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arXiv2022

Direct data-driven forecast of local turbulent heat flux in Rayleigh-Bénard convection

A combined convolutional autoencoder-recurrent neural network machine learning model is presented to analyse and forecast the dynamics and low-order statistics of the local convective heat flux field in a two-dimensional turbulent Rayleigh-Bénard convection flow at Prandtl number ${\rm Pr}=7$ and Rayleigh number ${\rm Ra}=10^7$. Two recurrent neural networks are applied for the temporal advancement of flow data in the reduced latent data space, a reservoir computing model in the form of an echo state network and a recurrent gated unit. Thereby, the present work exploits the modular combination of three different machine learning algorithms to build a fully data-driven and reduced model for the dynamics of the turbulent heat transfer in a complex thermally driven flow. The convolutional autoencoder with 12 hidden layers is able to reduce the dimensionality of the turbulence data to about 0.2 \% of their original size. Our results indicate a fairly good accuracy in the first- and second-order statistics of the convective heat flux. The algorithm is also able to reproduce the intermittent plume-mixing dynamics at the upper edges of the thermal boundary layers with some deviations. The same holds for the probability density function of the local convective heat flux with differences in the far tails. Furthermore, we demonstrate the noise resilience of the framework which suggests the present model might be applicable as a reduced dynamical model that delivers transport fluxes and their variations to the coarse grid cells of larger-scale computational models, such as global circulation models for the atmosphere and ocean.

physics.flu-dyn↗

arXiv2013

Global drag-induced instabilities in protoplanetary disks

We use the Fokker-Planck equation and model the dispersive dynamics of solid particles in annular protoplanetary disks whose gas component is more massive than the particle phase. We model particle--gas interactions as hard sphere collisions, determine the functional form of diffusion coefficients, and show the existence of two global unstable modes in the particle phase. These modes have spiral patterns with the azimuthal wavenumber $m=1$ and rotate slowly. We show that in ring-shaped disks, the phase space density of solid particles increases linearly in time towards an accumulation point near the location of pressure maximum, while instabilities grow exponentially. Therefore, planetesimals and planetary cores can be efficiently produced near the peaks of unstable density waves. In this mechanism, particles migrating towards the accumulation point will not participate in the formation of planets, and should eventually form a debris ring like the main asteroid belt or classical Kuiper belt objects. We present the implications of global instabilities to the formation of ice giants and terrestrial planets in the solar system.

astro-ph.EP↗

arXiv2013

Can planetesimals form by collisional fusion?

As a test bed for the growth of protoplanetary bodies in a turbulent circumstellar disk we examine the fate of a boulder using direct numerical simulations of particle seeded gas flowing around it. We provide an accurate description of the flow by imposing no-slip and non-penetrating boundary conditions on the boulder surface using the immersed boundary method pioneered by Peskin (2002). Advected by the turbulent disk flow, the dust grains collide with the boulder and we compute the probability density function (PDF) of the normal component of the collisional velocity. Through this examination of the statistics of collisional velocities we test the recently developed concept of collisional fusion which provides a physical basis for a range of collisional velocities exhibiting perfect sticking. A boulder can then grow sufficiently rapidly to settle into a Keplerian orbit on disk evolution time scales.

astro-ph.EP↗

arXiv2013

Convective overshoot mixing in stellar interior models

The convective overshoot mixing plays an important role in stellar structure and evolution. However, the overshoot mixing is a long standing problem. The uncertainty of the overshoot mixing is one of the most uncertain factors in stellar physics. As it is well known, the convective and overshoot mixing is determined by the radial chemical component flux. In this paper, a local model of the radial chemical component flux is established based on the hydrodynamic equations and some model assumptions. The model is tested in stellar models. The main conclusions are as follows. (i) The local model shows that the convective and overshoot mixing could be regarded as a diffusion process, and the diffusion coefficient for different chemical element is the same. However, if the non-local terms, i.e., the turbulent convective transport of radial chemical component flux, are taken into account, the diffusion coefficient for each chemical element should be in general different. (ii) The diffusion coefficient of convective / overshoot mixing shows different behaviors in convection zone and in overshoot region because the characteristic length scale of the mixing is large in the convection zone and small in the overshoot region. The overshoot mixing should be regarded as a weak mixing process. (iii) The result of the diffusion coefficient of mixing is tested in stellar models. It is found that a single choice of our central mixing parameter leads to consistent results for a solar convective envelope model as well as for core convection models of stars with mass from 2M to 10M.

