Hydrodynamic Equations Of Motion Research Articles

Hydrodynamics with triangular point group

When continuous rotational invariance of a two-dimensional fluid is broken to the discrete, dihedral subgroup D_6D6 - the point group of an equilateral triangle - the resulting anisotropic hydrodynamics breaks both spatial-inversion and time-reversal symmetries, while preserving their combination. In this work, we present the hydrodynamics of such D_6D6-symmetric fluids, identifying new symmetry-allowed dissipative terms in the hydrodynamic equations of motion. We propose two experiments - both involving high-purity solid-state materials with D_6D6-invariant Fermi surfaces - that are sensitive to these new coefficients in a D_6D6-invariant electron fluid. In particular, we propose a local current imaging experiment (which is present-day realizable with nitrogen vacancy center magnetometry) in a hexagonal device, whose D_6D6-exploiting boundary conditions enable the unambiguous detection of these novel transport coefficients.

Attenuation of Acoustic-Gravity Waves in an Isothermal Atmosphere: Consideration with the Modified Navier-Stokes and Heat-Transfer Equations

Within the model of a dissipative isothermal atmosphere, the attenuation of acoustic−gravity waves (AGWs) is studied on the basis of the modified Navier−Stokes and heat-transfer equations. Besides the usually considered velocity gradient, the modification of these equations takes into account the additional transfer of the momentum and energy induced by AGWs due to the density gradient. This results in that additional terms appear in the hydrodynamic equations of motion and heat transfer. Under these assumptions, the local dispersion equation for AGWs in an isothermal dissipative atmosphere, as well as an expression for the damping decrement, is obtained. In the limiting cases of high frequencies (sound waves) and low frequencies (gravitational waves), the nature of the attenuation allows a clear physical interpretation. Special aspects of the time-dependent attenuation for the evanescent acoustic−gravity modes of various types, including the Lamb waves and Brent−Vaisala oscillations, are also considered.

River channel deformations in the area of damless water intake

A mathematical model of the unsteady uneven movement of the river flow in the area of the damless water intake, flowing in deformable channels, was developed and numerically implemented. In the developed model of the deformation of the river channel, flowing on easily eroded beds, adapted formulas of the transporting ability of the flow are used, the hydrodynamic equations of motion and continuity of the flow, deformation of the channel, and sediment balance. To close the system of differential equations, we use the adapted formula of the conveying ability of the flow–Benold. In the calculations, the non-erosion speed was taken according to the formula C.E. Mirtschulava, taking into account standard values of adaptive coefficients. It is suitable for describing deformation processes, taking into account the drift of dredging slots. The model contains the minimum number of equations and empirical constants. In the present work, a numerical model is proposed for predicting channel processes in river beds in the area of damless water intakes and is verified on the results of experimental studies. The figures show sequential deformations of the channel, arising due to natural causes, as well as due to channel adjustment and treatment works (discharge of soil from the supply channel into the river). As can be seen from these figures, the channel from multi-sleeve is gradually turning into one-sleeve. It has been established that after 1 year of observation at low water, as a result of discharge of sediment from the sewage treatment works, the river ducts die off. These ducts are observed only in the flood. Note that below the Karshi main channel (KMCh), the left bank eroded by about 150 m. After a 10-year course, the low-water course turned into a one-arm riverbed. As a result of the erosion of the left-bank islands, it turned into the river itself. During the flood, there are also no pronounced sleeves, a significant erosion of the left bank is noted, up to 700 m. After that, this bank was strengthened. In the future, the channel process did not undergo significant changes. Towards the end of the 10th year of observation, the channel broadened somewhat, and the flood depth decreased in the flood. Comparison of the results of field and numerical studies shows that the developed model gives good results. For low-water conditions, coincidence is better than for flood conditions. During the flood, under natural conditions, somewhat greater depths are observed on the floodplain than in the calculations. It should be noted that both in calculations and in kind:- there was a significant erosion of the left bank below the KMCh;- the channel of the Amudarya river in the considered section from multi-sleeve turned into practically one-sleeve.

Hydrodynamic Fluctuations in Relativistic Heavy-Ion Collisions

We present a novel approach to the treatment of thermal fluctuations in the (3+1)-D viscous hydrodynamic simulation MUSIC. The phenomenological impact of thermal fluctuations on hadronic observables is investigated using the IP-Glasma + hydrodynamics + hadronic cascade hybrid approach. The anisotropic flow observed in heavy-ion collision experiments is mostly attributed to the hydrodynamic response to the event-by-event collision geometry and to the sub-nucleon quantum fluctuations. However, hydrodynamic fluctuations are present during the dynamical evolution of the Quark Gluon Plasma (QGP) and are quantified by the fluctuation-dissipation theorem. They can leave their imprint on final-state observables. By analyzing the thermal noise mode-by-mode, we provide a consistent scheme of treating these fluctuations as the source terms for hydrodynamic fields. These source terms are then evolved together with hydrodynamic equations of motion. Such a treatment captures the non-perturbative nature of the evolution for these thermal fluctuations.

