Ideal Fluid Dynamics Research Articles

Emergent symmetries of relativistic fluid dynamics from local ergodicity

We show that volume-preserving diffeomorphisms and the chemical shift symmetry defining relativistic Lagrangian ideal fluid dynamics can be derived as an emerging symmetry when ergodicity is assumed to apply locally in a way that is invariant under smooth spacetime foliations. This can be used as a way to derive the ideal hydrodynamic limit in a strongly coupled but strongly fluctuating medium. We comment on the connection with thermalization in small systems, the eigenstate thermalization hypothesis and deviations from the ideal limit. Published by the American Physical Society 2024

Nambu Bracket for 3D Ideal Fluid Dynamics and Magnetohydrodynamics

Abstract The ideal magnetohydrodynamics (MHD) as well as the ideal fluid dynamics is governed by a Hamilton equation with respect to the Lie–Poisson bracket. The Nambu bracket manifestly represents the Lie–Poisson structure in terms of derivatives of the Casimir invariants. We construct a compact Nambu bracket representation for the 3D ideal MHD equations with the use of three Casimirs for the second Hamiltonians, the total entropy, and the magnetic and cross-helicities, whose coefficients are all constant. The Lie–Poisson bracket induced by this Nambu bracket does not coincide with the original one, but is supplemented by terms with an auxiliary variable. The supplemented Lie–Poisson bracket qualifies the cross-helicity as the Casimir. By appealing to Noether’s theorem, we show that the cross-helicity is an integral invariant associated with the particle-relabeling symmetry. Employing a Lagrange label function as the independent variable in the variational framework facilitates implementation of the relabeling transformation. By incorporating the divergence symmetry, other known topological invariants are put on the same ground as Noether’s theorem.

Computational fluid dynamics modeling of a discrete feed atomic layer deposition reactor: Application to reactor design and operation

Novel transistor fabrication methods such as area-selective atomic layer deposition (AS-ALD) are crucial to improving nanopatterning, which is essential for facilitating transistor stacking in semiconducting wafers. However, transistor surfaces are subjected to nonuniformities during the initial AS-ALD adsorption reactions that are attributed to steric hindrance effects. To minimize the role of steric hindrance generated by an oversaturation of reagent on the substrate surface, a discrete feed method is proposed for an ALD reactor configuration where reagent is introduced in short pulses through a perpendicular delivery system. An optimal reactor configuration is developed by modifying the inlet geometries of the reactor to ensure ideal fluid dynamics conditions (e.g., minimal vortices, radial flow distribution) are achieved. Detailed computational fluid dynamics simulations demonstrate the performance of the new reactor configuration and operational strategy.

Lagrangian reduction and wave mean flow interaction

How does one derive models of dynamical feedback effects in multiscale, multiphysics systems such as wave mean flow interaction (WMFI)? We shall address this question for hybrid dynamical systems, defined as systems whose motion can be expressed as the composition of two or more Lie-group actions. Hybrid systems abound in fluid dynamics. Examples include: the dynamics of complex fluids such as liquid crystals; wind-driven waves propagating with the currents moving on the sea surface; turbulence modelling in fluids and plasmas; and classical–quantum hydrodynamic models in molecular chemistry. From among these examples, the motivating question here is: How do wind-driven waves produce ocean surface currents?The paper first summarises the geometric mechanics approach for deriving hybrid models of multiscale, multiphysics motions in ideal fluid dynamics. It then illustrates this approach for WMFI in the examples of 3D WKB waves and 2D wave amplitudes governed by the nonlinear Schrödinger (NLS) equation propagating in the frame of motion of an ideal incompressible inhomogeneous Euler fluid flow. The results for these examples tell us that the mean flow in WMFI does not create waves, although it does transport the waves. However, feedback in the opposite direction is possible, since the 3D WKB and 2D NLS wave dynamics discussed here do in fact create circulatory mean flow.

Dissipation-induced acoustic nonreciprocity

Linear acoustic transmission through a stationary elastic medium possesses Rayleigh reciprocal symmetry with respect to pressure produced by a source at point A(B) and measured at point B(A), pA(rB) = pB(rA). In ideal (inviscid) fluids, pressure plays the role of the scalar potential for velocity, v∼∇p. The Rayleigh reciprocity theorem is formulated for velocity potentials but not for their gradients. Any function of the absolute value of velocity, v(r), lacks reciprocal symmetry. In particular, acoustic intencity I = pv is not symmetric, IA(rB) ≠ IB(rA). Dynamics of ideal fluid is time-reversible, and lack of reciprocal symmetry is attributed to asymmetry in scattering. However, in a viscous environment dissipation breaks T symmetry making fluid dynamics irreversible. We report that acoustic transmission is not only irreversible but also becomes nonreciprocal due to different amount of dissipated energy for forward and backward propagation, provided that mirror symmetry (P symmetry) is broken. Since dissipation occurs within a narrow viscous layer at solid–fluid interface, the amount of nonreciprocity in transmission strongly depends on the quality of the surface of scatterers. Experiments performed with scatterers of different surface quality show how surface roughness affects the level of nonreciprocity. In a series of experiments with asymmetric phononic crystal, Tesla valve, and acoustic cavity, we demonstrate dissipation-induced nonreciprocity in transmission. [This work is supported by the NSF under EFRI Grant No. 1741677.]