astro-ph.SR↗

arXiv2011

Using multiscale norms to quantify mixing and transport

Mixing is relevant to many areas of science and engineering, including the pharmaceutical and food industries, oceanography, atmospheric sciences, and civil engineering. In all these situations one goal is to quantify and often then to improve the degree of homogenisation of a substance being stirred, referred to as a passive scalar or tracer. A classical measure of mixing is the variance of the concentration of the scalar, which can be related to the $L^2$ norm of the concentration field. Recently other norms have been used to quantify mixing, in particular the mix-norm as well as negative Sobolev norms. These norms have the advantage that unlike variance they decay even in the absence of diffusion, and their decay corresponds to the flow being mixing in the sense of ergodic theory. General Sobolev norms weigh scalar gradients differently, and are known as multiscale norms for mixing. We review the applications of such norms to mixing and transport, and show how they can be used to optimise the stirring and mixing of a decaying passive scalar. We then review recent work on the less-studied case of a continuously-replenished scalar field --- the source-sink problem. In that case the flows that optimally reduce the norms are associated with transport rather than mixing: they push sources onto sinks, and vice versa.

physics.flu-dyn↗

arXiv2013

Non-linear relationship of cell hit and transformation probabilities in low dose of inhaled radon progenies

Cellular hit probabilities of alpha particles emitted by inhaled radon progenies in sensitive bronchial epithelial cell nuclei were simulated at low exposure levels to obtain useful data for the rejection or in support of the linear-non-threshold (LNT) hypothesis. In this study, local distributions of deposited inhaled radon progenies in airway bifurcation models were computed at exposure conditions, which are characteristic of homes and uranium mines. Then, maximum local deposition enhancement factors at bronchial airway bifurcations, expressed as the ratio of local to average deposition densities, were determined to characterize the inhomogeneity of deposition and to elucidate their effect on resulting hit probabilities. The results obtained suggest that in the vicinity of the carinal regions of the central airways the probability of multiple hits can be quite high even at low average doses. Assuming a uniform distribution of activity there are practically no multiple hits and the hit probability as a function of dose exhibits a linear shape in the low dose range. The results are quite the opposite in the case of hot spots revealed by realistic deposition calculations, where practically all cells receive multiple hits and the hit probability as a function of dose is non-linear in the average dose range of 10-100 mGy.

physics.med-ph↗

arXiv2013

Morphological instabilities of stratified epithelia: a mechanical instability in tumour formation

Interfaces between stratified epithelia and their supporting stromas commonly exhibit irregular shapes. Undulations are particularly pronounced in dysplastic tissues and typically evolve into long, finger-like protrusions in carcinomas. In a previous work (Basan et al., Phys. Rev. Lett. 106, 158101 (2011)), we demonstrated that an instability arising from viscous shear stresses caused by the constant flow due to cell turnover in the epithelium could drive this phenomenon. While interfacial tension between the two tissues as well as mechanical resistance of the stroma tend to maintain a flat interface, an instability occurs for sufficiently large viscosity, cell-division rate and thickness of the dividing region in the epithelium. Here, extensions of this work are presented, where cell division in the epithelium is coupled to the local concentration of nutrients or growth factors diffusing from the stroma. This enhances the instability by a mechanism similar to that of the Mullins-Sekerka instability in single-diffusion processes of crystal growth. We furthermore present the instability for the generalized case of a viscoelastic stroma.

physics.bio-ph↗

arXiv2013

Characterization of coherent structures in three-dimensional flows using the finite-size Lyapunov exponent

In this paper we use the finite size Lyapunov Exponent (FSLE) to characterize Lagrangian coherent structures in three-dimensional (3d) turbulent flows. Lagrangian coherent structures act as the organizers of transport in fluid flows and are crucial to understand their stirring and mixing properties. Generalized maxima (ridges) of the FSLE fields are used to locate these coherent structures. Three-dimensional FSLE fields are calculated in two phenomenologically distinct turbulent flows: a wall-bounded flow (channel flow) and a regional oceanic flow obtained by numerical solution of the primitive equations where two-dimensional turbulence dominates. In the channel flow, autocorrelations of the FSLE field show that the structure is substantially different from the near wall to the mid-channel region and relates well to the more widely studied Eulerian coherent structure of the turbulent channel flow. The ridges of the FSLE field have complex shapes due to the 3d character of the turbulent fluctuations. In the oceanic flow, strong horizontal stirring is present and the flow regime is similar to that of 2d turbulence where the domain is populated by coherent eddies that interact strongly. This in turn results in the presence of high FSLE lines throughout the domain leading to strong non-local mixing. The ridges of the FSLE field are quasi-vertical surfaces, indicating that the horizontal dynamics dominates the flow. Indeed, due to rotation and stratification, vertical motions in the ocean are much less intense than horizontal ones. This suppression is absent in the channel flow, as the 3d character of the FSLE ridges shows.

