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arXiv2018

Hydrodynamic convection in accretion discs

The prevalence and consequences of convection perpendicular to the plane of accretion discs have been discussed for several decades. Recent simulations combining convection and the magnetorotational instability have given fresh impetus to the debate, as the interplay of the two processes can enhance angular momentum transport, at least in the optically thick outburst stage of dwarf novae. In this paper we seek to isolate and understand the most generic features of disc convection, and so undertake its study in purely hydrodynamical models. First, we investigate the linear phase of the instability, obtaining estimates of the growth rates both semi-analytically, using one-dimensional spectral computations, as well as analytically, using WKBJ methods. Next we perform three-dimensional, vertically stratified, shearing box simulations with the conservative, finite-volume code PLUTO, both with and without explicit diffusion coefficients. We find that hydrodynamic convection can, in general, drive outward angular momentum transport, a result that we confirm with ATHENA, an alternative finite-volume code. Moreover, we establish that the sign of the angular momentum flux is sensitive to the diffusivity of the numerical scheme. Finally, in sustained convection, whereby the system is continuously forced to an unstable state, we observe the formation of various coherent structures, including large- scale and oscillatory convective cells, zonal flows, and small vortices.

astro-ph.SR↗

arXiv2014

3D morphology of a random field from its 2D cross-section

We show that both aspect ratios of randomly oriented triaxial ellipsoids (representing isosurfaces of an isotropic 3D random field) can be determined from a single 2D cross-section of their sample using the probability distribution of the filamentarity F of the structures seen in the cross-section (F=0 for a circle and F=1 for a line). The probability distribution of F has a robust form with a sharp maximum and truncation that are sensitive to the ellipsoids' aspect ratios. We show that the aspect ratios of triaxial ellipsoids with randomly distributed dimensions can still be recovered from the probability distribution of F. This method is applicable to many shape recognition and classification problems, here illustrated with neutral hydrogen density in the turbulent interstellar medium of the Milky Way. The gas distribution is shown to be filamentary with the mean axis ratio 1:2:20.

physics.flu-dyn↗

arXiv2018

Angular momentum and local gravitational instability in galaxy discs: does $Q$ correlate with $j$ or $M\,$?

We introduce a new diagnostic for exploring the link between angular momentum and local gravitational instability in galaxy discs. Our diagnostic incorporates the latest developments in disc instability research, is fully consistent with approximations that are widely used for measuring the stellar specific angular momentum, $j_{\star}=J_{\star}/M_{\star}$, and is also very simple. We show that such a disc instability diagnostic hardly correlates with $j_{\star}$ or $M_{\star}$, and is remarkably constant across spiral galaxies of any given type (Sa$\!-\!$Sd), stellar mass ($M_{\star}=10^{9.5}\!-\!10^{11.5}\,\mathrm{M}_{\odot}$) and velocity dispersion anisotropy ($σ_{z\star}/σ_{R\star}=0\!-\!1$). The fact that $M_{\star}$ is tightly correlated with star formation rate ($\mathrm{SFR}$), molecular gas mass ($M_{\mathrm{mol}}$), metallicity ($12+\log\mathrm{O/H}$) and other fundamental galaxy properties thus implies that nearby star-forming spirals self-regulate to a quasi-universal disc stability level. This proves the existence of the self-regulation process postulated by several star formation models, but also raises important caveats.

astro-ph.GA↗

arXiv2013

Jet-induced jammed states of granular jet impacts

The impacts of granular jets for both frictional and frictionless grains in two dimensions are numerically investigated. A dense flow with a dead zone emerges during the impact. From our two-dimensional simulation, we evaluate the equations of state and the con- stitutive equations of the flow. The asymptotic divergences of pressure and shear stress similar to the situation near the jamming transition appear for the frictionless case, while their exponents are smaller than those of the sheared granular systems, and are close to the extrapolation from the kinetic theoretical regime. In a similar manner to the jam- ming for frictional grains, the critical density decreases as the friction constant of grains increases. For bi-disperse systems, the effective friction constant defined as the ratio of shear stress to normal stress, monotonically increases from near zero, as the strain rate increases. On the other hand, the effective friction constant has two metastable branches for mono-disperse systems because of the coexistence of a crystallized state and a liquid state.

cond-mat.stat-mech↗

arXiv2014

Cellular burdens and biological effects on tissue level caused by inhaled radon progenies

