Ordinary Hydrodynamics Research Articles

Linear mode analysis and spin relaxation

In this paper, a detailed analysis on normal modes of the linearized Hermite collision operator is presented, which follows from linearizing spin Boltzmann equation for massive fermions proposed in [Phys. Rev. D 104, 016022 (2021)] with the nondiagonal part of the transition rate neglected and approximating what we got with a mutilated operator. With the assumption of total angular momentum conservation, the collision term is proven to well describe the equilibrium state and gives proper interpretation for collisional invariants, thus is relevant for the research on local spin polarization. Following the familiar fashion as used in quantum mechanics, we treat the problem of solving normal modes as a degenerate perturbation problem and calculate the dispersion relations for intriguing eleven zero modes, which form one-to-one correspondence to all collisional invariants. We find that the results of spinless modes appearing in ordinary hydrodynamics are consistent with available conclusions in textbooks. As for spin-related modes, we obtain the frequencies up to second order in a wave vector and relate them with the dissipation of spin density fluctuation. In addition, the ratio of two relaxation timescales for spin and momentum is shown as a function of reduced mass, which reads that based on present framework spin equilibration is almost as slow as momentum equilibration as far as the strange quark spins in quark gluon plasma (QGP) are concerned.

Rapidity decorrelation of anisotropic flow caused by hydrodynamic fluctuations

We investigate the effect of hydrodynamic fluctuations on the rapidity decorrelations of anisotropic flow in high-energy nuclear collisions using a (3+1)-dimensional integrated dynamical model. The integrated dynamical model consists of twisted initial conditions, fluctuating hydrodynamics, and hadronic cascades on an event-by-event basis. To understand the rapidity decorrelation, we analyze the factorization ratio in the longitudinal direction. Comparing the factorization ratios between fluctuating hydrodynamics and ordinary viscous hydrodynamics, we find a sizable effect of hydrodynamic fluctuations on rapidity decorrelations. We also propose to calculate the Legendre coefficients of the flow magnitude and the event-plane angle to understand the decorrelation of anisotropic flow in the longitudinal direction.

Transport and hydrodynamics in the chiral limit

We analyze the evolution of hydrodynamic fluctuations for QCD matter below $T_c$ in the chiral limit, where the pions (the Goldstone modes) must be treated as additional non-abelian superfluid degrees of freedom, reflecting the broken $SU_L(2) \times SU_R(2)$ symmetry of the theory. In the presence of a finite pion mass $m_{\pi}$, the hydrodynamic theory is ordinary hydrodynamics at long distances, and superfluid-like at short distances. The presence of the superfluid degrees of freedom then gives specific contributions to the bulk viscosity, the shear viscosity, and diffusion coefficients of the ordinary theory at long distances which we compute. This determines, in some cases, the leading dependence of the transport parameters of QCD on the pion mass. We analyze the predictions of this computation, as the system approaches the $O(4)$ critical point.

Acoustic modes in He I and He II in the presence of an alternating electric field

The vibrational modes in isotropic nonpolar dielectrics He I and He II are studied in the presence of an alternating electric field E = E0izsin(k0z–ω0t), by solving the equations of ordinary and two-fluid hydrodynamics. There is a “coupling” between the electric field and the density fluctuations, since the density gradient leads to the spontaneous polarization Ps, and the electric force contains the term (Ps∇) E. Analysis shows that the wave velocities of the first- and second-sounds propagating along E change according to the formula uj ≈ cj + χjE02 (where j = 1, 2; cj is the speed of the jth sound at E0 = 0, and χj is a constant). It is found that the field E, together with the wave of the first- (second) sound (ω, k), should create in He II hybrid acoustoelectric (thermoelectric) density waves (ω + lω0, k + lk0), where l = ± 1, ± 2,… The amplitudes of the acoustoelectric waves and the quantity |u1−c1| are negligibly small, but at certain ω and ω0 they should increase resonantly. The first resonance seems to correspond to the decay of a photon into two photons with the recoil momentum being transferred to the liquid as a whole. Therefore, the electromagnetic signal spectrum should have a narrow absorption line, similar to the Mössbauer effect.

Generalization of the Kutta–Joukowski theorem for the hydrodynamic forces acting on a quantized vortex

The hydrodynamic forces acting on a quantized vortex in a superfluid have long been a highly controversial issue. A new approach, originally developed in the astrophysical context of compact stars, is presented to determine these forces by considering small perturbations of the asymptotically uniform flows in the region far from the vortex in the framework of Landau–Khalatnikov two-fluid model. Focusing on the irrotational part of the flows in the Helmholtz decomposition, the classical Kutta–Joukowski theorem from ordinary hydrodynamics is thus generalized to superfluid systems. The same method is applied to predict the hydrodynamic forces acting on vortices in cold atomic condensates and superfluid mixtures.

