arXiv subjects

Rafail V. Abramov

Publications and source records attributed to Rafail V. Abramov.

At least 19 recordsLinked to original sources

arXiv2026

Power spectra via the van der Waals effect in the two-dimensional Poiseuille and Couette flow

We numerically simulate the two-dimensional inertial flow with the van der Waals effect in a straight periodic channel around the Poiseuille and Couette stationary states. Even though the flow remains laminar macroscopically, we observe complex dynamics and power decay of the Fourier spectra of small fluctuations of the density, velocity divergence, vorticity and kinetic energy of the flow near their respective stationary background states. Remarkably, pinning the vorticity to its background state, and leaving only the density and velocity divergence as the variables, results in the dynamics and power decay of the Fourier spectra qualitatively similar to those of the full system. This strongly indicates that the underlying physics of the power spectra reside primarily in the density and velocity divergence variables, and are not directly related to the vorticity of the flow.

physics.flu-dyn↗

arXiv2025

A molecular-kinetic hypothesis on the mechanics of compressible gas flow at low Mach numbers

In recent works, we proposed a theory of turbulence creation via the second coefficient of the virial expansion (i.e. the van der Waals effect). This theory relies, in part, on the empirically observed "equilibrated" behavior of pressure in compressible flows at low Mach numbers. However, a fundamental explanation for such a behavior of pressure does not currently exist, because the conventional kinetic theory leads instead to the adiabatic flow in the form of the usual compressible Euler or Navier-Stokes equations. To explain this behavior of pressure from the molecular-kinetic perspective, in the current work we introduce a novel correction into the pair correlation function in the closure of the Bogoliubov-Born-Green-Kirkwood-Yvon hierarchy. This correction matches the rate of change of the average distance between particles to the macroscopic compression or expansion rate of the gas. Remarkably, the novel correction introduces strong dissipation into the pressure equation at low Mach numbers, which stabilizes the pressure solution. At small scales, the novel dissipation effect manifests as the second viscosity in the momentum equation, which selectively suppresses the velocity divergence. As a result, the second viscosity governs the linear instability which creates turbulent dynamics, thereby setting the critical value of the Reynolds number. The ratio of the second and shear viscosities, together with the critical value of the Reynolds number, are proportional to the reciprocal of the packing fraction.

physics.flu-dyn↗

arXiv2023

Turbulence via intermolecular potential: Uncovering the origin

In recent works, we proposed a hypothesis, according to which turbulence in gases is created by the mean field effect of an intermolecular potential. We discovered that, in a numerically simulated inertial flow, turbulent solutions indeed spontaneously emerge from a laminar initial condition, as observed in nature and experiments. To study the origin of turbulent dynamics, in the current work we examine the equations of a two-dimensional inertial flow, linearized around a large scale constant vorticity state. Remarkably, even in this simplified setting, we find that turbulent dynamics emerge as linearly unstable fluctuations of the velocity divergence. In particular, for the linearized dynamics at a high Reynolds number, we find that, at short time scales, the coupling of the mean field potential with the large scale background vorticity creates linearly unstable, rapidly oscillating fluctuations of the divergence of velocity at inertial scales. In the asymptotic time limit, we find a persistent eigenvector, also aligned largely with the divergence of velocity, which allows these fluctuations to propagate in the form of traveling waves in the Fourier domain. Remarkably, these traveling waves decay at a constant, scale-independent exponential rate, which is rather unusual, because all explicitly dissipative terms in the equations are viscous. Furthermore, it appears that the famous Kolmogorov scaling of the kinetic energy is produced by this persistent velocity divergence, due to a cubic relation between the physical time variable, and a pseudo-time variable, in which the dynamics become asymptotically autonomous. These effects vanish when the mean field potential is removed.

physics.flu-dyn↗

arXiv2022

Turbulence via intermolecular potential: A weakly compressible model of gas flow at low Mach number

In our recent works we proposed a theory of turbulence in inertial gas flow via the mean field effect of an intermolecular potential. We found that, in inertial flow, turbulence indeed spontaneously develops from a laminar initial condition, just as observed in nature and experiments. However, we also found that density and temperature in our inertial flow model behave unrealistically. The goal of the current work is to demonstrate technical possibility of modeling compressible, turbulent flow at low Mach number where both density and temperature behave in a more realistic fashion. Here we focus on a new treatment of the pressure variable, which constitutes a compromise between compressible, incompressible and inertial flow. Similarly to incompressible flow, the proposed equation for the pressure variable is artificial, rather than derived directly from kinetic formulation. However, unlike that for incompressible flow, our pressure equation only damps the divergence of velocity, instead of setting it directly to zero. We find that turbulence develops in our weakly compressible model much like it does in the inertial flow model, but density and temperature behave more realistically.

