438 research outputs found
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 sensitivity of rapidly rotating Rayleigh--B\'enard convection to Ekman pumping
The dependence of the heat transfer, as measured by the nondimensional
Nusselt number , on Ekman pumping for rapidly rotating Rayleigh-B\'enard
convection in an infinite plane layer is examined for fluids with Prandtl
number . A joint effort utilizing simulations from the Composite
Non-hydrostatic Quasi-Geostrophic model (CNH-QGM) and direct numerical
simulations (DNS) of the incompressible fluid equations has mapped a wide range
of the Rayleigh number - Ekman number parameter space within the
geostrophic regime of rotating convection. Corroboration of the -
relation at from both methods along with higher covered by
DNS and lower by the asymptotic model allows for this range of the heat
transfer results. For stress-free boundaries, the relation has the dissipation-free scaling of for all
. This is directly related to a geostrophic turbulent interior
that throttles the heat transport supplied to the thermal boundary layers. For
no-slip boundaries, the existence of ageostrophic viscous boundary layers and
their associated Ekman pumping yields a more complex 2D surface in
parameter space. For results suggest that the surface can be
expressed as indicating the
dissipation-free scaling law is enhanced by Ekman pumping by the multiplicative
prefactor where . It follows for
that the geostrophic turbulent interior remains the flux bottleneck
in rapidly rotating Rayleigh-B\'enard convection. For , where DNS
and asymptotic simulations agree quantitatively, it is found that the effects
of Ekman pumping are sufficiently strong to influence the heat transport with
diminished exponent and .Comment: 9 pages, 14 figure
The effects of Ekman pumping on quasi-geostrophic Rayleigh-Benard convection
Numerical simulations of 3D, rapidly rotating Rayleigh-Benard convection are
performed using an asymptotic quasi-geostrophic model that incorporates the
effects of no-slip boundaries through (i) parameterized Ekman pumping boundary
conditions, and (ii) a thermal wind boundary layer that regularizes the
enhanced thermal fluctuations induced by pumping. The fidelity of the model,
obtained by an asymptotic reduction of the Navier-Stokes equations that
implicitly enforces a pointwise geostrophic balance, is explored for the first
time by comparisons of simulations against the findings of direct numerical
simulations and laboratory experiments. Results from these methods have
established Ekman pumping as the mechanism responsible for significantly
enhancing the vertical heat transport. This asymptotic model demonstrates
excellent agreement over a range of thermal forcing for Pr ~1 when compared
with results from experiments and DNS at maximal values of their attainable
rotation rates, as measured by the Ekman number (E ~ 10^{-7}); good qualitative
agreement is achieved for Pr > 1. Similar to studies with stress-free
boundaries, four spatially distinct flow morphologies exists. Despite the
presence of frictional drag at the upper and/or lower boundaries, a strong
non-local inverse cascade of barotropic (i.e., depth-independent) kinetic
energy persists in the final regime of geostrophic turbulence and is dominant
at large scales. For mixed no-slip/stress-free and no-slip/no-slip boundaries,
Ekman friction is found to attenuate the efficiency of the upscale energy
transport and, unlike the case of stress-free boundaries, rapidly saturates the
barotropic kinetic energy. For no-slip/no-slip boundaries, Ekman friction is
strong enough to prevent the development of a coherent dipole vortex
condensate. Instead vortex pairs are found to be intermittent, varying in both
time and strength.Comment: 20 pages, 10 figure
Numerically determined transport laws for fingering ("thermohaline") convection in astrophysics
We present the first three-dimensional simulations of fingering convection
performed in a parameter regime close to the one relevant for astrophysics, and
reveal the existence of simple asymptotic scaling laws for turbulent heat and
compositional transport. These laws can straightforwardly be extrapolated to
the true astrophysical regime. Our investigation also indicates that
thermocompositional "staircases," a key consequence of fingering convection in
the ocean, cannot form spontaneously in the fingering regime in stellar
interiors. Our proposed empirically-determined transport laws thus provide
simple prescriptions for mixing by fingering convection in a variety of
astrophysical situations, and should, from here on, be used preferentially over
older and less accurate parameterizations. They also establish that fingering
convection does not provide sufficient extra mixing to explain observed
chemical abundances in RGB stars.Comment: Submitted to ApJ Letters on October 29th. 15 pages, 4 figures. See
Garaud 2010 for companion pape
Gameplay experience in a gaze interaction game
Assessing gameplay experience for gaze interaction games is a challenging
task. For this study, a gaze interaction Half-Life 2 game modification was
created that allowed eye tracking control. The mod was deployed during an
experiment at Dreamhack 2007, where participants had to play with gaze
navigation and afterwards rate their gameplay experience. The results show low
tension and negative affects scores on the gameplay experience questionnaire as
well as high positive challenge, immersion and flow ratings. The correlation
between spatial presence and immersion for gaze interaction was high and yields
further investigation. It is concluded that gameplay experience can be
correctly assessed with the methodology presented in this paper.Comment: pages 49-54, The 5th Conference on Communication by Gaze Interaction
- COGAIN 2009: Gaze Interaction For Those Who Want It Most, ISBN:
978-87-643-0475-
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
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