A study of the stability properties in simulation of wave propagation with SPH method

When ordinary Smoothed Particle Hydrodynamics (SPH) method is used to simulate wave propagation in a wave tank, it is usually observed that the wave height decays and the wave length elongates along the direction of wave propagation. Accompanied with this phenomenon, the pressure under water decays either and shows a big oscillation simultaneously. The reason is the natural potential tensile instability of modeling water motion with ordinary SPH which is caused by particle negative stress in the computation. To deal with the problems, a new sextic kernel function is proposed to reduce this instability. An appropriate smooth length is given and its computation criterion is also suggested. At the same time, a new kind dynamic boundary condition is introduced. Based on these improvements, the new SPH method named stability improved SPH (SISPH) can simulate the wave propagation well. Both the water surface and pressure can be well expressed and the oscillation of pressure is nearly eliminated. Compared with other improved methods, SISPH can truly reveal the physical reality without bringing some new problems in a simple way.

Holographic thermalization with radial flow

Recently, a lot of effort has been put into describing the thermalization of the quark-gluon plasma using the gauge/gravity duality. In this context, we here present a full numerical solution of the early far-from-equilibrium formation of the plasma, which is expanding radially in the transverse plane and is boost invariant along the collision axis. This can model the early stage of a head-on relativistic heavy ion collision. The resulting momentum distribution quickly reaches local equilibrium, after which it can be evolved using ordinary hydrodynamics. We comment on general implications for these hydrodynamic simulations, both for central and noncentral collisions, and including fluctuations in the initial state.

Dissipation in relativistic superfluid neutron stars

We analyze damping of oscillations of general relativistic superfluid neutron stars. To this aim we extend the method of decoupling of superfluid and normal oscillation modes first suggested in [Gusakov & Kantor PRD 83, 081304(R) (2011)]. All calculations are made self-consistently within the finite temperature superfluid hydrodynamics. The general analytic formulas are derived for damping times due to the shear and bulk viscosities. These formulas describe both normal and superfluid neutron stars and are valid for oscillation modes of arbitrary multipolarity. We show that: (i) use of the ordinary one-fluid hydrodynamics is a good approximation, for most of the stellar temperatures, if one is interested in calculation of the damping times of normal f-modes; (ii) for radial and p-modes such an approximation is poor; (iii) the temperature dependence of damping times undergoes a set of rapid changes associated with resonance coupling of neighboring oscillation modes. The latter effect can substantially accelerate viscous damping of normal modes in certain stages of neutron-star thermal evolution.

On isotropic turbulence in the dark fluid universe

As a first part of this work, experimental information about the decay of isotropic turbulence in ordinary hydrodynamics, $\overline{\mathbf{u}^{2}(t)}\propto t^{-6/5}$ , is used as input in FRW equations in order to investigate how an initial fraction f of turbulent kinetic energy in the cosmic fluid influences the cosmological development in the late, quintessence/phantom, universe. First order perturbative theory to the first order in f is employed. It turns out that both in the Hubble factor and in the energy density, the influence from the turbulence fades away at late times. The divergences in these quantities near the Big Rip behave essentially as in a non-turbulent fluid. However, for the scale factor, the turbulence modification turns out to diverge logarithmically. As a second part of our work, we consider the full FRW equation in which the turbulent part of the dark energy is accounted for by a separate term. It is demonstrated that turbulence occurrence may change the future universe evolution due to dissipation of dark energy. For instance, the phantom-dominated universe becomes asymptotically a de Sitter one in the future, thus avoiding the Big Rip singularity.

On the analogy between streamlined magnetic and solid obstacles

Analogies are elaborated in the qualitative description of two systems: the magnetohydrodynamic (MHD) flow moving through a region where an external local magnetic field (magnetic obstacle) is applied and the ordinary hydrodynamic flow around a solid obstacle. The former problem is of interest both practically and theoretically, and the latter one is a classical problem being well understood in ordinary hydrodynamics. The first analogy is the formation in the MHD flow of an impenetrable region—core of the magnetic obstacle—as the interaction parameter N, i.e., strength of the applied magnetic field, increases significantly. The core of the magnetic obstacle is streamlined both by the upstream flow and by the induced cross-stream electric currents, such as a foreign insulated insertion placed inside the ordinary hydrodynamic flow. In the core, closed streamlines of the mass flow resemble contour lines of electric potential, while closed streamlines of the electric current resemble contour lines of pressure. The second analogy is the breaking away of attached vortices from the recirculation pattern produced by the magnetic obstacle when the Reynolds number Re, i.e., velocity of the upstream flow, is larger than a critical value. This breaking away of vortices from the magnetic obstacle is similar to that occurring past a solid obstacle. Depending on the inlet and/or initial conditions, the observed vortex shedding can be either symmetric or asymmetric.