An efficient geometric method for incompressible hydrodynamics on the sphere

We present an efficient and highly scalable geometric numerical method for two-dimensional ideal fluid dynamics on the sphere. The starting point is Zeitlin's finite-dimensional model of hydrodynamics. The efficiency stems from exploiting a tridiagonal splitting of the discrete spherical Laplacian combined with highly optimized, scalable numerical algorithms. For time-stepping, we adopt a recently developed isospectral integrator able to preserve the geometric structure of Euler's equations, in particular conservation of the Casimir functions. To overcome previous computational bottlenecks, we formulate the matrix Lie algebra basis through a sequence of tridiagonal eigenvalue problems, efficiently solved by well-established linear algebra libraries. The same tridiagonal splitting allows for computation of the stream matrix, involving the inverse Laplacian, for which we design an efficient parallel implementation on distributed memory systems. The resulting overall computational complexity is O(N3) per time-step for N2 spatial degrees of freedom. The dominating computational cost is matrix-matrix multiplication, carried out via the parallel library ScaLAPACK. Scaling tests show approximately linear scaling up to around 2500 cores for the matrix size N=4096 with a computational time per time-step of about 0.55 seconds. These results allow for long-time simulations and the gathering of statistical quantities while simultaneously conserving the Casimir functions. We illustrate the developed algorithm for Euler's equations at the resolution N=2048.

Ideal gas law and fluid dynamics simulation: characterizing an air bubble rising from the bottom of a lake

The use of animations, simulations, and remote lab experiments has taken a new turn during the pandemic. When teaching introductory-level physics courses, the simulations and animations play an important role. Carefully designed simulations assist students visualize real-life situations and help understand complex physics concepts behind them. Some of these simulations guide students to understand the problem itself and encourage them to adjust variables and observe the changes. Not to mention, both students and instructors can benefit from these simulations in any environment, remote, or in-person. We designed a simulation to demonstrate the rise of an air bubble from a certain depth of a lake. Assuming the gas trapped inside the air bubble to be ideal, using Ideal Gas Law, we designed the simulation to show how the volume of the bubble expands as it ascends. To solve for volume as it reaches the surface, we employed knowledge from fluid dynamics. We incorporated equations to account for the pressure variations with the depth. Unlike in other simulations, here we share a link with the user, permitting them to alter the program. This gives users an opportunity to understand the coding of the simulation, if they are interested in creating similar animations in the future.

The kinetic origin of the fluid helicity—A symmetry in the kinetic phase space

Helicity, a topological degree that measures the winding and linking of vortex lines, is preserved by ideal (barotropic) fluid dynamics. In the context of the Hamiltonian description, the helicity is a Casimir invariant characterizing a foliation of the associated Poisson manifold. Casimir invariants are special invariants that depend on the Poisson bracket, not on the particular choice of the Hamiltonian. The total mass (or particle number) is another Casimir invariant, whose invariance guarantees the mass (particle) conservation (independent of any specific choice of the Hamiltonian). In a kinetic description (e.g., that of the Vlasov equation), the helicity is no longer an invariant (although the total mass remains a Casimir of the Vlasov’s Poisson algebra). The implication is that some “kinetic effect” can violate the constancy of the helicity. To elucidate how the helicity constraint emerges or submerges, we examine the fluid reduction of the Vlasov system; the fluid (macroscopic) system is a “sub-algebra” of the kinetic (microscopic) Vlasov system. In the Vlasov system, the helicity can be conserved if a special helicity symmetry condition holds. To put it another way, breaking helicity symmetry induces a change in the helicity. We delineate the geometrical meaning of helicity symmetry and show that for a special class of flows (the so-called epi-two-dimensional flows), the helicity symmetry is written as ∂γ = 0 for a coordinate γ of the configuration space.

Numerical Calculations of the GRP Scheme for Nonconservative Ideal Fluid Mechanics Equations Relying on Parallel Calculation of Multifluid Grids

In order to solve the numerical method of nonconservative ideal hydrodynamics equations, the viscous perturbation technique for solving nonconservative hydrodynamics equations is improved and tested by solving the Riemann problem. The calculation of nonconservative ideal fluid mechanics is based on the GRP format. This article aims at the calculation method of nonconservative ideal fluid mechanics in the GRP format. Riemann and the corresponding periodic vortex are processed. The multifluid network processing method in the article is compared with the current method. The result can prove that this format can be used to solve the nonconservative ideal fluid dynamics equation of multiple values in the GRP format group, its computing power is strong, and the result of the solution is accurate.

