148 research outputs found
Mesogranulation and small-scale dynamo action in the quiet Sun
Regions of quiet Sun generally exhibit a complex distribution of small-scale
magnetic field structures, which interact with the near-surface turbulent
convective motions. Furthermore, it is probable that some of these magnetic
fields are generated locally by a convective dynamo mechanism. In addition to
the well-known granular and supergranular convective scales, various
observations have indicated that there is an intermediate scale of convection,
known as mesogranulation, with vertical magnetic flux concentrations
accumulating preferentially at mesogranular boundaries. Our aim is to
investigate the small-scale dynamo properties of a convective flow that
exhibits both granulation and mesogranulation, comparing our findings with
solar observations. Adopting an idealised model for a localised region of quiet
Sun, we use numerical simulations of compressible magnetohydrodynamics, in a 3D
Cartesian domain, to investigate the parametric dependence of this system
(focusing particularly upon the effects of varying the aspect ratio and the
Reynolds number). In purely hydrodynamic convection, we find that
mesogranulation is a robust feature of this system provided that the domain is
wide enough to accommodate these large-scale motions. The mesogranular peak in
the kinetic energy spectrum is more pronounced in the higher Reynolds number
simulations. We investigate the dynamo properties of this system in both the
kinematic and the nonlinear regimes and we find that the dynamo is always more
efficient in larger domains, when mesogranulation is present. Furthermore, we
use a filtering technique in Fourier space to demonstrate that it is indeed the
larger scales of motion that are primarily responsible for driving the dynamo.
In the nonlinear regime, the magnetic field distribution compares very
favourably to observations, both in terms of the spatial distribution and the
measured field strengths.Comment: 12 pages, 11 figures, accepted for publication in Astronomy &
Astrophysic
Rayleigh-B\'enard convection with a melting boundary
We study the evolution of a melting front between the solid and liquid phases
of a pure incompressible material where fluid motions are driven by unstable
temperature gradients. In a plane layer geometry, this can be seen as classical
Rayleigh-B\'enard convection where the upper solid boundary is allowed to melt
due to the heat flux brought by the fluid underneath. This free-boundary
problem is studied numerically in two dimensions using a phase-field approach,
classically used to study the melting and solidification of alloys, which we
dynamically couple with the Navier-Stokes equations in the Boussinesq
approximation. The advantage of this approach is that it requires only moderate
modifications of classical numerical methods. We focus on the case where the
solid is initially nearly isothermal, so that the evolution of the topography
is related to the inhomogeneous heat flux from thermal convection, and does not
depend on the conduction problem in the solid. From a very thin stable layer of
fluid, convection cells appears as the depth -- and therefore the effective
Rayleigh number of the layer increases. The continuous melting of the solid
leads to dynamical transitions between different convection cell sizes and
topography amplitudes. The Nusselt number can be larger than its value for a
planar upper boundary, due to the feedback of the topography on the flow, which
can stabilize large-scale laminar convection cells.Comment: 36 pages, 16 figure
Parametric instability and wave turbulence driven by tidal excitation of internal waves
We investigate the stability of stratified fluid layers undergoing
homogeneous and periodic tidal deformation. We first introduce a local model
which allows to study velocity and buoyancy fluctuations in a Lagrangian domain
periodically stretched and sheared by the tidal base flow. While keeping the
key physical ingredients only, such a model is efficient to simulate planetary
regimes where tidal amplitudes and dissipation are small. With this model, we
prove that tidal flows are able to drive parametric subharmonic resonances of
internal waves, in a way reminiscent of the elliptical instability in rotating
fluids. The growth rates computed via Direct Numerical Simulations (DNS) are in
very good agreement with WKB analysis and Floquet theory. We also investigate
the turbulence driven by this instability mechanism. With spatio-temporal
analysis, we show that it is a weak internal wave turbulence occurring at small
Froude and buoyancy Reynolds numbers. When the gap between the excitation and
the Brunt-V\"ais\"al\"a frequencies is increased, the frequency spectrum of
this wave turbulence displays a -2 power law reminiscent of the high-frequency
branch of the Garett and Munk spectrum (Garrett & Munk 1979) which has been
measured in the oceans. In addition, we find that the mixing efficiency is
altered compared to what is computed in the context of DNS of stratified
turbulence excited at small Froude and large buoyancy Reynolds numbers and is
consistent with a superposition of waves.Comment: Accepted for publication in Journal of Fluid Mechanics, 27 pages, 21
figure
On the effect of rotation on magnetohydrodynamic turbulence at high magnetic Reynolds number
This article is focused on the dynamics of a rotating electrically conducting
fluid in a turbulent state. As inside the Earth's core or in various industrial