Anomalous Flow Deflection at Earth’s Low-Alfvén-Mach-Number Bow Shock

Earth's magnetosphere is an obstacle to the supersonic solar wind and the bow shock is formed in the front side of it. In ordinary hydrodynamics, the flow decelerated at the shock is diverted around the obstacle symmetrically about the Earth-Sun line, which is indeed observed in the magnetosheath most of the time. Here we show a case under a very low-density solar wind in which duskward flow was observed in the dawnside magnetosheath. A Rankine-Hugoniot test shows that the magnetic effect is crucial for this "wrong flow" to appear. A full three-dimensional magnetohydrodynamics (MHD) simulation of the situation confirming this interpretation and earlier simulations is also performed. It is illustrated that in addition to the "wrong flow" feature, various peculiar characteristics appear in the global picture of the MHD flow interaction with the obstacle.

Experimental study of liquid metal channel flow under the influence of a nonuniform magnetic field

We present an experimental study of a liquid metal flow in a rectangular channel under the influence of an inhomogeneous magnetic field. This is a fundamental problem of liquid metal magnetohydrodynamics that is relevant to the technique of electromagnetic braking in the process of continuous casting of steel as well as for Lorentz force velocimetry. Based on local velocity and electric potential measurements we identify three distinct flow regions; namely (i) a turbulence suppression region, (ii) a vortical region, and (iii) a wall jet region. It is shown that in region (i) the applied inhomogeneous magnetic field brakes the incoming flow in its central part and transforms the velocity profile, which is initially flat, into an M-shaped form. In the central part of the flow, the intensity of the velocity fluctuations is found to decrease strongly. In region (ii) where the magnetic field is strongest, the flow is characterized by large-scale vortical structures which are time dependent for certain values of the control parameters. In region (iii), downstream of the magnetic system, two sidewall boundary layers are observed which generate velocity fluctuations with intensity up to 25% of the mean flow. These boundary layers bear close resemblance to wall jets known from ordinary hydrodynamics. Our experimental data provide a comprehensive database against which numerical simulations and turbulence models can be tested.

Modeling NIF experimental designs with adaptive mesh refinement and Lagrangian hydrodynamics

Incorporation of adaptive mesh refinement (AMR) into Lagrangian hydrodynamics algorithms allows for the creation of a highly powerful simulation tool effective for complex target designs with three-dimensional structure. We are developing an advanced modeling tool that includes AMR and traditional arbitrary Lagrangian-Eulerian (ALE) techniques. Our goal is the accurate prediction of vaporization, disintegration and fragmentation in National Ignition Facility (NIF) experimental target elements. Although our focus is on minimizing the generation of shrapnel in target designs and protecting the optics, the general techniques are applicable to modern advanced targets that include three-dimensional effects such as those associated with capsule fill tubes. Several essential computations in ordinary radiation hydrodynamics need to be redesigned in order to allow for AMR to work well with ALE, including algorithms associated with radiation transport. Additionally, for our goal of predicting fragmentation, we include elastic/plastic flow into our computations. We discuss the integration of these effects into a new ALE-AMR simulation code. Applications of this newly developed modeling tool as well as traditional ALE simulations in two and three dimensions are applied to NIF early-light target designs.

Thermal conduction in cosmological SPH simulations

Thermal conduction in the intracluster medium has been proposed as a possible heating mechanism for offsetting central cooling losses in rich clusters of galaxies. In this study, we introduce a new formalism to model conduction in a diffuse ionised plasma using smoothed particle hydrodynamics (SPH), and we implement it in the parallel TreePM/SPH-code GADGET-2. We consider only isotropic conduction and assume that magnetic suppression can be described in terms of an effective conductivity, taken as a fixed fraction of the temperature-dependent Spitzer rate. We also account for saturation effects in low-density gas. Our formulation manifestly conserves thermal energy even for individual and adaptive timesteps, and is stable in the presence of small-scale temperature noise. This allows us to evolve the thermal diffusion equation with an explicit time integration scheme along with the ordinary hydrodynamics. We use a series of simple test problems to demonstrate the robustness and accuracy of our method. We then apply our code to spherically symmetric realizations of clusters, constructed under the assumptions of hydrostatic equilibrium and a local balance between conduction and radiative cooling. While we confirm that conduction can efficiently suppress cooling flows for an extended period of time in these isolated systems, we do not find a similarly strong effect in a first set of clusters formed in self-consistent cosmological simulations. However, their temperature profiles are significantly altered by conduction, as is the X-ray luminosity.