nlin.CD↗

arXiv2013

A General Theory of Turbulent Fragmentation

We develop an analytic framework to understand fragmentation in turbulent, self-gravitating media. Previously, we showed some properties of turbulence can be predicted with the excursion-set formalism. Here, we generalize to fully time-dependent gravo-turbulent fragmentation & collapse. We show that turbulent systems are always gravitationally unstable (in a probabilistic sense). The fragmentation mass spectra, size/mass relations, correlation functions, range of scales over which fragmentation occurs, & time-dependent rates of fragmentation are predictable. We show how this depends on bulk turbulent properties (Mach numbers & power spectra). We also generalize to include rotation, complicated equations of state, collapsing/expanding backgrounds, magnetic fields, intermittency, & non-normal statistics. We derive how fragmentation is suppressed with 'stiffer' equations of state or different driving mechanisms. Suppression appears at an 'effective sonic scale' where Mach(R,rho)~1. Gas becomes stable below this scale for polytropic gamma>4/3, but fragmentation still occurs on larger scales. The scale-free nature of turbulence and gravity generically drives mass spectra and correlation functions towards universal shapes, with weak dependence on many properties of the media. Correlated fluctuation structures, non-Gaussian density distributions, & intermittency have surprisingly small effects on the fragmentation process. This is because fragmentation cascades on small scales are 'frozen in' when large-scale modes push the 'parent' region above the collapse threshold; though they collapse, their statistics are only weakly modified by the collapse process. With thermal support, structure develops 'top-down' in time via fragmentation cascades; but strong rotational support reverses this to 'bottom-up' growth via mergers & introduces a maximal instability scale distinct from the Toomre scale.

astro-ph.CO↗

arXiv2013

A Model for (Non-Lognormal) Density Distributions in Isothermal Turbulence

We propose a new, physically motivated fitting function for density PDFs in turbulent gas. Although it is known that when gas is isothermal, the PDF is approximately lognormal in the core, high-resolution simulations show large deviations from exact log-normality. The proposed function provides an extraordinarily accurate description of the density PDFs in simulations with Mach numbers ~0.1-15 and dispersion in log(rho) from ~0.01-4 dex. Compared to a lognormal or lognormal-skew-kurtosis model, the fits are improved by orders of magnitude in the wings of the distribution (with fewer free parameters). This is true in simulations using distinct numerical methods, including or excluding magnetic fields. Deviations from lognormality are represented by a parameter T that increases with the compressive Mach number. The proposed distribution can be derived from intermittent cascade models of the longitudinal (compressive) velocity differences, which should be directly related to density fluctuations, and we provide a simple interpretation of the density PDF as the product of a continuous-time relaxation process. As such the parameter T is consistent with the same parameter needed to explain the (intermittent) velocity structure functions; its behavior is consistent with turbulence becoming more intermittent as it becomes more dominated by strong shocks. It provides a new and unique probe of the role of intermittency in the density (not just velocity) structure of turbulence. We show that this naturally explains some apparent contradictory results in the literature based on use of different moments of the density PDF, as well as differences based on whether volume-weighted or mass-weighted quantities are measured. We show how these are fundamentally related to the fact that mass conservation requires violations of log-normal statistics.

astro-ph.GA↗

arXiv2013

Influence of initial conditions on the large-scale dynamo growth rate

To investigate the effect of energy and helicity on the growth of magnetic field, helical kinetic forcing was applied to the magnetohydrodynamic(MHD) system that had a specific distribution of energy and helicity as initial conditions. Simulation results show the saturation of a system is not influenced by the initial conditions, but the growth rate of large scale magnetic field is proportionally dependent on the initial large scale magnetic energy and helicity. It is already known that the helical component of small scale magnetic field(i.e., current helicity $<{\bf j}\cdot {\bf b}>$) quenches the growth of large scale magnetic field. However, $<{\bf j}\cdot {\bf b}>$ can also boost the growth of large scale magnetic field by changing its sign and magnitude. In addition, simulation shows the nonhelical magnetic field can suppress the velocity field through Lorentz force. Comparison of the profiles of evolving magnetic and kinetic energy indicates that kinetic energy migrates backward when the external energy flows into the three dimensional MHD system, which means the velocity field may play a preceding role in the very early MHD dynamo stage.

