2,084 research outputs found
Marginally-Stable Thermal Equilibria of Rayleigh-B\'enard Convection
Natural convection is ubiquitous throughout the physical sciences and
engineering, yet many of its important properties remain elusive. To study
convection in a novel context, we derive and solve a quasilinear form of the
Rayleigh-B\'enard problem by representing the perturbations in terms of
marginally-stable eigenmodes. The amplitude of each eigenmode is determined by
requiring that the background state maintains marginal stability. The
background temperature profile evolves due to the advective flux of every
marginally-stable eigenmode, as well as diffusion. To ensure marginal stability
and to obtain the eigenfunctions at every timestep, we perform a
one-dimensional eigenvalue solve on each of the allowable wavenumbers. The
background temperature field evolves to an equilibrium state, where the
advective flux from the marginally-stable eigenmodes and the diffusive flux sum
to a constant. These marginally-stable thermal equilibria (MSTE) are exact
solutions of the quasilinear equations. The mean temperature profile has
thinner boundary layers and larger Nusselt numbers than thermally-equilibrated
2D and 3D simulations of the full nonlinear equations. We find the Nusselt
number scales like . When an MSTE is used as initial
conditions for a 2D simulation, we find that Nu quickly equilibrates without
the burst of turbulence often induced by purely conductive initial conditions,
but we also find that the kinetic energy is too large and viscously attenuates
on a long viscous time scale. This is due to the thin temperature boundary
layers which diffuse heat very effectively, thereby requiring high-velocity
advective flows to reach an equilibrium
Internally heated and fully compressible convection: flow morphology and scaling laws
In stars and planets natural processes heat convective flows in the bulk of a
convective region rather than at hard boundaries. By characterizing how
convective dynamics are determined by the strength of an internal heating
source we can gain insight into the processes driving astrophysical convection.
Internally heated convection has been studied extensively in incompressible
fluids, but the effects of stratification and compressibility have not been
examined in detail. In this work, we study fully compressible convection driven
by a spatially uniform heating source in 2D and 3D Cartesian, hydrodynamic
simulations. We use a fixed temperature upper boundary condition which results
in a system that is internally heated in the bulk and cooled at the top. We
find that the flow speed, as measured by the Mach number, and turbulence, as
measured by the Reynolds number, can be independently controlled by separately
varying the characteristic temperature gradient from internal heating and the
diffusivities. 2D simulations at a fixed Mach number (flow speed) demonstrate
consistent power at low wavenumber as diffusivities are decreased. We observe
convection where the velocity distribution is skewed towards cold, fast
downflows, and that the flow speed is related to the length scale and entropy
gradient of the upper boundary where the downflows are driven. We additionally
find a heat transport scaling law which is consistent with prior incompressible
work.Comment: 22 pages, 12 figures, submitted to Phys. Rev. Fluid
Rotation reduces convective mixing in Jupiter and other gas giants
Recent measurements of Jupiter's gravitational moments by the Juno spacecraft
and seismology of Saturn's rings suggest that the primordial composition
gradients in the deep interior of these planets have persisted since their
formation. One possible explanation is the presence of a double-diffusive
staircase below the planet's outer convection zone, which inhibits mixing
across the deeper layers. However, hydrodynamic simulations have shown that
these staircases are not long-lasting and can be disrupted by overshooting
convection. In this paper we suggests that planetary rotation could be another
factor for the longevity of primordial composition gradients. Using rotational
mixing-length theory and 3D hydrodynamic simulations, we demonstrate that
rotation significantly reduces both the convective velocity and the mixing of
primordial composition gradients. In particular, for Jovian conditions at
after formation, rotation reduces the convective
velocity by a factor of 6, and in turn, the kinetic energy flux available for
mixing gets reduced by a factor of . This leads to an entrainment
timescale that is more than two orders of magnitude longer than without
rotation. We encourage future hydrodynamic models of Jupiter and other gas
giants to include rapid rotation, because the decrease in the mixing efficiency
could explain why Jupiter and Saturn are not fully mixed.Comment: Accepted for publication in the Astrophysical Journal Letter
Observed Extra Mixing Trends in Red Giants are Reproduced by the Reduced Density Ratio in Thermohaline Zones
Observations show an almost ubiquitous presence of extra mixing in low-mass
upper giant branch stars. The most commonly invoked explanation for this is the
thermohaline instability. One dimensional stellar evolution models include
prescriptions for thermohaline mixing, but our ability to make direct
comparisons between models and observations has thus far been limited. Here, we
propose a new framework to facilitate direct comparison: Using carbon to
nitrogen measurements from the SDSS-IV APOGEE survey as a probe of mixing and a
fluid parameter known as the reduced density ratio from one dimensional stellar
evolution programs, we compare the observed amount of extra mixing on the upper
giant branch to predicted trends from three-dimensional fluid dynamics
simulations. By applying this method, we are able to place empirical
constraints on the efficiency of mixing across a range of masses and
metallicities. We find that the observed amount of extra mixing is strongly
correlated with the reduced density ratio and that trends between reduced
density ratio and fundamental stellar parameters are robust across choices for
modeling prescription. We show that stars with available mixing data tend to
have relatively low density ratios, which should inform the regimes selected
for future simulation efforts. Finally, we show that there is increased mixing
at low values of the reduced density ratio, which is consistent with current
hydrodynamical models of the thermohaline instability. The introduction of this
framework sets a new standard for theoretical modeling efforts, as validation
for not only the amount of extra mixing, but trends between the degree of extra
mixing and fundamental stellar parameters is now possible.Comment: 19 pages, 7 figures, submitted to Ap
Stellar Convective Penetration: Parameterized Theory and Dynamical Simulations
Most stars host convection zones in which heat is transported directly by fluid motion, but the behavior of convective boundaries is not well-understood. Here, we present 3D numerical simulations that 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" , which compares how far the radiative gradient deviates from the adiabatic gradient on either side of the Schwarzschild convective boundary. Following Roxburgh and Zahn, we construct an energy-based theoretical model in which controls the extent of penetration. We test this theory using 3D numerical simulations that employ a simplified Boussinesq model of stellar convection. The convection is driven by internal heating, and we use a height-dependent radiative conductivity. This allows us to separately specify and the stiffness of the radiative–convective boundary. 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 stars, we expect , 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 that employs our parameterization of convective penetration as a proof of concept. Finally, we discuss prospects for extending these results to more realistic stellar contexts.
</p
- …