The history of star formation in a cold dark matter universe

Employing hydrodynamic simulations of structure formation in a A cold dark matter cosmology, we study the history of cosmic star formation from the 'dark ages' at redshift z ∼20 to the present. In addition to gravity and ordinary hydrodynamics, our model includes radiative heating and cooling of gas, star formation, supernova feedback and galactic winds. By making use of a comprehensive set of simulations on interlocking scales and epochs, we demonstrate numerical convergence of our results on all relevant halo mass scales, ranging from 10 8 to 10 1 5 h - 1 M O .. The predicted density of cosmic star formation, ρ * (z), is broadly consistent with measurements, given the observational uncertainty. From the present epoch, ρ * (z) gradually rises by approximately a factor of 10 to a peak at z ∼5-6, which is beyond the redshift range where it has been estimated observationally. In our model, fully 50 per cent of the stars are predicted to have formed by redshift z ≃ 2.14, and are thus older than 10.4 Gyr, while only 25 per cent form at redshifts lower than z ≃ 1. The mean age of all stars at the present is approximately 9 Gyr. Our model predicts a total stellar density at z = 0 of Ω * = 0.004, corresponding to approximately 10 per cent of all baryons being locked up in long-lived stars, in agreement with recent determinations of the luminosity density of the Universe. We determine the 'multiplicity function of cosmic star formation' as a function of redshift; i.e. the distribution of star formation with respect to halo mass. At redshifts around z ≃ 10, star formation occurs preferentially in haloes of mass 10 8 -10 1 0 h - 1 M O ., while at lower redshifts, the dominant contribution to ρ * (z) comes from progressively more massive haloes. Integrating over time, we find that approximately 50 per cent of all stars formed in haloes less massive than 10 1 1 . 5 h - 1 M O ., with nearly equal contributions per logarithmic mass interval in the range 10 1 0 -10 1 3 . 5 h - 1 M O ., making up ∼70 per cent of the total. We also briefly examine possible implications of our predicted star formation history for reionization of hydrogen in the Universe. According to our model, the stellar contribution to the ionizing background is expected to rise for redshifts z > 3, at least up to redshift z ∼5, in accord with estimates from simultaneous measurements of the H and He opacities of the Lyman-a forest. This suggests that the ultraviolet background will be dominated by stars for z > 4, provided that there are not significantly more quasars at high z than are presently known. We measure the clumping factor of the gas from the simulations and estimate the growth of cosmic H II regions, assuming a range of escape fractions for ionizing photons. We find that the star formation rate predicted by the simulations is sufficient to account for hydrogen reionization by z ∼6, but only if a high escape fraction close to unity is assumed.

Magnetohydrodynamic Heat Transfer Research Related to the Design of Fusion Blankets