physics.flu-dyn↗

arXiv2022

Turbulence via intermolecular potential: Viscosity and transition range of the Reynolds number

Turbulence in fluids is an ubiquitous phenomenon, characterized by spontaneous transition of a smooth, laminar flow to rapidly changing, chaotic dynamics. In 1883, Reynolds experimentally demonstrated that, in an initially laminar flow of water, turbulent motions emerge without any measurable external disturbance. To this day, turbulence remains a major unresolved phenomenon in fluid mechanics; in particular, there is a lack of a mathematical model where turbulent dynamics emerge naturally from a laminar flow. Recently, we proposed a new theory of turbulence in gases, according to which turbulent motions are created in an inertial gas flow by the mean field effect of the intermolecular potential. In the current work, we investigate the effect of viscosity in our turbulence model, by numerically simulating the air flow at normal conditions in a straight pipe for different values of the Reynolds number. We find that the transition between the laminar and turbulent flows in our model occurs without any deliberate perturbations as the Reynolds number increases from 2000 to 4000. As the simulated flow becomes turbulent, the decay rate of the time averaged Fourier spectrum of the kinetic energy in our model approaches Kolmogorov's inverse five-thirds law. Both results are consistent with experiments and observations.

physics.flu-dyn↗

arXiv2022

Creation of turbulence in polyatomic gas flow via an intermolecular potential

We develop a tractable interaction model for a polyatomic gas, whose kinetic equation combines a Vlasov-type mean field forcing due to an intermolecular potential, and a Boltzmann-type collision integral due to rotational interactions. We construct a velocity moment hierarchy for the new kinetic equation, and find that, under the high Reynolds number condition, the pressure equation becomes decoupled from the angular momentum and stress. For the heat flux, we propose a novel closure by prescribing the specific heat capacity of the gas flow. Setting the specific heat capacity to that of a constant-pressure process leads to the system of equations for a balanced flow, where the momentum transport equation contains the mean field forcing, which is an averaged effect of the intermolecular potential. Remarkably, the balanced flow equations do not contain any information about internal thermodynamic properties of the gas, and are thereby applicable to a broad range of different gases. We conduct numerical simulations for an air-like gas at normal conditions in the inertial flow regime, where the pressure is constant throughout the domain. We find that the presence of the intermolecular potential produces a distinctly turbulent flow, whose time-averaged Fourier spectra of the kinetic energy and temperature exhibit Kolmogorov's power decay.

physics.flu-dyn↗

arXiv2021

Turbulence in large scale two-dimensional balanced hard sphere gas flow

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. Yet, the air density rapidly decays with altitude, roughly by an order of magnitude each 15-20 kilometers. 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.

physics.flu-dyn↗

arXiv2021

Macroscopic turbulent flow via hard sphere potential

In recent works, we proposed a hypothesis that the turbulence in gases could be produced by particles interacting via a potential, and examined the proposed mechanics of turbulence formation in a simple model of two particles for a variety of different potentials. In this work, we use the same hypothesis to develop new fluid mechanics equations which model turbulent gas flow on a macroscopic scale. The main difference between our approach and the conventional formalism is that we avoid replacing the potential interaction between particles with the Boltzmann collision integral. Due to this difference, the velocity moment closure, which we implement for the shear stress and heat flux, relies upon the high Reynolds number condition, rather than the Newton law of viscosity and the Fourier law of heat conduction. The resulting system of equations of fluid mechanics differs considerably from the standard Euler and Navier-Stokes equations. A numerical simulation of our system shows that a laminar Bernoulli jet of an argon-like hard sphere gas in a straight pipe rapidly becomes a turbulent flow. The time-averaged Fourier spectra of the kinetic energy of this flow exhibit Kolmogorov's negative five-thirds power decay rate.

physics.flu-dyn↗

arXiv2021

Formation of turbulence via an interaction potential

In a recent work, we proposed a hypothesis that the turbulence in gases could be produced by particles interacting via a potential - for example, the interatomic potential at short ranges, and the electrostatic potential at long ranges. Here, we examine the proposed mechanics of turbulence formation in a simple model of two particles, which interact solely via a potential. Following the kinetic theory approach, we derive a hierarchy of the velocity moment transport equations, and then truncate it via a novel closure based on the high Reynolds number condition. While standard closures of the velocity moment hierarchy of the Boltzmann equation lead to the compressible Euler and Navier-Stokes systems of equations, our closure leads to a transport equation for the velocity alone, which is driven by the potential forcing. Starting from a large scale laminar shear flow, we numerically simulate the solutions of our velocity transport equation for the electrostatic, gravity, Thomas-Fermi and Lennard-Jones potentials, as well as the Vlasov-type large scale mean field potential. In all studied scenarios, the time-averaged Fourier spectra of the kinetic energy clearly exhibit Kolmogorov's "five-thirds" power decay rate.

