10,492 research outputs found
A Heuristic Framework for Next-Generation Models of Geostrophic Convective Turbulence
Many geophysical and astrophysical phenomena are driven by turbulent fluid
dynamics, containing behaviors separated by tens of orders of magnitude in
scale. While direct simulations have made large strides toward understanding
geophysical systems, such models still inhabit modest ranges of the governing
parameters that are difficult to extrapolate to planetary settings. The
canonical problem of rotating Rayleigh-B\'enard convection provides an
alternate approach - isolating the fundamental physics in a reduced setting.
Theoretical studies and asymptotically-reduced simulations in rotating
convection have unveiled a variety of flow behaviors likely relevant to natural
systems, but still inaccessible to direct simulation. In lieu of this, several
new large-scale rotating convection devices have been designed to characterize
such behaviors. It is essential to predict how this potential influx of new
data will mesh with existing results. Surprisingly, a coherent framework of
predictions for extreme rotating convection has not yet been elucidated. In
this study, we combine asymptotic predictions, laboratory and numerical
results, and experimental constraints to build a heuristic framework for
cross-comparison between a broad range of rotating convection studies. We
categorize the diverse field of existing predictions in the context of
asymptotic flow regimes. We then consider the physical constraints that
determine the points of intersection between flow behavior predictions and
experimental accessibility. Applying this framework to several upcoming devices
demonstrates that laboratory studies may soon be able to characterize
geophysically-relevant flow regimes. These new data may transform our
understanding of geophysical and astrophysical turbulence, and the conceptual
framework developed herein should provide the theoretical infrastructure needed
for meaningful discussion of these results.Comment: 36 pages, 8 figures. CHANGES: in revision at Geophysical and
Astrophysical Fluid Dynamic
New subgrid-scale models for large-eddy simulation of Rayleigh-BĂ©nard convection
Published under licence in Journal of Physics: Conference Series by IOP Publishing Ltd.
Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.At the crossroad between flow topology analysis and the theory of turbulence, a new eddy-viscosity model for Large-eddy simulation has been recently proposed by Trias et al.[PoF, 27, 065103 (2015)]. The S3PQR-model has the proper cubic near-wall behaviour and no intrinsic limitations for statistically inhomogeneous flows. In this work, the new model has been tested for an air turbulent Rayleigh-Benard convection in a rectangular cell of aspect ratio unity and n span-wise open-ended distance. To do so, direct numerical simulation has been carried out at two Rayleigh numbers Ra = 108 and 1010, to assess the model performance and investigate a priori the effect of the turbulent Prandtl number. Using an approximate formula based on the Taylor series expansion, the turbulent Prandtl number has been calculated and revealed a constant and Ra-independent value across the bulk region equals to 0.55. It is found that the turbulent components of eddy-viscosity and eddy-diffusivity are positively prevalent to maintain a turbulent wind essentially driven by the mean buoyant force at the sidewalls. On the other hand, the new eddy-viscosity model is preliminary tested for the case of Ra = 108 and showed overestimation of heat flux within the boundary layer but fairly good prediction of turbulent kinetics at this moderate turbulent flow.Peer ReviewedPostprint (published version
Passive scalars in turbulent channel flow at high Reynolds number
We study passive scalars in turbulent plane channels at computationally high Reynolds number, thus allowing us to observe previously unnoticed effects. The mean scalar profiles are found to obey a generalized logarithmic law which includes a linear correction term in the whole lower half-channel, and they follow a universal parabolic defect profile in the core region. This is consistent with recent findings regarding the mean velocity profiles in channel flow. The scalar variances also exhibit a near universal parabolic distribution in the core flow and hints of a sizeable log layer, unlike the velocity variances. The energy spectra highlight the formation of large scalar-bearing eddies with size proportional to the channel height which are caused by a local production excess over dissipation, and which are clearly visible in the flow visualizations. Close correspondence of the momentum and scalar eddies is observed, with the main difference being that the latter tend to form sharper gradients, which translates into higher scalar dissipation. Another notable Reynolds number effect is the decreased correlation of the passive scalar field with the vertical velocity field, which is traced to the reduced effectiveness of ejection event
Toroidal and poloidal energy in rotating Rayleigh-B\'enard convection
We consider rotating Rayleigh-B\'enard convection of a fluid with a Prandtl
number of in a cylindrical cell with an aspect ratio .
Direct numerical simulations were performed for the Rayleigh number range and the inverse Rossby number range .