Lithium or any lithium alloy like the lithium lead alloy Pb-17Li is an attractive breeder material used in blankets of fusion power reactors because it allows the breeding of tritium and, in the case of self-cooled blankets, the transfer of the heat generated within the liquid metal and the walls of the cooling ducts to an external heat exchanger. Nevertheless, this type of liquid-metal-cooled blanket, called a self-cooled blanket, requires specific design of the coolant ducts, because the interaction of the circulating fluid and the plasma-confining magnetic fields causes magnetohydrodynamic (MHD) effects, yielding completely different flow patterns compared to ordinary hydrodynamics (OHD) and pressure drops significantly higher than there. In contrast to OHD, MHD flows depend strongly on the electrical properties of the wall. Also, MHD flows reveal anisotropic turbulence behavior and are quite sensitive to obstacles exposed to the fluid flow.A comprehensive study of the heat transfer characteristics of free and forced convective MHD flows at fusion-relevant conditions is conducted. The general ideas of the analytical and numerical models to describe MHD heat transfer phenomena in this parameter regime are discussed. The MHD laboratory being installed, the experimental program established, and the experiments on heat transfer of free and forced convective flow being conducted are described. The theoretical results are compared to the results of a series of experiments in forced and free convective MHD flows with different wall properties, such as electrically insulating as well as electric conducting ducts. Based on this knowledge, methods to improve the heat transfer by means of electromagnetic/mechanic turbulence promoters (TPs) or sophisticated, arranged electrically conducting walls are discussed, experimental results are shown, and a cost-benefit analysis related to these methods is performed. Nevertheless, a few experimental results obtained should be highlighted:1. The heat flux removable in rectangular electrically conducting ducts at walls parallel to the magnetic field is by a factor of 2 higher than in the slug flow model previously used in design calculations. Conditions for which this heat transfer enhancement is attainable are presented. The measured dimensionless pressure gradient coincides with the theoretical one and is constant throughout the whole Reynolds number regime investigated (Re = 103 → 105), although the flow turns from laminar to turbulent. The use of electromagnetic TPs close to the heated wall leads to nonmeasurable increase of the heat transfer in the same Re regime as long as they do not lead to an interaction with the wall adjacent boundary layers.2. Mechanical TPs used in an electrically insulated rectangular duct improved the heat transfer up to seven times compared to slug flow, but the pressure drop can increase also up to 300%. In a cost-benefit analysis, the advantageous parameter regime for applying this method is determined.3. Experiments performed in a flat box both in a vertical and a horizontal arrangement within a horizontal magnetic field show the expected increase of damping of the fluid motion with increasing Hartmann number M. At high M, buoyant convection will be completely suppressed in the horizontal case. In the vertical setup, the fluid motion is reduced to one large vortex leading to a decreasing heat transfer between heated and cooled plate to pure heat conduction.From an analysis of the experimental and theoretical results, general design criteria are derived for the orientation and shape of the first wall coolant ducts of self-cooled liquid metal blankets. Methods to generate additional turbulence within the flow, which can improve the heat transfer further are elaborated.

Motion of magnetic flux lines in magnetohydrodynamics

A gauge-free description of magnetohydrodynamic flows of an ideal incompressible fluid, which takes into account the freezing-in of the magnetic field and the presence of cross invariants containing the vorticity, is obtained. This description is an extension of the canonical formalism well-known in ordinary hydrodynamics to the dynamics of frozen-in flux lines. Magnetohydrodynamics is studied as the long-wavelength limit of the two-fluid model of a plasma, in which the existence of two frozen-in fields — curls of the generalized momenta of the electron and ion fluids — follows from the symmetry of each component with respect to relabeling of the Lagrangian labels. The cross invariants in magnetohydrodynamics are limits of special combinations of topological invariants of the two-fluid model. A variational principle is formulated for the dynamics of frozen-in magnetic flux lines, and the Casimir functionals of the noncanonical Poisson brackets are found.

Hydrodynamics of modulated finite-amplitude waves in dispersive media

Analytic approaches are developed for integrating the nondiagonalizable Whitham equations for the generation and propagation of nonlinear modulated finite-amplitude waves in dissipationless dispersive media. Natural matching conditions for these equations are stated in a general form analogous to the Gurevich-Pitaevskii conditions for the averaged Korteweg-de Vries equations. Exact relationships between the hydrodynamic quantities on different sides of a dissipationless shock wave, an analog of the shock adiabat in ordinary dissipative hydrodynamics and first proposed on the basis of physical considerations by Gurevich and Meshcherkin, are obtained. The boundaries of a self similar, dissipationless shock wave are determined analytically as a function of the density jump. Some specific examples are considered.

The Ponderomotive Force on a Charge q, Moving in an Electromagnetic Field

AbstractEquations of motion of a single charged particle are derived to second order in E where E is an electromagnetic field. By averaging over the wave‐period we find the ponderomotive force on the particle. This force may lead to a transport of matter as is also the case in ordinary hydrodynamics. There the effect is called acoustic streaming. We also suggest that the well‐known Landau damping may be considered as beeing due to a ponderomotive force.

The Dynamics of Thin Films on Reaction Surfaces

Abstract A model is proposed for heterogeneous ignition and extinction in terms of the dynamics of a thin inert layer covering the surfaces of condensed-phase components in a combustion reaction, the layer consisting of reaction products or impurities which collect in the reaction surface. Heterogeneous ignition then is associated with the formation and the spreading of ruptures and punctures in the surface layer, whereas extinction is associated with the formation and the spreading of layer fragments in the form of “caps” or “islands”. For a liquid layer, the model describes the dynamics of a liquid edge where the layer thickness changes from macroscopic to microscopic values. Such a description is in terms of ordinary hydrodynamics only for layer thicknesses which are large enough. Consequently, an intermediate “mesoscopic” range exists which separates macroscopic from microscopic thicknesses, designating the transition range where ordinary hydrodynamics changes over into different forms of transport. T...