In the case of radon exposure, the spatial distribution of deposited radioactive particles is highly inhomogeneous in the central airways. The objective of this research is to investigate the consequences of this heterogeneity regarding cellular burdens in the bronchial epithelium and to study the possible biological effects on tissue level. Applying a computational fluid dynamics program, the deposition distribution of inhaled radon daughters has been determined in a bronchial airway model for 23 minutes of work in the New Mexico uranium mine corresponding to 0.0129 WLM exposure. A numerical epithelium model based on experimental data has been utilized in order to quantify cellular hits and doses. Finally, a carcinogenesis model considering cell death induced cell cycle shortening has been applied to assess the biological responses. Computations present, that cellular dose may reach 1.5 Gy, which is several orders of magnitude higher than tissue dose. The results are in agreement with the histological finding that the uneven deposition distribution of radon progenies may lead to inhomogeneous spatial distribution of tumours in the bronchial airways. In addition, on macroscopic level, the relationship between cancer risk and radiation burden seems to be non-linear.

physics.med-ph↗

arXiv2014

Manipulating flow separation: sensitivity of stagnation points, separatrix angles and recirculation area to steady actuation

A variational technique is used to derive analytical expressions for the sensitivity of several geometric indicators of flow separation to steady actuation. Considering the boundary layer flow above a wall-mounted bump, the six following representative quantities are considered: the locations of the separation point and reattachment point connected by the separatrix, the separation angles at these stagnation points, the backflow area and the recirculation area. For each geometric quantity, linear sensitivity analysis allows us to identify regions which are the most sensitive to volume forcing and wall blowing/suction. Validations against full non-linear Navier-Stokes calculations show excellent agreement for small-amplitude control for all considered indicators. With very resemblant sensitivity maps, the reattachment point, the backflow and recirculation areas are seen to be easily manipulated. In contrast, the upstream separation point and the separatrix angles are seen to remain extremely robust with respect to external steady actuation.

physics.flu-dyn↗

arXiv2018

From arteries to boreholes: Transient response of a poroelastic cylinder to fluid injection

The radially outward flow of fluid through a porous medium occurs in many practical problems, from transport across vascular walls to the pressurisation of boreholes in the subsurface. When the driving pressure is non-negligible relative to the stiffness of the solid structure, the poromechanical coupling between the fluid and the solid can control both the steady-state and the transient mechanics of the system. Very large pressures or very soft materials lead to large deformations of the solid skeleton, which introduce kinematic and constitutive nonlinearity that can have a nontrivial impact on these mechanics. Here, we study the transient response of a poroelastic cylinder to sudden fluid injection. We consider the impacts of kinematic and constitutive nonlinearity, both separately and in combination, and we highlight the central role of driving method in the evolution of the response. We show that the various facets of nonlinearity may either accelerate or decelerate the transient response relative to linear poroelasticity, depending on the boundary conditions and the initial geometry, and that an imposed fluid pressure leads to a much faster response than an imposed fluid flux.

physics.flu-dyn↗

arXiv2014

The prospect of using LES and DES in engineering design, and the research required to get there

In this paper we try to look into the future to divine how large eddy and detached eddy simulations (LES and DES, respectively) will be used in the engineering design process about 20-30 years from now. Some key challenges specific to the engineering design process are identified, and some of the critical outstanding problems and promising research directions are discussed.

physics.flu-dyn↗

arXiv2021

$λ$-Navier-Stokes turbulence

We investigate numerically the model proposed in Sahoo et al [Phys. Rev. Lett. 118, 164501, (2017)] where a parameter $λ$ is introduced in the Navier-Stokes equations such that the weight of homochiral to heterochiral interactions is varied while preserving all original scaling symmetries and inviscid invariants. Decreasing the value of $λ$ leads to a change in the direction of the energy cascade at a critical value $λ_c \sim 0.3$. In this work, we perform numerical simulations at varying $λ$ in the forward energy cascade range and at changing the Reynolds number $\mathrm{Re}$. We show that for a fixed injection rate, as $λ\to λ_c$, the kinetic energy diverges with a scaling law $\mathcal{E} \propto (λ-λ_c)^{-2/3}$. The energy spectrum is shown to display a larger bottleneck as $λ$ is decreased. The forward heterochiral flux and the inverse homochiral flux both increase in amplitude as $λ_c$ is approached while keeping their difference fixed and equal to the injection rate. As a result, very close to $λ_c$ a stationary state is reached where the two opposite fluxes are of much higher amplitude than the mean flux and large fluctuations are observed. Furthermore, we show that intermittency as $λ_c$ is approached is reduced. The possibility of obtaining a statistical description of regular Navier-Stokes turbulence as an expansion around this newly found critical point is discussed.