Topological-distance-dependent transition in flocks with binary interactions.

We have studied a flocking model with binary interactions (binary flock), where the velocity of an agent depends on the velocity of only another agent and its own velocity, topped by the angular noise. The other agent is selected as the nth topological neighbor; the specific value of n being a fixed parameter of the problem. On the basis of extensive numerical simulation results, we argue that for n = 1, the phase transition from the ordered to the disordered phase of the flock is a special kind of discontinuous transition. Here, the order parameter does not flip-flop between multiple metastable states. It continues its initial disordered state for a period t(c), then switches over to the ordered state and remains in this state ever after. For n = 2, it is the usual discontinuous transition between two metastable states. Beyond this range, the continuous transitions are observed for n≥3. Such a system of binary flocks has been further studied using the hydrodynamic equations of motion. Linear stability analysis of the homogeneous polarized state shows that such a state is unstable close to the critical point and above some critical speed, which increases as we increase n. The critical noise strengths, which depend on the average correlation between a pair of topological neighbors, are estimated for five different values of n, which match well with their simulated values.

Nonlinear dynamics of spin and charge in spin-Calogero model

The fully nonlinear dynamics of spin and charge in spin-Calogero model is studied. The latter is an integrable one-dimensional model of quantum spin-1/2 particles interacting through inverse-square interaction and exchange. Classical hydrodynamic equations of motion are written for this model in the regime where gradient corrections to the exact hydrodynamic formulation of the theory may be neglected. In this approximation variables separate in terms of dressed Fermi momenta of the model. Hydrodynamic equations reduce to a set of decoupled Riemann-Hopf (or inviscid Burgers') equations for the dressed Fermi momenta. We study the dynamics of some nonequilibrium spin-charge configurations for times smaller than the time scale of the gradient catastrophe. We find an interesting interplay between spin and charge degrees of freedom. In the limit of large coupling constant the hydrodynamics reduces to the spin hydrodynamics of the Haldane-Shastry model.

Memory effects and transport coefficients for non-Newtonian fluids

We discuss the roles of viscosity in relativistic fluid dynamics from the point of view of memory effects. Depending on the type of quantity to which the memory effect is applied, different terms appear in higher order corrections. We show that when the memory effect applies on the extensive quantities, the hydrodynamic equations of motion become non-singular. We further discuss the question of memory effect in the derivation of transport coefficients from a microscopic theory. We generalize the application of the Green–Kubo–Nakano (GKN) formula to calculate transport coefficients in the framework of projection operator formalism, and derive the general formula when the fluid is non-Newtonian.

Hydrodynamic of Active Liquid Crystals: A Hybrid Lattice Boltzmann Approach

Active gels or active liquid crystals are soft materials which are driven out of equilibrium by their continuum use of chemical energy. Physical realisations of active gels are solutions of cytoskeletal filaments with molecular motors, and concentrated suspensions of bacterial swimmers. Here we focus on the active nematic phase which is exhibited by these materials, and study their hydrodynamics when confined in a slab of a finite height. We solve the hydrodynamic equations of motion by means of a hybrid lattice Boltzmann algorithm. The homogeneous flow is known to be unstable for sufficiently large activity, leading to a state with spontaneous flow in steady state. We characterise the form of this flow in 1 and 2 dimensions with extensile and contractile flow aligning materials.

Viscoelastic Flows of Cholesteric Liquid Crystals

We numerically solve the hydrodynamic equations of motion for a cholesteric liquid crystal under an imposed Poiseuille flow, by means of lattice Boltzmann simulations. The elasticity of the cholesteric helix couples to the external flow to give rise to a highly viscoelastic flow. This is a technically difficult problem for standard flow solvers due to its fully two-dimensional nature. We consider a helix with axis parallel to the boundaries, and at the same time to either the primary flow or the vorticity direction (we identify these two flow modes as permeation and vorticity mode respectively). We quantify the large difference found in the steady state director and velocity profiles, and in the apparent viscosities obtained in the two cases.