astro-ph.EP↗

arXiv2013

Following the flow: tracer particles in astrophysical fluid simulations

We present two numerical schemes for passive tracer particles in the hydrodynamical moving-mesh code AREPO, and compare their performance for various problems, from simple setups to cosmological simulations. The purpose of tracer particles is to allow the flow to be followed in a Lagrangian way, tracing the evolution of the fluid with time, and allowing the thermodynamical history of individual fluid parcels to be recorded. We find that the commonly-used `velocity field tracers', which are advected using the fluid velocity field, do not in general follow the mass flow correctly, and explain why this is the case. This method can result in orders-of-magnitude biases in simulations of driven turbulence and in cosmological simulations, rendering the velocity field tracers inappropriate for following these flows. We then discuss a novel implementation of `Monte Carlo tracers', which are moved along with fluid cells, and are exchanged probabilistically between them following the mass flux. This method reproduces the mass distribution of the fluid correctly. The main limitation of this approach is that it is more diffusive than the fluid itself. Nonetheless, we show that this novel approach is more reliable than what has been employed previously and demonstrate that it is appropriate for following hydrodynamical flows in mesh-based codes. The Monte Carlo tracers can also naturally be transferred between fluid cells and other types of particles, such as stellar particles, so that the mass flow in cosmological simulations can be followed in its entirety.

astro-ph.IM↗

arXiv2013

A mean field dynamo from negative eddy diffusivity

Using direct numerical simulations, we verify that "flow IV" of Roberts (1972) exhibits dynamo action dominated by horizontally averaged large-scale magnetic field. With the test-field method we compute the turbulent magnetic diffusivity and find that it is negative and overcomes the molecular diffusivity, thus explaining quantitatively the large-scale dynamo for magnetic Reynolds numbers above $\approx8$. As expected for a dynamo of this type, but contrary to $α$-effect dynamos, the two horizontal field components grow independently of each other and have arbitrary amplitude ratios and phase differences. Small length scales of the mean magnetic field are shown to be stabilized by the turbulent magnetic diffusivity becoming positive at larger wavenumbers. Oscillatory decaying or growing solutions have also been found in certain wavenumber intervals and sufficiently large values of the magnetic Reynolds number. For magnetic Reynolds numbers below $\approx0.5$ the turbulent magnetic diffusivity is confirmed to be positive, as expected for all incompressible flows. Earlier claims of a dynamo driven by a modified Taylor-Green flow through negative eddy diffusivity could not be confirmed.

astro-ph.SR↗

arXiv2018

Pseudorapidity distribution and decorrelation of anisotropic flow within CLVisc hydrodynamics

Studies of fluctuations and correlations of soft hadrons and hard and electromagnetic probes of the dense and strongly interacting medium require event-by-event hydrodynamic simulations of high-energy heavy-ion collisions that are computing intensive. We develop a (3+1)D viscous hydrodynamic model -- CLVisc that is parallelized on Graphics Processing Unit (GPU) using Open Computing Language (OpenCL) with 60 times performance increase for space-time evolution and more than 120 times for the Cooper-Frye particlization relative to that without GPU parallelization. The pseudo-rapidity dependence of anisotropic flow $v_n(η)$ are then computed in CLVisc with initial conditions given by the A Multi-Phase Transport (AMPT) model, with energy density fluctuations both in the transverse plane and along the longitudinal direction. Although the magnitude of $v_n(η)$ and the ratios between $v_2(η)$ and $v_3(η)$ are sensitive to the effective shear viscosity over entropy density ratio $η_v/s$, the shape of the $v_{n}(η)$ distributions in $η$ do not depend on the value of $η_v/s$. The decorrelation of $v_n$ along the pseudo-rapidity direction due to the twist and fluctuation of the event-planes in the initial parton density distributions is also studied. The decorrelation observable $r_n(η^a, η^b)$ between $v_n\{-η^a\}$ and $v_n\{η^a\}$ with the auxiliary reference window $η^b$ is found not sensitive to $η_v/s$ when there is no initial fluid velocity. For small $η_v/s$, the initial fluid velocity from mini-jet partons introduces sizable splitting of $r_n(η^a, η^b)$ between the two reference rapidity windows $η^b \in [3, 4]$ and $η^b \in [4.4, 5.0]$, as has been observed in experiment. The implementation of CLVisc and guidelines on how to efficiently parallelize scientific programs on GPUs are also provided.