physics.flu-dyn↗

arXiv2013

Quantum-statistics-induced flow patterns in driven ideal Fermi gases

While classical or quantum interacting liquids become turbulent under sufficiently strong driving, it is not obvious what flow pattern an ideal quantum gas develops under similar conditions. Unlike classical noninteracting particles which exhibit rather trivial flow, ideal fermions have to satisfy the exclusion principle, which acts as a form of collective repulsion. We thus study the flow of an ideal Fermi gas as it is driven out of a narrow orifice of width comparable to the Fermi wavelength, employing both a microcanonical approach to transport, and solving a Lindblad equation for Markovian driving leads. Both methods are in good agreement and predict an outflowing current density with a complex microscopic pattern of vorticity in the steady state. Applying a bias of the order of the chemical potential results in a short-range correlated antiferromagnetic vorticity pattern, corresponding to local moments of the order of a tenth of a magneton, $e\hbar/2m$, if the fermions are charged. The latter may be detectable by magnetosensitive spectroscopy in strongly driven cold gases (atoms) or clean electronic nanostructures (electrons).

cond-mat.quant-gas↗

arXiv2013

Universal scaling at non-thermal fixed points of a two-component Bose gas

Quasi-stationary far-from-equilibrium critical states of a two-component Bose gas are studied in two spatial dimensions. After the system has undergone an initial dynamical instability it approaches a non-thermal fixed point. At this critical point the structure of the gas is characterised by ensembles of (quasi-)topological defects such as vortices, skyrmions and solitons which give rise to universal power-law behaviour of momentum correlation functions. The resulting power-law spectra can be interpreted in terms of strong-wave-turbulence cascades driven by particle transport into long-wave-length excitations. Scaling exponents are determined on both sides of the miscible-immiscible transition controlled by the ratio of the intra-species to inter-species couplings. Making use of quantum turbulence methods, we explain the specific values of the exponents from the presence of transient (quasi-)topological defects.

cond-mat.quant-gas↗

arXiv2014

Bose-Einstein condensation and Berezinskii-Kosterlitz-Thouless transition in 2D Nonlinear Schrödinger model

We analyse the Bose-Einstein condensation process and the Berezinskii-Kosterlitz-Thouless phase transition within the Gross-Pitaevskii model and their interplay with wave turbulence theory. By using numerical experiments we study how the condensate fraction and the first order correlation function behave with respect to the mass, the energy and the size of the system. By relating the free-particle energy to the temperature we are able to estimate the Berezinskii-Kousterlitz-Thouless transition temperature. Below this transition we observe that for a fixed temperature the superfluid fraction appears to be size-independent leading to a power-law dependence of the condensate fraction with respect to the system size.

physics.flu-dyn↗

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↗

arXiv2014

On the relative importance of second-order terms in relativistic dissipative fluid dynamics

In Denicol et al., Phys. Rev. D 85, 114047 (2012), the equations of motion of relativistic dissipative fluid dynamics were derived from the relativistic Boltzmann equation. These equations contain a multitude of terms of second order in Knudsen number, in inverse Reynolds number, or their product. Terms of second order in Knudsen number give rise to non-hyperbolic (and thus acausal) behavior and must be neglected in (numerical) solutions of relativistic dissipative fluid dynamics. The coefficients of the terms which are of the order of the product of Knudsen and inverse Reynolds numbers have been explicitly computed in the above reference, in the limit of a massless Boltzmann gas. Terms of second order in inverse Reynolds number arise from the collision term in the Boltzmann equation, upon expansion to second order in deviations from the single-particle distribution function in local thermodynamical equilibrium. In this work, we compute these second-order terms for a massless Boltzmann gas with constant scattering cross section. Consequently, we assess their relative importance in comparison to the terms which are of the order of the product of Knudsen and inverse Reynolds numbers.