processes, a flow is altered by the presence of both background rotation and a
large scale magnetic field. In this context, we present a set of 3D direct
numerical simulations of incompressible decaying turbulence. We focus on
parameters similar to the ones encountered in geophysical and astrophysical
flows, so that the Rossby number is small, the interaction parameter is large,
but the Elsasser number, defining the ratio between Coriolis and Lorentz
forces, is about unity. These simulations allow to quantify the effect of
rotation and thus inertial waves on the growth of magnetic fluctuations due to
Alfv\'en waves. Rotation prevents the occurrence of equipartition between
kinetic and magnetic energies, with a reduction of magnetic energy at
decreasing Elsasser number {\Lambda}. It also causes a decrease of energy
transfer mediated by cubic correlations. In terms of flow structure, a decrease
of {\Lambda} corresponds to an increase in the misalignment of velocity and
magnetic field.Comment: 18 pages, 12 figure
Order Out of Chaos: Slowly Reversing Mean Flows Emerge from Turbulently Generated Internal Waves
We demonstrate via direct numerical simulations that a periodic, oscillating
mean flow spontaneously develops from turbulently generated internal waves. We
consider a minimal physical model where the fluid self-organizes in a
convective layer adjacent to a stably stratified one. Internal waves are
excited by turbulent convective motions, then nonlinearly interact to produce a
mean flow reversing on timescales much longer than the waves' period. Our
results demonstrate for the first time that the three-scale dynamics due to
convection, waves, and mean flow is generic and hence can occur in many
astrophysical and geophysical fluids. We discuss efforts to reproduce the mean
flow in reduced models, where the turbulence is bypassed. We demonstrate that
wave intermittency, resulting from the chaotic nature of convection, plays a
key role in the mean-flow dynamics, which thus cannot be captured using only
second-order statistics of the turbulent motions
The linear instability of the stratified plane Couette flow
We present the stability analysis of a plane Couette flow which is stably
stratified in the vertical direction orthogonally to the horizontal shear.
Interest in such a flow comes from geophysical and astrophysical applications
where background shear and vertical stable stratification commonly coexist. We
perform the linear stability analysis of the flow in a domain which is periodic
in the stream-wise and vertical directions and confined in the cross-stream
direction. The stability diagram is constructed as a function of the Reynolds
number Re and the Froude number Fr, which compares the importance of shear and
stratification. We find that the flow becomes unstable when shear and
stratification are of the same order (i.e. Fr 1) and above a moderate
value of the Reynolds number Re700. The instability results from a
resonance mechanism already known in the context of channel flows, for instance
the unstratified plane Couette flow in the shallow water approximation. The
result is confirmed by fully non linear direct numerical simulations and to the
best of our knowledge, constitutes the first evidence of linear instability in
a vertically stratified plane Couette flow. We also report the study of a
laboratory flow generated by a transparent belt entrained by two vertical
cylinders and immersed in a tank filled with salty water linearly stratified in
density. We observe the emergence of a robust spatio-temporal pattern close to
the threshold values of F r and Re indicated by linear analysis, and explore
the accessible part of the stability diagram. With the support of numerical
simulations we conclude that the observed pattern is a signature of the same
instability predicted by the linear theory, although slightly modified due to
streamwise confinement
Subcritical turbulent condensate in rapidly rotating Rayleigh-B\'enard convection
The possibility of subcritical behaviour in the geostrophic turbulence regime
of rapidly rotating thermally driven convection is explored. In this regime a
non-local inverse energy transfer may compete with the more traditional and
local direct cascade. We show that, even for control parameters for which no
inverse cascade has previously been observed, a subcritical transition towards
a large-scale vortex state can occur when the system is initialized with a
vortex dipole of finite amplitude. This new example of bistability in a
turbulent flow, which may not be specific to rotating convection, opens up new
avenues for studying energy transfer in strongly anisotropic three-dimensional
flows.Comment: 12 pages, 6 figure
Suppression of wall modes in rapidly rotating Rayleigh-B\'enard convection by narrow horizontal fins
The heat transport by rapidly-rotating Rayleigh-B\'enard convection is of
fundamental importance to many geophysical flows. Laboratory measurements are
impeded by robust wall modes which develop along vertical walls, significantly
perturbing the heat flux. We show that narrow horizontal fins along the
vertical walls efficiently suppress wall modes ensuring that their contribution
to the global heat flux is negligible compared with bulk convection in the
geostrophic regime, thereby paving the way for new experimental studies of
geophysically relevant regimes of rotating convection.Comment: 6 pages, 6 figure
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