We propose a method to capture regime transitions based on the decomposition of
the velocity field into toroidal and poloidal parts. We identify four different
regimes. First, a buoyancy dominated regime occurring as long as the toroidal
energy is not affected by rotation and remains equal to that in the
non-rotating case, . Second, a rotation influenced regime, starting
at rotation rates where and ending at a critical inverse
Rossby number that is determined by the balance of the toroidal and
poloidal energy, . Third, a rotation dominated regime, where
the toroidal energy is larger than both, and .
Fourth, a geostrophic turbulence regime for high rotation rates where the
toroidal energy drops below the value of non-rotating convection
Mean Temperature Profiles in Turbulent Thermal Convection
To predict the mean temperature profiles in turbulent thermal convection, the
thermal boundary layer (BL) equation including the effects of fluctuations has
to be solved. In Shishkina et al., Phys. Rev. Lett. 114 (2015), the thermal BL
equation with the fluctuations taken into account as an eddy thermal
diffusivity has been solved for large Prandtl-number fluids for which the eddy
thermal diffusivity and the velocity field can be approximated respectively as
a cubic and a linear function of the distance from the plate. In the present
work we make use of the idea of Prandtl's mixing length model and relate the
eddy thermal diffusivity to the stream function. With this proposed relation,
we can solve the thermal BL equation and obtain a closed-form expression for
the dimensionless mean temperature profile in terms of two independent
parameters for fluids with a general Prandtl number. With a proper choice of
the parameters, our predictions of the temperature profiles are in excellent
agreement with the results of our direct numerical simulations for a wide range
of Prandtl numbers from 0.01 to 2547.9 and Rayleigh numbers from 10^7 to 10^9.Comment: 8 pages, 4 figure
Axially-homogeneous Rayleigh-Benard convection in a cylindrical cell
Previous numerical studies have shown that the "ultimate regime of thermal
convection" can be attained in a Rayleigh-Benard cell when the kinetic and
thermal boundary layers are eliminated by replacing the walls with periodic
boundary conditions (homogeneous Rayleigh-Benard convection). Then, the heat
transfer scales like Nu ~ Ra^{1/2} and turbulence intensity as Re ~ Ra^{1/2},
where the Rayleigh number Ra indicates the strength of the driving force.
However, experiments never operate in unbounded domains and it is important to
understand how confinement might alter the approach to this ultimate regime.
Here we consider homogeneous Rayleigh-Benard convection in a laterally confined
geometry - a small aspect-ratio vertical cylindrical cell - and show evidence
of the ultimate regime as Ra is increased: In spite of the confinement and the
resulting kinetic boundary layers, we still find Nu ~ Re ~ Ra^{1/2}. The system
supports exact solutions composed of modes of exponentially growing vertical
velocity and temperature fields, with Ra as the critical parameter determining
the properties of these modes. Counterintuitively, in the low Ra regime, or for
very narrow cylinders, the numerical simulations are susceptible to these
solutions which can dominate the dynamics and lead to very high and unsteady
heat transfer. As Ra is increased, interaction between modes stabilizes the
system, evidenced by the increasing homogeneity and reduced fluctuations in the
r.m.s. velocity and temperature fields. We also test that physical results
become independent of the periodicity length of the cylinder, a purely
numerical parameter, as the aspect ratio is increased
Supersonic flow calculation using a Reynolds-stress and an eddy thermal diffusivity turbulence model
A second-order model for the velocity field and a two-equation model for the temperature field are used to calculate supersonic boundary layers assuming negligible real gas effects. The modeled equations are formulated on the basis of an incompressible assumption and then extended to supersonic flows by invoking Morkovin's hypothesis, which proposes that compressibility effects are completely accounted for by mean density variations alone. In order to calculate the near-wall flow accurately, correction functions are proposed to render the modeled equations asymptotically consistent with the behavior of the exact equations near a wall and, at the same time, display the proper dependence on the molecular Prandtl number. Thus formulated, the near-wall second order turbulence model for heat transfer is applicable to supersonic flows with different Prandtl numbers. The model is validated against flows with different Prandtl numbers and supersonic flows with free-stream Mach numbers as high as 10 and wall temperature ratios as low as 0.3. Among the flow cases considered, the momentum thickness Reynolds number varies from approximately 4,000 to approximately 21,000. Good correlation with measurements of mean velocity, temperature, and its variance is obtained. Discernible improvements in the law-of-the-wall are observed, especially in the range where the big-law applies
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