72 research outputs found
Double-Diffusive Convection
Much progress has recently been made in understanding and quantifying
vertical mixing induced by double-diffusive instabilities such as fingering
convection (usually called thermohaline convection) and oscillatory
double-diffusive convection (a process closely related to semiconvection). This
was prompted in parts by advances in supercomputing, which allow us to run
Direct Numerical Simulations of these processes at parameter values approaching
those relevant in stellar interiors, and in parts by recent theoretical
developments in oceanography where such instabilities also occur. In this paper
I summarize these recent findings, and propose new mixing parametrizations for
both processes that can easily be implemented in stellar evolution codes.Comment: To be published in the proceedings of the conference "New Advances in
Stellar Physics: from microscopic to macroscopic processes", Roscoff, 27-31st
May 201
Turbulent transport by diffusive stratified shear flows: from local to global models. III. A closure model
Being able to account for the missing mixing in stellar radiative zones is a
key step toward a better understanding of stellar evolution. Zahn (1974) argued
that thermally diffusive shear-induced turbulence might be responsible for some
of this mixing. In Part I and Part II of this series of papers we showed that
Zahn's (1974, 1992) mixing model applies when the properties of the turbulence
are local. But we also discovered limitations of the model when this locality
condition fails, in particular near the edge of a turbulent region. In this
paper, we propose a second-order closure model for the transport of momentum
and chemical species by shear-induced turbulence in strongly stratified,
thermally diffusive environments (the so-called low P\'eclet number limit),
which builds upon the work of Garaud \& Ogilvie (2005). Comparison against
direct numerical simulations (DNSs) shows that the model is able to predict the
vertical profiles of the mean flow and of the stress tensor (including the
momentum transport) in diffusive shear flows, often with a reasonably good
precision, and at least within a factor of order unity in the worst case
scenario. The model is sufficiently simple to be implemented in stellar
evolution codes, and all the model constants have been calibrated against DNSs.
While significant limitations to its use remain (e.g. it can only be used in
the low P\'eclet number, slowly rotating limit), we argue that it is more
reliable than most of the astrophysical prescriptions that are used in stellar
evolution models today
2D or not 2D: the effect of dimensionality on the dynamics of fingering convection at low Prandtl number
Fingering convection (otherwise known as thermohaline convection) is an
instability that occurs in stellar radiative interiors in the presence of
unstable compositional gradients. Numerical simulations have been used in order
to estimate the efficiency of mixing induced by this instability. However,
fully three-dimensional (3D) computations in the parameter regime appropriate
for stellar astrophysics (i.e. low Prandtl number) are prohibitively expensive.
This raises the question of whether two-dimensional (2D) simulations could be
used instead to achieve the same goals. In this work, we address this issue by
comparing the outcome of 2D and 3D simulations of fingering convection at low
Prandtl number. We find that 2D simulations are never appropriate. However, we
also find that the required 3D computational domain does not have to be very
wide: the third dimension need only contain a minimum of two wavelengths of the
fastest-growing linearly unstable mode to capture the essentially 3D dynamics
of small-scale fingering. Narrow domains, however, should still be used with
caution since they could limit the subsequent development of any large-scale
dynamics typically associated with fingering convection.Comment: Submitted to Ap
Turbulent transport in a strongly stratified forced shear layer with thermal diffusion
This work presents numerical results on the transport of heat and chemical
species by shear-induced turbulence in strongly stratified but thermally
diffusive environments. The shear instabilities driven in this regime are
sometimes called "secular" shear instabilities, and can take place even when
the gradient Richardson number of the flow (the square of the ratio of the
buoyancy frequency to the shearing rate) is large, provided the P\'eclet number
(the ratio of the thermal diffusion timescale to the turnover timescale of the
turbulent eddies) is small. We have identified a set of simple criteria to
determine whether these instabilities can take place or not. Generally
speaking, we find that they may be relevant whenever the thermal diffusivity of
the fluid is very large (typically larger than cm/s), which is the
case in the outer layers of high-mass stars () for instance.
Using a simple model setup in which the shear is forced by a spatially
sinusoidal, constant-amplitude body-force, we have identified several regimes
ranging from effectively unstratified to very strongly stratified, each with
its own set of dynamical properties. Unless the system is in one of the two
extreme regimes (effectively unstratified or completely stable), however, we
find that (1) only about 10% of the input power is used towards heat transport,
while the remaining 90% is viscously dissipated; (2) that the effective
compositional mixing coefficient is well-approximated by the model of Zahn
(1992), with where is the thermal
diffusivity and is the gradient Richardson number. These results need to be
confirmed, however, with simulations in different model setups and at higher
effective Reynolds number.Comment: Submitted to Ap
Weakly non-Boussinesq convection in a gaseous spherical shell
We examine the dynamics associated with weakly compressible convection in a
spherical shell by running 3D direct numerical simulations using the Boussinesq
formalism [1]. Motivated by problems in astrophysics, we assume the existence
of a finite adiabatic temperature gradient and use mixed
boundary conditions for the temperature with fixed flux at the inner boundary
and fixed temperature at the outer boundary. This setup is intrinsically more
asymmetric than the more standard case of Rayleigh-B\'{e}nard convection in
liquids between parallel plates with fixed temperature boundary conditions.
Conditions where there is substantial asymmetry can cause a dramatic change in
the nature of convection and we demonstrate that this is the case here. The
flows can become pressure- rather than buoyancy- dominated leading to anomalous
heat transport by upflows. Counter-intuitively, the background temperature
gradient can develop a subadiabatic layer (where
, where
is gravity) although convection remains vigorous at every
point across the shell. This indicates a high degree of non-locality.Comment: 19 figure
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