nucl-th↗

arXiv2014

Fluctuating hydrodynamics of multi-species, non-reactive mixtures

In this paper we discuss the formulation of the fuctuating Navier-Stokes (FNS) equations for multi-species, non-reactive fluids. In particular, we establish a form suitable for numerical solution of the resulting stochastic partial differential equations. An accurate and efficient numerical scheme, based on our previous methods for single species and binary mixtures, is presented and tested at equilibrium as well as for a variety of non-equilibrium problems. These include the study of giant nonequilibrium concentration fluctuations in a ternary mixture in the presence of a diffusion barrier, the triggering of a Rayleigh-Taylor instability by diffusion in a four-species mixture, as well as reverse diffusion in a ternary mixture. Good agreement with theory and experiment demonstrates that the formulation is robust and can serve as a useful tool in the study of thermal fluctuations for multi-species fluids. The extension to include chemical reactions will be treated in a sequel paper.

physics.flu-dyn↗

arXiv2021

Theory and simulation of shock waves: Entropyproduction and energy conversion

We have considered a shock wave as a surface of discontinuity and computed the entropy production using non-equilibrium thermodynamics for surfaces. The results from this method, which we call the "Gibbs excess method" (GEM), were compared with results from three alternative methods, all based on the entropy balance in the shock front region, but with different assumptions about local equilibrium. Non-equilibrium molecular dynamics (NEMD) simulations were used to simulate a thermal blast in a one-component gas consisting of particles interacting with the Lennard-Jones/spline potential. This provided data for the theoretical analysis. Two cases were studied, a weak shock with Mach number $M \approx 2$ and a strong shock with $M \approx 6$ and with a Prandtl number of the gas $Pr \approx 1.4$ in both cases. The four theoretical methods gave consistent results for the time-dependent surface excess entropy production for both Mach numbers. The internal energy was found to deviate only slightly from equilibrium values in the shock front. The pressure profile was found to be consistent with the Navier-Stokes equations. The entropy production in the weak and strong shocks were approximately proportional to the square of the Mach number and decayed with time at approximately the same relative rate. In both cases, some 97 \% of the total entropy production in the gas occurred in the shock wave. The GEM showed that most of the shock's kinetic energy was converted reversibly into enthalpy and entropy, and a small amount was dissipated as produced entropy. The shock waves traveled at almost constant speed and we found that the overpressure determined from NEMD simulations agreed well with the Rankine-Hugoniot conditions for steady-state shocks.

physics.flu-dyn↗

arXiv2022

Characterizing scale dependence of effective diffusion driven by fluid flows

We study the scale dependence of effective diffusion of fluid tracers, specifically, its dependence on the Péclet number, a dimensionless parameter of the ratio between advection and molecular diffusion. Here, we address the case that length and time scales on which the effective diffusion can be described are not separated from those of advection and molecular diffusion. For this, we propose a new method for characterizing the effective diffusivity without relying on the scale separation. For a given spatial domain inside which the effective diffusion can emerge, a time constant related to the diffusion is identified by considering the spatio-temporal evolution of a test advection-diffusion equation, where its initial condition is set at a pulse function. Then, the value of effective diffusivity is identified by minimizing the $L_\infty$ distance between solutions of the above test equation and the diffusion one with mean drift. With this method, for time-independent gyre and time-periodic shear flows, we numerically show the scale dependence of the effective diffusivity and its discrepancy from the classical limits that were derived on the assumption of the scale separation. The kinematic origins of the discrepancy are revealed as the development of the molecular diffusion across flow cells of the gyre and as the suppression of the drift motion due to a temporal oscillation in the shear.

physics.flu-dyn↗

arXiv2018

A diffuse-interface model for smoothed particle hydrodynamics

Diffuse-interface theory provides a foundation for the modeling and simulation of microstructure evolution in a very wide range of materials, and for the tracking/capturing of dynamic interfaces between different materials on larger scales. Smoothed particle hydrodynamics (SPH) is also widely used to simulate fluids and solids that are subjected to large deformations and have complex dynamic boundaries and/or interfaces, but no explicit interface tracking/capturing is required, even when topological changes such as fragmentation and coalescence occur, because of its Lagrangian particle nature. Here we developed an SPH model for single-component two-phase fluids that is based on diffuse-interface theory. In the model, the interface has a finite thickness and a surface tension that depend on the coefficient, k, of the gradient contribution to the Helmholtz free energy functional and the density dependent homogeneous free energy. In this model, there is no need to locate the surface (or interface) or to compute the curvature at and near the interface. One- and two-dimensional SPH simulations were used to validate the model.

physics.comp-ph↗