87 research outputs found
A model for Rayleigh-B\'enard magnetoconvection
A model for three-dimensional Rayleigh-B\'{e}nard convection in
low-Prandtl-number fluids near onset with rigid horizontal boundaries in the
presence of a uniform vertical magnetic field is constructed and analyzed in
detail. The kinetic energy , the convective entropy and the
convective heat flux () show scaling behaviour with near
onset of convection, where is the reduced Rayleigh number. The model is
also used to investigate various magneto-convective structures close to the
onset. Straight rolls, which appear at the primary instability, become unstable
with increase in and bifurcate to three-dimensional structures. The
straight rolls become periodically varying wavy rolls or quasiperiodically
varying structures in time with increase in depending on the values of
Prandtl number . They become irregular in time, with increase in . These
standing wave solutions bifurcate first to periodic and then quasiperiodic
traveling wave solutions, as is raised further. The variations of the
critical Rayleigh number and the frequency at the onset
of the secondary instability with are also studied for different values of
Chandrasekhar's number .Comment: 11 pages (To appear in EPJB
Anelastic Versus Fully Compressible Turbulent Rayleigh-B\'enard Convection
Numerical simulations of turbulent Rayleigh-B\'enard convection in an ideal
gas, using either the anelastic approximation or the fully compressible
equations, are compared. Theoretically, the anelastic approximation is expected
to hold in weakly superadiabatic systems with , where denotes the superadiabatic temperature drop over the
convective layer and the bottom temperature. Using direct numerical
simulations, a systematic comparison of anelastic and fully compressible
convection is carried out. With decreasing superadiabaticity , the
fully compressible results are found to converge linearly to the anelastic
solution with larger density contrasts generally improving the match. We
conclude that in many solar and planetary applications, where the
superadiabaticity is expected to be vanishingly small, results obtained with
the anelastic approximation are in fact more accurate than fully compressible
computations, which typically fail to reach small for numerical
reasons. On the other hand, if the astrophysical system studied contains
regions, such as the solar photosphere, fully compressible
simulations have the advantage of capturing the full physics. Interestingly,
even in weakly superadiabatic regions, like the bulk of the solar convection
zone, the errors introduced by using artificially large values for
for efficiency reasons remain moderate. If quantitative errors of the order of
are acceptable in such low regions, our work suggests that
fully compressible simulations can indeed be computationally more efficient
than their anelastic counterparts.Comment: 24 pages, 9 figure
The Sun's Supergranulation
Supergranulation is a fluid-dynamical phenomenon taking place in the solar
photosphere, primarily detected in the form of a vigorous cellular flow pattern
with a typical horizontal scale of approximately 30--35~megameters, a dynamical
evolution time of 24--48~h, a strong 300--400~m/s (rms) horizontal flow
component and a much weaker 20--30~m/s vertical component. Supergranulation was
discovered more than sixty years ago, however, explaining its physical origin
and most important observational characteristics has proven extremely
challenging ever since, as a result of the intrinsic multiscale, nonlinear
dynamical complexity of the problem concurring with strong observational and
computational limitations. Key progress on this problem is now taking place
with the advent of 21st-century supercomputing resources and the availability
of global observations of the dynamics of the solar surface with high spatial
and temporal resolutions. This article provides an exhaustive review of
observational, numerical and theoretical research on supergranulation, and
discusses the current status of our understanding of its origin and dynamics,
most importantly in terms of large-scale nonlinear thermal convection, in the
light of a selection of recent findings.Comment: Major update of 2010 Liv. Rev. Sol. Phys. review. Addresses many new
theoretical, numerical and observational developments. All sections,
including discussion, revised extensively. Also includes previously
unpublished results on nonlinear dynamics of convection in large domains, and
lagrangian transport at the solar surfac
Large-scale instabilities in a non-rotating turbulent convection
Formation of large-scale coherent structures in a turbulent convection via
excitation of large-scale instability is studied. The redistribution of the
turbulent heat flux due to non-uniform large-scale motions plays a crucial role
in the formation of the coherent large-scale structures in the turbulent
convection. The modification of the turbulent heat flux results in strong
reduction of the critical Rayleigh number (based on the eddy viscosity and
turbulent temperature diffusivity) required for the excitation of the
large-scale instability. The mean-field equations which describe the
large-scale instability, are solved numerically. We determine the key
parameters that affect formation of the large-scale coherent structures in the
turbulent convection. In particular, the degree of thermal anisotropy and the
lateral background heat flux strongly modify the growth rates of the
large-scale instability, the frequencies of the generated convective-shear
waves and change the thresholds required for the excitation of the large-scale
instability. This study elucidates the origins of the large-scale circulations
and rolls in the atmospheric convective boundary layers and the meso-granular
structures in the solar convection.Comment: 13 pages, 13 figures, Physics of Fluids, in pres
Zonal flow regimes in rotating anelastic spherical shells: an application to giant planets
The surface zonal winds observed in the giant planets form a complex jet
pattern with alternating prograde and retrograde direction. While the main
equatorial band is prograde on the gas giants, both ice giants have a
pronounced retrograde equatorial jet.
We use three-dimensional numerical models of compressible convection in
rotating spherical shells to explore the properties of zonal flows in different
regimes where either rotation or buoyancy dominates the force balance. We
conduct a systematic parameter study to quantify the dependence of zonal flows
on the background density stratification and the driving of convection.
We find that the direction of the equatorial zonal wind is controlled by the
ratio of buoyancy and Coriolis force. The prograde equatorial band maintained
by Reynolds stresses is found in the rotation-dominated regime. In cases where
buoyancy dominates Coriolis force, the angular momentum per unit mass is
homogenised and the equatorial band is retrograde, reminiscent to those
observed in the ice giants. In this regime, the amplitude of the zonal jets
depends on the background density contrast with strongly stratified models
producing stronger jets than comparable weakly stratified cases. Furthermore,
our results can help to explain the transition between solar-like and
"anti-solar" differential rotations found in anelastic models of stellar
convection zones.
In the strongly stratified cases, we find that the leading order force
balance can significantly vary with depth (rotation-dominated inside and
buoyancy-dominated in a thin surface layer). This so-called "transitional
regime" has a visible signature in the main equatorial jet which shows a
pronounced dimple where flow amplitudes notably decay towards the equator. A
similar dimple is observed on Jupiter, which suggests that convection in the
planet interior could possibly operate in this regime.Comment: 20 pages, 15 figures, 4 tables, accepted for publication in Icaru
Hysteresis phenomenon in turbulent convection
Coherent large-scale circulations of turbulent thermal convection in air have
been studied experimentally in a rectangular box heated from below and cooled
from above using Particle Image Velocimetry. The hysteresis phenomenon in
turbulent convection was found by varying the temperature difference between
the bottom and the top walls of the chamber (the Rayleigh number was changed
within the range of ). The hysteresis loop comprises the one-cell
and two-cells flow patterns while the aspect ratio is kept constant (). We found that the change of the sign of the degree of the anisotropy of
turbulence was accompanied by the change of the flow pattern. The developed
theory of coherent structures in turbulent convection (Elperin et al. 2002;
2005) is in agreement with the experimental observations. The observed coherent
structures are superimposed on a small-scale turbulent convection. The
redistribution of the turbulent heat flux plays a crucial role in the formation
of coherent large-scale circulations in turbulent convection.Comment: 10 pages, 9 figures, REVTEX4, Experiments in Fluids, 2006, in pres
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