond the Schwarzschild boundary by up to ∼20-30% of a mixing length. We present a MESA stellar model of the Sun which employs our parameterization of convective penetration as a proof of concept. We discuss prospects for extending these results to more realistic stellar contexts.

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The Magnitude of Viscous Dissipation in Strongly Stratified Two-dimensional Convection

Cited by 15 publications

References 23 publications

A playground for compressible natural convection with a nearly uniform density

A playground for compressible natural convection with a nearly uniform density

Convection with misaligned gravity and rotation: simulations and rotating mixing length theory

Stellar convective penetration: parameterized theory and dynamical simulations

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