physics.flu-dyn↗

arXiv2020

Turbulent energy spectrum via an interaction potential

For a large system of identical particles interacting by means of a potential, we find that a strong large scale flow velocity can induce motions in the inertial range via the potential coupling. This forcing lies in special bundles in the Fourier space, which are formed by pairs of particles. These bundles are not present in the Boltzmann, Euler and Navier-Stokes equations, because they are destroyed by the Bogoliubov-Born-Green-Kirkwood-Yvon formalism. However, measurements of the flow can detect certain bulk effects shared across these bundles, such as the power scaling of the kinetic energy. We estimate the scaling effects produced by two types of potentials: the Thomas-Fermi interatomic potential (as well as its variations, such as the Ziegler-Biersack-Littmark potential), and the electrostatic potential. In the near-viscous inertial range, our estimates yield the inverse five-thirds power decay of the kinetic energy for both the Thomas-Fermi and electrostatic potentials. The electrostatic potential is also predicted to produce the inverse cubic power scaling of the kinetic energy at large inertial scales. Standard laboratory experiments confirm the scaling estimates for both the Thomas-Fermi and electrostatic potentials at near-viscous scales. Surprisingly, the observed kinetic energy spectrum in the Earth atmosphere at large scales behaves as if induced by the electrostatic potential. Given that the Earth atmosphere is not electrostatically neutral, we cautiously suggest a hypothesis that the atmospheric kinetic energy spectra in the inertial range are indeed driven by the large scale flow via the electrostatic potential coupling.

physics.flu-dyn↗

arXiv2020

The effect of the Enskog collision terms on the steady shock structure in a hard sphere gas

In this work we study the effect of the Enskog collision terms on the steady shock transitions in the supersonic flow of a hard sphere gas. We start by examining one-dimensional, nonlinear, nondispersive planar wave solutions of the Enskog-Navier-Stokes equations, which move in a fixed direction at a constant speed. By further equating the speed of the reference frame with the speed of such a wave, we reduce the Enskog-Navier-Stokes equations into a more simple system of two ordinary differential equations, whose solutions depend on a single scalar spatial variable. We then observe that this system has two fixed points, which are taken to be the states of the gas before and after the shock, and compute the corresponding shock transition in the form of the heteroclinic orbit connecting these two states. We find that the Enskog correction affects both the difference between the fixed points, and the thickness of the transition. In particular, for a given state of the gas before the shock transition, the difference between the fixed points is reduced, while the shock thickness is increased, with the relative impact on the properties of transition being more prominent at low Mach numbers. We also compute the speed of sound in the Enskog-Navier-Stokes equations, and find that, for the same thermodynamic state, it is somewhat faster than that in the conventional Navier-Stokes equations, with an additional dependence on the density of the gas.

physics.flu-dyn↗

arXiv2019

A theory of average response to large jump perturbations

A key feature of the classical Fluctuation Dissipation theorem is its ability to approximate the average response of a dynamical system to a sufficiently small external perturbation from an appropriate time correlation function of the unperturbed dynamics of this system. In the present work, we examine the situation where the state of a nonlinear dynamical system is perturbed by a finitely large, instantaneous external perturbation (jump) -- for example, the Earth climate perturbed by an extinction level event. Such jump can be either deterministic or stochastic, and in the case of a stochastic jump its randomness can be spatial, or temporal, or both. We show that, even for large instantaneous jumps, the average response of the system can be expressed in the form of a suitable time correlation function of the corresponding unperturbed dynamics. For stochastic jumps, we consider two situations: one where a single spatially random jump of a system state occurs at a predetermined time, and another where jumps occur randomly in time with small space-time dependent statistical intensity. For all studied configurations, we compute the corresponding average response formulas in the form of suitable time correlation functions of the unperturbed dynamics. Some efficiently computable approximations are derived for practical modeling scenarios.

math-ph↗

arXiv2019

The random gas of hard spheres

The inconsistency between the time-reversible Liouville equation and time-irreversible Boltzmann equation has been pointed out long ago by Loschmidt. To avoid Loschmidt's objection, here we propose a new dynamical system to model the motion of atoms of gas, with their interactions triggered by a random point process. Despite being random, this model can approximate the collision dynamics of rigid spheres via adjustable parameters. We compute the exact statistical steady state of the system, and determine the form of its marginal distributions for a large number of spheres. We find that the Kullback-Leibler entropy (a generalization of the conventional Boltzmann entropy) of the full system of random gas spheres is a nonincreasing function of time. Unlike the conventional hard sphere model, the proposed random gas model results in a variant of the Enskog equation, which is known to be a more accurate model of dense gas than the Boltzmann equation. We examine the hydrodynamic limit of the derived Enskog equation for spheres of constant mass density, and find that the corresponding Enskog-Euler and Enskog-Navier-Stokes equations acquire additional effects in both the advective and viscous terms. In the dilute gas approximation, the Enskog equation simplifies to the Boltzmann equation, while the Enskog-Euler and Enskog-Navier-Stokes equations become the conventional Euler and Navier-Stokes equations.

