scholarly journals Condensates in thin-layer turbulence

2019 ◽  
Vol 864 ◽  
pp. 490-518 ◽  
Author(s):  
Adrian van Kan ◽  
Alexandros Alexakis
Keyword(s):  
Steady State ◽  
Layer Thickness ◽  
Turbulent Flows ◽  
Mean Field ◽  
Direct Numerical Simulations ◽  
Thin Layers ◽  
Scale Model ◽  
Two Dimensional ◽  
Critical Height ◽  
Basic Features

We examine the steady state of turbulent flows in thin layers using direct numerical simulations. It is shown that when the layer thickness is smaller than a critical height, an inverse cascade arises which leads to the formation of a steady state condensate where most of the energy is concentrated in the largest scale of the system. For layers of thickness smaller than a second critical height, the flow at steady state becomes exactly two-dimensional. The amplitude of the condensate is studied as a function of layer thickness and Reynolds number. Bi-stability and intermittent bursts are found close to the two critical points. The results are interpreted based on a mean-field three-scale model that reproduces some of the basic features of the numerical results.

Measurement of a Recirculating, Two-Dimensional, Turbulent Flow and Comparison to Turbulence Model Predictions. I: Steady State Case

1983 ◽  
Vol 105 (4) ◽  
pp. 439-446 ◽  
Author(s):  
D. R. Boyle ◽  
M. W. Golay
Keyword(s):  
Steady State ◽  
Turbulent Flow ◽  
Turbulence Model ◽  
Turbulence Models ◽  
Scale Model ◽  
Test Facility ◽  
Two Dimensional ◽  
Mean Velocity ◽  
Flow Area ◽  
Flow Measurements

Turbulent flow measurements have been performed in a two-dimensional flow cell which is a 1/15-scale model of the Fast Flux Test Facility nuclear reactor outlet plenum. In a steady water flow, maps of the mean velocity field, turbulence kinetic energy, and Reynolds stress have been obtained using a laser doppler anemometer. The measurements are compared to numerical simulations using both the K–ε and K–σ two-equation turbulence models. A relationship between K–σ and K–ε turbulence models is derived, and the two models are found to be nearly equivalent. The steady-state mean velocity data are predicted well through-out most of the test cell. Calculated spatial distributions of the scalar turbulence quantities are qualitatively similar for both models; however, the predicted distributions do not match the data over major portions of the flow area. The K–σ model provides better estimates of the turbulence quantity magnitudes. The predicted results are highly sensitive to small changes in the turbulence model constants and depend heavily on the levels of inlet turbulence. However, important differences between prediction and measurement cannot be significantly reduced by simple changes to the model’s constants.

scholarly journals Turbulence in Large-Scale Two-Dimensional Balanced Hard Sphere Gas Flow

Atmosphere ◽  
2021 ◽  
Vol 12 (11) ◽  
pp. 1520
Author(s):  
Rafail V. Abramov
Keyword(s):  
Turbulent Flows ◽  
Hard Sphere ◽  
Large Scale ◽  
Gas Flow ◽  
Spatial Scales ◽  
Mean Field ◽  
Current Work ◽  
Two Dimensional ◽  
Dynamical Mechanism ◽  
Wide Range

In recent works, we developed a model of balanced gas flow, where the momentum equation possesses an additional mean field forcing term, which originates from the hard sphere interaction potential between the gas particles. We demonstrated that, in our model, a turbulent gas flow with a Kolmogorov kinetic energy spectrum develops from an otherwise laminar initial jet. In the current work, we investigate the possibility of a similar turbulent flow developing in a large-scale two-dimensional setting, where a strong external acceleration compresses the gas into a relatively thin slab along the third dimension. The main motivation behind the current work is the following. According to observations, horizontal turbulent motions in the Earth atmosphere manifest in a wide range of spatial scales, from hundreds of meters to thousands of kilometers. However, the air density rapidly decays with altitude, roughly by an order of magnitude each 15–20 km. This naturally raises the question as to whether or not there exists a dynamical mechanism which can produce large-scale turbulence within a purely two-dimensional gas flow. To our surprise, we discover that our model indeed produces turbulent flows and the corresponding Kolmogorov energy spectra in such a two-dimensional setting.

scholarly journals Statistical steady state in turbulent droplet condensation

2016 ◽  
Vol 810 ◽  
pp. 254-280 ◽  
Author(s):  
Christoph Siewert ◽  
Jérémie Bec ◽  
Giorgio Krstulovic
Keyword(s):  
Steady State ◽  
Numerical Simulations ◽  
Turbulent Flows ◽  
Initial Conditions ◽  
Turbulent Transport ◽  
Direct Numerical Simulations ◽  
Numerical Studies ◽  
Transport And Mixing ◽  
Two Parameters ◽  
Droplet Size Distributions

Motivated by systems in which droplets grow and shrink in a turbulence-driven supersaturation field, we investigate the problem of turbulent condensation in a general manner. Using direct numerical simulations, we show that the turbulent fluctuations of the supersaturation field offer different conditions for the growth of droplets which evolve in time due to turbulent transport and mixing. Based on this, we propose a Lagrangian stochastic model for condensation and evaporation of small droplets in turbulent flows. It consists of a set of stochastic integro-differential equations for the joint evolution of the squared radius and the supersaturation along the droplet trajectories. The model has two parameters fixed by the total amount of water and the thermodynamic properties, as well as the Lagrangian integral time scale of the turbulent supersaturation. The model reproduces very well the droplet size distributions obtained from direct numerical simulations and their time evolution. A noticeable result is that, after a stage where the squared radius simply diffuses, the system converges exponentially fast to a statistical steady state independent of the initial conditions. The main mechanism involved in this convergence is a loss of memory induced by a significant number of droplets undergoing a complete evaporation before growing again. The statistical steady state is characterized by an exponential tail in the droplet mass distribution. These results reconcile those of earlier numerical studies, once these various regimes are considered.

