239,013 research outputs found
On stratified regions
Type and effect systems are a tool to analyse statically the behaviour of
programs with effects. We present a proof based on the so called reducibility
candidates that a suitable stratification of the type and effect system entails
the termination of the typable programs. The proof technique covers a simply
typed, multi-threaded, call-by-value lambda-calculus, equipped with a variety
of scheduling (preemptive, cooperative) and interaction mechanisms (references,
channels, signals)
Penetrative Convection in Partly Stratified Rapidly Rotating Spherical Shells
Celestial objects host interfaces between convective and stable stratified
interior regions. The interaction between both, e.g., the transfer of heat,
mass, or angular momentum depends on whether and how flows penetrate into the
stable layer. Powered from the unstable, convective regions, radial flows can
pierce into the stable region depending on their inertia (overshooting). In
rapidly rotating systems, the dynamics are strongly influenced by the Coriolis
force and radial flows penetrate in stratified regions due to the geostrophic
invariance of columnar convection even in the limit of vanishing inertia.
Within this study, we numerically investigate both mechanisms and hence explore
the nature of penetrative convection in rapidly rotating spherical shells. The
study covers a broad range of system parameters, such as the strength of the
stratification relative to the Coriolis force or the inertia. Guided by the
application to Saturn, we model a sandwiched stable stratified layer (SSL)
surrounded by two convective zones. A comprehensive analysis of the damping
behavior of convective flows at the edges of the SSL showed that the mean
penetration depth is controlled by the ratio of stratified and unstratified
buoyancy gradients and is hence independent of rotation. A scaling law is
derived and suggests that the penetration depth decreases with the square root
of the ratio of unstabilizing and stabilizing entropy gradients. The influence
of the Coriolis force, however, is evident by a modulation of the penetration
depth along latitude, since convective columns are elongated vertically and
hence pierce predominantly into the SSL around mid-latitudes and outside the
tangent cylinder. Our result also show that the penetration depth decreases
linearly with the flow length scale (low pass filter), confirming predictions
from the linear theory of rotating partially stratified convection
Energy Conservation and Gravity Waves in Sound-proof Treatments of Stellar Interiors: Part I Anelastic Approximations
Typical flows in stellar interiors are much slower than the speed of sound.
To follow the slow evolution of subsonic motions, various sound-proof equations
are in wide use, particularly in stellar astrophysical fluid dynamics. These
low-Mach number equations include the anelastic equations. Generally, these
equations are valid in nearly adiabatically stratified regions like stellar
convection zones, but may not be valid in the sub-adiabatic, stably stratified
stellar radiative interiors. Understanding the coupling between the convection
zone and the radiative interior is a problem of crucial interest and may have
strong implications for solar and stellar dynamo theories as the interface
between the two, called the tachocline in the Sun, plays a crucial role in many
solar dynamo theories. Here we study the properties of gravity waves in
stably-stratified atmospheres. In particular, we explore how gravity waves are
handled in various sound-proof equations. We find that some anelastic
treatments fail to conserve energy in stably-stratified atmospheres, instead
conserving pseudo-energies that depend on the stratification, and we
demonstrate this numerically. One anelastic equation set does conserve energy
in all atmospheres and we provide recommendations for converting low-Mach
number anelastic codes to this set of equations.Comment: Accepted for publication in ApJ. 20 pages emulateapj format, 7
figure
Large-scale magnetic flux concentrations from turbulent stresses
In this study we provide the first numerical demonstration of the effects of
turbulence on the mean Lorentz force and the resulting formation of large-scale
magnetic structures. Using three-dimensional direct numerical simulations (DNS)
of forced turbulence we show that an imposed mean magnetic field leads to a
decrease of the turbulent hydromagnetic pressure and tension. This phenomenon
is quantified by determining the relevant functions that relate the sum of the
turbulent Reynolds and Maxwell stresses with the Maxwell stress of the mean
magnetic field. Using such a parameterization, we show by means of
two-dimensional and three-dimensional mean-field numerical modelling that an
isentropic density stratified layer becomes unstable in the presence of a
uniform imposed magnetic field. This large-scale instability results in the
formation of loop-like magnetic structures which are concentrated at the top of
the stratified layer. In three dimensions these structures resemble the
appearance of bipolar magnetic regions in the Sun. The results of DNS and
mean-field numerical modelling are in good agreement with theoretical
predictions. We discuss our model in the context of a distributed solar dynamo
where active regions and sunspots might be rather shallow phenomena.Comment: 9 pages, 10 figures, Astron. Nachr. (submitted
Energy and water vapor transport across a simplified cloud-clear air interface
We consider a simplified physics of the could interface where condensation,
evaporation and radiation are neglected and momentum, thermal energy and water
vapor transport is represented in terms of the Boussinesq model coupled to a
passive scalar transport equation for the vapor. The interface is modeled as a
layer separating two isotropic turbulent regions with different kinetic energy
and vapor concentration. In particular, we focus on the small scale part of the
inertial range as well as on the dissipative range of scales which are
important to the micro-physics of warm clouds. We have numerically investigated
stably stratified interfaces by locally perturbing at an initial instant the
standard temperature lapse rate at the cloud interface and then observing the
temporal evolution of the system. When the buoyancy term becomes of the same
order of the inertial one, we observe a spatial redistribution of the kinetic
energy which produce a concomitant pit of kinetic energy within the mixing
layer. In this situation, the mixing layer contains two interfacial regions
with opposite kinetic energy gradient, which in turn produces two intermittent
sublayers in the velocity fluctuations field. This changes the structure of the
field with respect to the corresponding non-stratified shearless mixing: the
communication between the two turbulent region is weak, and the growth of the
mixing layer stops. These results are discussed with respect to experimental
results with and without stratification.Comment: 12 pages, 8 figure
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