2,503 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
Dynamics of fingering convection I: Small-scale fluxes and large-scale instabilities
Double-diffusive instabilities are often invoked to explain enhanced
transport in stably-stratified fluids. The most-studied natural manifestation
of this process, fingering convection, commonly occurs in the ocean's
thermocline and typically increases diapycnal mixing by two orders of magnitude
over molecular diffusion. Fingering convection is also often associated with
structures on much larger scales, such as thermohaline intrusions, gravity
waves and thermohaline staircases. In this paper, we present an exhaustive
study of the phenomenon from small to large scales. We perform the first
three-dimensional simulations of the process at realistic values of the heat
and salt diffusivities and provide accurate estimates of the induced turbulent
transport. Our results are consistent with oceanic field measurements of
diapycnal mixing in fingering regions. We then develop a generalized mean-field
theory to study the stability of fingering systems to large-scale
perturbations, using our calculated turbulent fluxes to parameterize
small-scale transport. The theory recovers the intrusive instability, the
collective instability, and the gamma-instability as limiting cases. We find
that the fastest-growing large-scale mode depends sensitively on the ratio of
the background gradients of temperature and salinity (the density ratio). While
only intrusive modes exist at high density ratios, the collective and
gamma-instabilities dominate the system at the low density ratios where
staircases are typically observed. We conclude by discussing our findings in
the context of staircase formation theory.Comment: 23 pages, 9 figures, submitted to JF
Double-diffusive convection in a rotating cylindrical annulus with conical caps
Double-diffusive convection driven by both thermal and compositional buoyancy
in a rotating cylindrical annulus with conical caps is considered with the aim
to establish whether a small fraction of compositional buoyancy added to the
thermal buoyancy (or vice versa) can significantly reduce the critical Rayleigh
number and amplify convection in planetary cores. It is shown that the neutral
surface describing the onset of convection in the double-buoyancy case is
essentially different from that of the well-studied purely thermal case, and
does indeed allow the possibility of low-Rayleigh number convection. In
particular, isolated islands of instability are formed by an additional
"double-diffusive" eigenmode in certain regions of the parameter space.
However, the amplitude of such low-Rayleigh number convection is relatively
weak. At similar flow amplitudes purely compositional and double-diffusive
cases are characterized by a stronger time dependence compared to purely
thermal cases, and by a prograde mean zonal flow near the inner cylindrical
surface. Implications of the results for planetary core convection are briefly
discussed.Comment: Accepted for publication in Physics of the Earth and Planetary
Interiors on 20 April 201
Double-diffusive erosion of the core of Jupiter
We present Direct Numerical Simulations of the transport of heat and heavy
elements across a double-diffusive interface or a double-diffusive staircase,
in conditions that are close to those one may expect to find near the boundary
between the heavy-element rich core and the hydrogen-helium envelope of giant
planets such as Jupiter. We find that the non-dimensional ratio of the buoyancy
flux associated with heavy element transport to the buoyancy flux associated
with heat transport lies roughly between 0.5 and 1, which is much larger than
previous estimates derived by analogy with geophysical double-diffusive
convection. Using these results in combination with a core-erosion model
proposed by Guillot et al. (2004), we find that the entire core of Jupiter
would be eroded within less than 1Myr assuming that the core-envelope boundary
is composed of a single interface. We also propose an alternative model that is
more appropriate in the presence of a well-established double-diffusive
staircase, and find that in this limit a large fraction of the core could be
preserved. These findings are interesting in the context of Juno's recent
results, but call for further modeling efforts to better understand the process
of core erosion from first principles.Comment: Accepted for publication in Ap
Direct Numerical Simulation of 3D Salt Fingers: From Secondary Instability to Chaotic Convection
The amplification and equilibration of three-dimensional salt fingers in
unbounded uniform vertical gradients of temperature and salinity is modeled
with a Direct Numerical Simulation in a triply periodic computational domain. A
fluid dynamics video of the simulation shows that the secondary instability of
the fastest growing square-planform finger mode is a combination of the
well-known vertical shear instability of two-dimensional fingers [Holyer, 1984]
and a new horizontal shear mode.Comment: APS DFD Gallery of Fluid Motion 200
Homoclinic snaking of localized states in doubly diffusive convection
Numerical continuation is used to investigate stationary spatially localized states in two-dimensional thermosolutal convection in a plane horizontal layer with no-slip boundary conditions at top and bottom. Convectons in the form of 1-pulse and 2-pulse states of both odd and even parity exhibit homoclinic snaking in a common Rayleigh number regime. In contrast to similar states in binary fluid convection, odd parity convectons do not pump concentration horizontally. Stable but time-dependent localized structures are present for Rayleigh numbers below the snaking region for stationary convectons. The computations are carried out for (inverse) Lewis number \tau = 1/15 and Prandtl numbers Pr = 1 and Pr >> 1
Dynamics of fingering convection II: The formation of thermohaline staircases
Regions of the ocean's thermocline unstable to salt fingering are often
observed to host thermohaline staircases, stacks of deep well-mixed convective
layers separated by thin stably-stratified interfaces. Decades after their
discovery, however, their origin remains controversial. In this paper we use 3D
direct numerical simulations to shed light on the problem. We study the
evolution of an analogous double-diffusive system, starting from an initial
statistically homogeneous fingering state and find that it spontaneously
transforms into a layered state. By analysing our results in the light of the
mean-field theory developed in Paper I, a clear picture of the sequence of
events resulting in the staircase formation emerges. A collective instability
of homogeneous fingering convection first excites a field of gravity waves,
with a well-defined vertical wavelength. However, the waves saturate early
through regular but localized breaking events, and are not directly responsible
for the formation of the staircase. Meanwhile, slower-growing, horizontally
invariant but vertically quasi-periodic gamma-modes are also excited and grow
according to the gamma-instability mechanism. Our results suggest that the
nonlinear interaction between these various mean-field modes of instability
leads to the selection of one particular gamma-mode as the staircase
progenitor. Upon reaching a critical amplitude, this progenitor overturns into
a fully-formed staircase. We conclude by extending the results of our
simulations to real oceanic parameter values, and find that the progenitor
gamma-mode is expected to grow on a timescale of a few hours, and leads to the
formation of a thermohaline staircase in about one day with an initial spacing
of the order of one to two metres.Comment: 18 pages, 9 figures, associated mpeg file at
http://earth.uni-muenster.de/~stellma/movie_small.mp4, submitted to JF
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