nucl-th↗

arXiv2011

Anomalous Scaling and Solitary Waves in Systems with Non-Linear Diffusion

We study a non-linear convective-diffusive equation, local in space and time, which has its background in the dynamics of the thickness of a wetting film. The presence of a non-linear diffusion predicts the existence of fronts as well as shock fronts. Despite the absence of memory effects, solutions in the case of pure non-linear diffusion exhibit an anomalous sub-diffusive scaling. Due to a balance between non-linear diffusion and convection we, in particular, show that solitary waves appear. For large times they merge into a single solitary wave exhibiting a topological stability. Even though our results concern a specific equation, numerical simulations supports the view that anomalous diffusion and the solitary waves disclosed will be general features in such non-linear convective-diffusive dynamics.

cond-mat.soft↗

arXiv2011

Perturbed breakup of gas bubbles in water: Memory, gas flow, and coalescence

The pinch-off of an air bubble from an underwater nozzle ends in a singularity with a remarkable sensitivity to a variety of perturbations. I report on experiments that break both the axial (i.e., vertical) and azimuthal symmetry of the singularity formation. The density of the inner gas influences the axial asymmetry of the neck near pinch-off. For denser gases, flow through the neck late in collapse changes the pinch-off dynamics. Gas density is also implicated in the formation of satellite bubbles. The azimuthal shape oscillations described by Schmidt et al., can be initiated by anisotropic boundary conditions in the liquid as well as with an asymmetric nozzle shape. I measure the n = 3 oscillatory mode, and observe the nonlinear, highly three-dimensional outcomes of pinch-off with large azimuthal perturbations. These are consistent with prior theory.

physics.flu-dyn↗

arXiv2011

On the stationarity of linearly forced turbulence in finite domains

A simple scheme of forcing turbulence away from decay was introduced by Lundgren some time ago, the `linear forcing', which amounts to a force term linear in the velocity field with a constant coefficient. The evolution of linearly forced turbulence towards a stationary final state, as indicated by direct numerical simulations (DNS), is examined from a theoretical point of view based on symmetry arguments. In order to follow closely the DNS the flow is assumed to live in a cubic domain with periodic boundary conditions. The simplicity of the linear forcing scheme allows one to re-write the problem as one of decaying turbulence with a decreasing viscosity. Scaling symmetry considerations suggest that the system evolves to a stationary state, evolution that may be understood as the gradual breaking of a larger approximate symmetry to a smaller exact symmetry. The same arguments show that the finiteness of the domain is intimately related to the evolution of the system to a stationary state at late times, as well as the consistency of this state with a high degree of isotropy imposed by the symmetries of the domain itself. The fluctuations observed in the DNS for all quantities in the stationary state can be associated with deviations from isotropy. Indeed, self-preserving isotropic turbulence models are used to study evolution from a direct dynamical point of view, emphasizing the naturalness of the Taylor microscale as a self-similarity scale in this system. In this context the stationary state emerges as a stable fixed point. Self-preservation seems to be the reason behind a noted similarity of the third order structure function between the linearly forced and freely decaying turbulence, where again the finiteness of the domain plays an significant role.

physics.flu-dyn↗

arXiv2011

Thermodynamic Geometry, Phase Transitions, and the Widom Line

We construct a novel approach, based on thermodynamic geometry, to characterize first-order phase transitions from a microscopic perspective, through the scalar curvature in the equilibrium thermodynamic state space. Our method resolves key theoretical issues in macroscopic thermodynamic constructs, and furthermore characterizes the Widom line through the maxima of the correlation length, which is captured by the thermodynamic scalar curvature. As an illustration of our method, we use it in conjunction with the mean field Van der Waals equation of state to predict the coexistence curve and the Widom line. Where closely applicable, it provides excellent agreement with experimental data. The universality of our method is indicated by direct calculations from the NIST database.

cond-mat.stat-mech↗