math-ph↗

arXiv2017

A mass diffusion effect in gas dynamics equations

In the current work we propose a theory for an additional mass diffusion effect in the conventional gas dynamics equations. We find that this effect appears as a homogenization time limit correction, when the deterministic interaction process of the real gas molecules is replaced with a simplified random interaction process for consistency with the Boltzmann equation. For the simplified random interaction processes represented by either a hard sphere random scattering model, or by a model which employs the Lennard-Jones potential for random molecular deflections, we compute the estimates of the corrective diffusion coefficient in the Euler, Navier-Stokes and Grad equations for some monatomic and polyatomic gases.

physics.flu-dyn↗

arXiv2017

Nonequilibrium diffusive gas dynamics: Poiseuille microflow

We test the recently developed hierarchy of diffusive moment closures for gas dynamics together with the near-wall viscosity scaling on the Poiseuille flow of argon and nitrogen in a one micrometer wide channel, and compare it against the corresponding Direct Simulation Monte Carlo computations. We find that the diffusive regularized Grad equations with viscosity scaling provide the most accurate approximation to the benchmark DSMC results. At the same time, the conventional Navier-Stokes equations without the near-wall viscosity scaling are found to be the least accurate among the tested closures.

physics.flu-dyn↗

arXiv2017

Gas near a wall: a shortened mean free path, reduced viscosity, and the manifestation of a turbulent Knudsen layer in the Navier-Stokes solution of a shear flow

For the gas near a solid planar wall, we propose a scaling formula for the mean free path of a molecule as a function of the distance from the wall, under the assumption of a uniform distribution of the incident directions of the molecular free flight. We subsequently impose the same scaling onto the viscosity of the gas near the wall, and compute the Navier-Stokes solution of the velocity of a shear flow parallel to the wall. This solution exhibits the Knudsen velocity boundary layer in agreement with the corresponding Direct Simulation Monte Carlo computations for argon and nitrogen. We also find that the proposed mean free path and viscosity scaling sets the second derivative of the velocity to infinity at the wall boundary of the flow domain, which suggests that the gas flow is formally turbulent within the Knudsen boundary layer near the wall.

physics.flu-dyn↗

arXiv2017

Diffusive Boltzmann equation, its fluid dynamics, Couette flow and Knudsen layers

In the current work we construct a multimolecule random process which leads to the Boltzmann equation in the appropriate limit, and which is different from the deterministic real gas dynamics process. We approximate the statistical difference between the two processes via a suitable diffusion process, which is obtained in the multiscale homogenization limit. The resulting Boltzmann equation acquires a new spatially diffusive term, which subsequently manifests in the corresponding fluid dynamics equations. We test the Navier-Stokes and Grad closures of the diffusive fluid dynamics equations in the numerical experiments with the Couette flow for argon and nitrogen, and compare the results with the corresponding Direct Simulation Monte Carlo (DSMC) computations. We discover that the full-fledged Knudsen velocity boundary layers develop with all tested closures when the viscosity and diffusivity are appropriately scaled in the vicinity of the walls. Additionally, we find that the component of the heat flux parallel to the direction of the flow is comparable in magnitude to its transversal component near the walls, and that the nonequilibrium Grad closure approximates this parallel heat flux with good accuracy.

physics.flu-dyn↗

arXiv2016

Leading order response of statistical averages of a dynamical system to small stochastic perturbations

The classical fluctuation-dissipation theorem predicts the average response of a dynamical system to an external deterministic perturbation via time-lagged statistical correlation functions of the corresponding unperturbed system. In this work we develop a fluctuation-response theory and test a computational framework for the leading order response of statistical averages of a deterministic or stochastic dynamical system to an external stochastic perturbation. In the case of a stochastic unperturbed dynamical system, we compute the leading order fluctuation-response formulas for two different cases: when the existing stochastic term is perturbed, and when a new, statistically independent, stochastic perturbation is introduced. We numerically investigate the effectiveness of the new response formulas for an appropriately rescaled Lorenz 96 system, in both the deterministic and stochastic unperturbed dynamical regimes.

nlin.CD↗