RAPID GRANULAR FLOWS

▪ Abstract The recent avalanche of research activity in the field of granular matter has yielded much progress. The use of state-of-the-art (and other) computational and experimental methods has led to the discovery of new states and patterns and enabled detailed tests of theories and models. The application of statistical mechanical methods and phenomenology has contributed to the understanding of the microscopic a nd macroscopic properties of granular systems. Some previously open problems seem to be solved. Fluidized granular systems (rapid granular flows), recently referred to as granular gases, are often modeled by hydrodynamic equations of motion, some of which are based on systematic expansions applied to the pertinent Boltzmann equation. The undeniable success of granular hydrodynamics is somewhat surprising in view of the lack of scale separation in these systems and the neglect of certain correlations in most derivations of the hydrodynamic equations. Microstructures have been recognized as key features of granular gases; explanations for their existence have been proposed, and many of their properties elucidated. Granular-gas multistability can often be traced back to microstructure dynamics. In spite of these and other impressive advances, this field still poses serious challenges.

Hydrodynamic flow of ions and atoms in partially ionized plasmas.

We have derived the hydrodynamic equations of motion for a partially ionized plasma, when the ionized component and the neutral components have different flow velocities and kinetic temperatures. Starting from the kinetic equations for a gas of ions and a gas of atoms we have considered various processes of encounters between the two species: self-collisions, interspecies collisions, ionization, recombination, and charge exchange. Our results were obtained by developing a general approach for the hydrodynamics of a gas in a binary mixture, in particular when the components drift with respect to each other. This was applied to a partially ionized plasma, when the neutral-species gas and the charged-species gas have separate velocities. We have further suggested a generalized version of the relaxation time approximation and obtained the contributions of the interspecies encounters to the transport equations.

Hydrodynamic Approach to Modeling the Thermal Plasma Distribution around a Moving Charged Satellite

The electric field distribution around a charged satellite in a rarefied magnetospheric plasma influences greatly the densities and trajectories of particles measured by onboard instruments. The simulation of macroparameters of thermal plasma near the moving charged satellite, which is necessary for correction of experimental measurements, encounters considerable computational difficulties. In this work, two three-dimensional models of the electric field distribution around the satellite are considered under the conditions when the Debye length is comparable to the geometrical size of the spacecraft. In the first model a system of hydrodynamic equations of continuity and motion was used, which was solved jointly with the Poisson equation. In the second model the hydrodynamic equation of motion was used for analyzing the motion of large particles by means of the method of particles in a cell. The numerical algorithms and the results of calculations of the potential near the satellite, as well as the distributions of densities of electrons and ions and of volume charge, are considered. The results of test calculations for some situations in the ambient plasma are presented, and the influence of the spatial electric field distribution on the thermal plasma measurements is considered.

The role of fenestrations and channels on the transverse motion of a soft contact lens.

Ineffectual removal of potentially harmful species from the postlens tear film (POLTF) may lead to adverse responses among extended wearers of soft contact lenses. It is apparently important to remove bacteria, cell debris, and metabolic products from the postlens tear film to the outer tear lake; the flushing or dispersion rate of these species is enhanced by increasing fluid movement in the tear film driven by periodic lens motion. The contact lens moves laterally (up-down) and transversally (in-out) due to the action of the eyelid forces during blinking. Viscous drag in the POLTF resists lens motion. Consequently, any design change in the lens that reduces viscous drag increases motion and improves flushing of unwanted species from the POLTF. We investigate quantitatively the effect of channels cut on the back surface of the lens and fenestrations (holes) drilled through the lens on transverse lens motion. We model the lens as a curved solid body with a periodic arrangement of channels/holes. The cornea is treated as a flat surface, and the hydrodynamic equations of motion are solved for Newtonian fluid transport in the POLTF assuming lubrication and creeping flow. POLTF pressure profiles, obtained by solving these equations, are integrated to determine the lens settling velocity in the transverse direction for a given amount of applied lid force. Lens settling velocity is then compared with the same velocity in the absence of channels/fenestrations. Further, we calculate the total transverse motion in a blink for lenses with and without channels/fenestrations to estimate the possible enhancement in transverse motion due to the channels/fenestrations. Variables that affect the fluid mixing in the POLTF are the postlens tear film thickness, lens thickness, channel length, depth and spacing, and the hole diameter, location, and spacing. We study the effect of each of these variables on the enhancement of transverse motion for channels and holes of diameters varying from 0.1 to 2 mm with spacing varying from 1 to 5 mm. We demonstrate that incorporation of channels and holes reduces viscous resistance and increases transverse lens motion, and thus increases fluid mixing and dispersive flushing from the POLTF. The increase in transverse motion depends strongly on the postlens tear film thickness. Enhancement of the transverse motion varies from a factor of about 2 to 20 depending on the particular lens design and the postlens tear film thickness. Because fluid mixing increases up to the square of the transverse motion, channels/holes are expected to render flushing of the POLTF considerably more effective. We find that channels and/or fenestrations, when appropriately designed, can provide significant improvement in flushing from the POLTF. This work provides a new quantitative tool for the efficient design of channels/holes in soft contact lenses.