scholarly journals Approximate transmission conditions through a rough thin layer: The case of periodic roughness

2009 ◽  
Vol 21 (1) ◽  
pp. 51-75 ◽  
Author(s):  
I. S. CIUPERCA ◽  
M. JAI ◽  
C. POIGNARD
Keyword(s):  
Steady State ◽  
Thin Layer ◽  
Ambient Medium ◽  
Transmission Conditions ◽  
Thin Layers ◽  
Two Dimensional ◽  
The Third ◽  
The Mean ◽  
Dimensional Object

We study the behaviour of the steady-state voltage potentials in a material composed of a two-dimensional object surrounded by a rough thin layer and embedded in an ambient medium. The roughness of the layer is supposed to be ϵ-periodic, ϵ being the magnitude of the mean thickness of the layer. For ϵ tending to zero, we determine approximate transmission conditions in order to replace the rough thin layer by these conditions on the boundary of the interior material. This paper extends the previous works (Poignard, 2009,Math. Meth. Appl. Sci., vol. 32, pp. 435–453; Poignardet al., 2008,IEEE Trans. Magnet., vol. 44, no. 6, pp. 1154–1157) of the third author, which deal with smooth thin layers.

scholarly journals Investigation of the Heteroepitaxial Process Optimization of Ge Layers on Si (001) by RPCVD

Nanomaterials ◽  
2021 ◽  
Vol 11 (4) ◽  
pp. 928
Author(s):  
Yong Du ◽  
Zhenzhen Kong ◽  
Muhammet Toprak ◽  
Guilei Wang ◽  
Yuanhao Miao ◽  
...  
Keyword(s):  
High Temperature ◽  
Buffer Layer ◽  
Layer Thickness ◽  
Growth Temperature ◽  
Crystalline Quality ◽  
Initial Growth ◽  
Two Dimensional ◽  
High Quality ◽  
Reduced Pressure

This work presents the growth of high-quality Ge epilayers on Si (001) substrates using a reduced pressure chemical vapor deposition (RPCVD) chamber. Based on the initial nucleation, a low temperature high temperature (LT-HT) two-step approach, we systematically investigate the nucleation time and surface topography, influence of a LT-Ge buffer layer thickness, a HT-Ge growth temperature, layer thickness, and high temperature thermal treatment on the morphological and crystalline quality of the Ge epilayers. It is also a unique study in the initial growth of Ge epitaxy; the start point of the experiments includes Stranski–Krastanov mode in which the Ge wet layer is initially formed and later the growth is developed to form nuclides. Afterwards, a two-dimensional Ge layer is formed from the coalescing of the nuclides. The evolution of the strain from the beginning stage of the growth up to the full Ge layer has been investigated. Material characterization results show that Ge epilayer with 400 nm LT-Ge buffer layer features at least the root mean square (RMS) value and it’s threading dislocation density (TDD) decreases by a factor of 2. In view of the 400 nm LT-Ge buffer layer, the 1000 nm Ge epilayer with HT-Ge growth temperature of 650 °C showed the best material quality, which is conducive to the merging of the crystals into a connected structure eventually forming a continuous and two-dimensional film. After increasing the thickness of Ge layer from 900 nm to 2000 nm, Ge surface roughness decreased first and then increased slowly (the RMS value for 1400 nm Ge layer was 0.81 nm). Finally, a high-temperature annealing process was carried out and high-quality Ge layer was obtained (TDD=2.78 × 107 cm−2). In addition, room temperature strong photoluminescence (PL) peak intensity and narrow full width at half maximum (11 meV) spectra further confirm the high crystalline quality of the Ge layer manufactured by this optimized process. This work highlights the inducing, increasing, and relaxing of the strain in the Ge buffer and the signature of the defect formation.

scholarly journals Modules or Mean-Fields?

Entropy ◽  
2020 ◽  
Vol 22 (5) ◽  
pp. 552 ◽  
Author(s):  
Thomas Parr ◽  
Noor Sajid ◽  
Karl J. Friston
Keyword(s):  
Steady State ◽  
Message Passing ◽  
Mean Field Theory ◽  
Functional Anatomy ◽  
Mean Field ◽  
State Density ◽  
Stochastic Dynamical Systems ◽  
Conditional Independency ◽  
The Brain ◽  
Non Equilibrium

The segregation of neural processing into distinct streams has been interpreted by some as evidence in favour of a modular view of brain function. This implies a set of specialised ‘modules’, each of which performs a specific kind of computation in isolation of other brain systems, before sharing the result of this operation with other modules. In light of a modern understanding of stochastic non-equilibrium systems, like the brain, a simpler and more parsimonious explanation presents itself. Formulating the evolution of a non-equilibrium steady state system in terms of its density dynamics reveals that such systems appear on average to perform a gradient ascent on their steady state density. If this steady state implies a sufficiently sparse conditional independency structure, this endorses a mean-field dynamical formulation. This decomposes the density over all states in a system into the product of marginal probabilities for those states. This factorisation lends the system a modular appearance, in the sense that we can interpret the dynamics of each factor independently. However, the argument here is that it is factorisation, as opposed to modularisation, that gives rise to the functional anatomy of the brain or, indeed, any sentient system. In the following, we briefly overview mean-field theory and its applications to stochastic dynamical systems. We then unpack the consequences of this factorisation through simple numerical simulations and highlight the implications for neuronal message passing and the computational architecture of sentience.

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