One-dimensional Thomas-Fermi model of atoms, molecules, and small clusters exposed to an intense laser field

We have developed a one-dimensional time-dependent Thomas-Fermi model of atoms, molecules, and small clusters exposed to an intense subpicosecond laser field. In this model, the dynamics of an electronic cloud is governed by the hydrodynamic equations of motion, whereas the nuclei move in accordance with the Newton equations. The quantum mechanics enters in this approach only through the constitutive relation between the pressure and the density, which is derived from the application of Fermi-Dirac statistics to a noninteracting $T=0$ temperature electron gas. The time-independent version of the model, formulated in terms of the integral equation for the electric potential, is also discussed. We present numerical results for diatomic molecules and small clusters irradiated by the strong laser pulses. In the case of molecules, we observe the multielectron ionization accompanied by dissociation. The kinetic energy defect, understood as a reduction of the energy of resulting ions in comparison with a simple Coulomb explosion picture, is explained in terms of a screening effect of escaping fragments by the ejected electrons. For small clusters we find that the explosion of the cluster has a stepwise character; the consecutive layers of atoms are stripped off one by one. We observe the highly energetic (as compared with diatomic systems) atomic fragments even for relatively low laser intensities and a few atoms clusters. Also, the model predicts the nonuniform energy distribution among the same charge state ions and supports the idea of hot electrons generated in the cluster via a mechanism of inverse bremsstrahlung.

Motion of matter in metric-affine theory of gravitation

Based on the Lie derivative technique in a general space with affine connection (L4, g), we show that in the metric-affine theory of gravitation, the law of conservation of the energy-momentum tensor for matter and consequently also the equations of motion for matter stemming from this law are (as in the general theory of relativity) a consequence of the gravitational field equations. We derive the hydrodynamic equation of motion for an ideal Weyssenhoff—Raabe spin fluid in Weyl space. We discuss the possibilities for observation of space—time nonmetricity.

The equation of state and ultrarelativistic energies in the hydrodynamic model

The contributions of the hydrodynamic model to the problem of extracting the equation of state of nuclear matter are discussed with special emphasis on the minimum experimental input needed and the role of viscosity. Then hydrodynamics at ultrarelativistic energies and the methods for obtaining a reliable and accurate solution are introduced, followed by a discussion of a simplified three-fluid model used to study pion production. Finally some fundamental problems concerning the hydrodynamic equations of motion in the dissipative case are indicated.

Model of the electron spin in stochastic physics

The electron is conceived here as a complex structure composed of a subparticle that is bound to a nearly circular motion. Although in quantum mechanics the spin is not representable, in classical stochastic physics this corresponds to the angular momentum of the subparticle. In fact, assuming Schrodinger-type hydrodynamic equations of motion for the subparticle, the spin-1/2 representation in configuration space and the corresponding Pauli matrices for the electron are obtained. The Hamiltonian of Pauli's theory as the nonrelativistic limit of Dirac's equation is also derived.

Multicomponent transport theoretical approach to ultrarelativistic heavy ion collisions

A new theoretical model is introduced which is able to describe the initial compression and thermalization stage of an ultrarelativistic heavy-ion collision in a hydrodynamical three-flow picture. The first and second fluid is attributed to the nucleons of target and projectile, while a third component is introduced in order to take into account the gradual thermalization of the incoming flow. Based on relativistic transport theory, hydrodynamic equations of motion are derived for each component including transitions of target and projectile nucleons to the thermalized matter component as well as mutual deceleration accompanied with gradual heat transfer between the components. Hence, the multicomponent formalism contains the former two fluid approach as a limiting case.

Electromagnetodynamics of polar liquids and suspensions

We study electric and magnetic effects on the dynamics of polar liquids and of fluid suspensions of particles carrying electric and/or magnetic dipole moments. The hydrodynamic equations of motion are discussed in detail and compared with equations proposed in the literature. We derive simplified equations valid on a slow timescale.

A mathematical model for salt intrusion in the Tay Estuary

SynopsisA numerical model based on a Galerkin finite element solution of the one-dimensional salt transport equation is used to simulate the unsteady longitudinal distribution of salinity in the Tay Estuary. Tidal discharges are provided by the hydrodynamical equations of motion and continuity whose solution is coupled to that for the transport of salt. Dispersion coefficients used in the model are estimated with the aid of field data collected during a spring and neap tide. These coefficients are shown to vary with longitudinal position.