Structure and dynamics of concentrated mesoscale vortices in planetary atmospheres

Concentrated vortices are spatially localized structures with nonzero vorticity surrounded by a potential flow. These structures include a broad class of mesoscale vortices, such as dust devils, water vortices, and fire vortices, as well as larger-scale and more intense tornados. From a rather broad class of concentrated mesoscale vortices, dust devils are selected as the simplest and most easily observable structures owing to dust particles that play the role of tracers. The aim of this review is to present the main results of studies of dust devils in the atmospheres of Earth and Mars. In the framework of ideal fluid dynamics, a recently proposed model is discussed that allows describing vortex structures that are fully localized in space. The results of numerical modeling of vortex dynamics and an analytic model of vortex generation in a convectively unstable atmosphere are briefly discussed.

Implications of Kunita\u2013It\xf4\u2013Wentzell Formula for k-Forms in Stochastic Fluid Dynamics

We extend the Itô–Wentzell formula for the evolution of a time-dependent stochastic field along a semimartingale to k-form-valued stochastic processes. The result is the Kunita–Itô–Wentzell (KIW) formula for k-forms. We also establish a correspondence between the KIW formula for k-forms derived here and a certain class of stochastic fluid dynamics models which preserve the geometric structure of deterministic ideal fluid dynamics. This geometric structure includes Eulerian and Lagrangian variational principles, Lie–Poisson Hamiltonian formulations and natural analogues of the Kelvin circulation theorem, all derived in the stochastic setting.

Penetration Behavior of High-Density Reactive Material Liner Shaped Charge.

The traditional polytetrafluoroethylene (PTFE)/Al reactive material liner shaped charge generally produces insufficient penetration depth, although it enlarges the penetration hole diameter by chemical energy release inside the penetration crater. As such, a novel high-density reactive material liner based on the PTFE matrix was fabricated, and the corresponding penetration performance was investigated. Firstly, the PTFE/W/Cu/Pb high-density reactive material liner was fabricated via a cold pressing/sintering process. Then, jet formation and penetration behaviors at different standoffs were studied by pulse X-ray and static experiments, respectively. The X-ray results showed that the PTFE/W/Cu/Pb high-density reactive material liner forms an excellent reactive jet penetrator, and the static experimental results demonstrated that the penetration depth of this high-density reactive jet increased firstly and then decreased by increasing the standoff. When the standoff was 1.5 CD (charge diameter), the penetration depth of this reactive jet reached 2.82 CD, which was significantly higher than that of the traditional PTFE/Al reactive jet. Moreover, compared with the conventional metal copper jet penetrating steel plates, the entrance hole diameter caused by this high-density reactive jet improved 29.2% at the same standoff. Lastly, the chemical reaction characteristics of PTFE/W/Cu/Pb reactive materials were analyzed, and a semi-empirical penetration model of the high-density reactive jet was established based on the quasi-steady ideal incompressible fluid dynamics theory.

Emergence of Self-Excited Oscillations in Flows of Inviscid Fluids in a Channel

The mechanism of self-excited oscillations arising in an ideal incompressible fluid flowing through a rectangular channel is studied numerically. The problem is formulated in the form of the Euler equations for ideal fluid dynamics in terms of vorticity and stream function with Yudovich’s boundary conditions. The vorticity intensity at the inlet of the channel is used as a bifurcation parameter. Grid approximations are employed to search for steady-state regimes and to analyze their stability, while the nonstationary problem is solved by applying the vortex-in-cell method. It is shown that a steady flow through the channel is established when the vorticity intensity at the inlet is low. As the vorticity intensity at the inlet grows, the steady-state regime becomes unstable in an oscillatory manner and self-excited oscillations emerge in its neighborhood. The evolution of the self-excited oscillations with an increasing bifurcation parameter is studied. In the case of high supercriticality, a chaotic flow regime is observed in the channel.

Design and performance evaluation of a portable hybrid desalination unit using direct contact membrane distillation in dual configuration

In this work, we propose a standalone portable desalination unit that is based on direct contact membrane distillation (DCMD) technology and is powered by hybrid solar energy. The novel dual channel DCMD module enables reserving the compact size of the unit and high production rates. The unit has a net membrane area of 0.042-m2 and is evaluated under several feed temperatures using both ideal assumptions and practical computational fluid dynamics (CFD) validated modeling. Results shows that at feed temperature of 40°C and permeate temperature of 25°C, the unit can produce 2.31 L/day of freshwater without any external heat source as two stages of heat utilization are allowed.

Hydrodynamic Models and Confinement Effects by Horizontal Boundaries

Confinement effects by rigid boundaries in the dynamics of ideal fluids are considered from the perspective of long-wave models and their parent Euler systems, with the focus on the consequences of establishing contacts of material surfaces with the confining boundaries. When contact happens, we show that the model evolution can lead to the dependent variables developing singularities in finite time. The conditions and the nature of these singularities are illustrated in several cases, progressing from a single layer homogeneous fluid with a constant pressure free surface and flat bottom, to the case of a two-fluid system contained between two horizontal rigid plates, and finally, through numerical simulations, to the full Euler stratified system. These demonstrate the qualitative and quantitative predictions of the models within a set of examples chosen to illustrate the theoretical results.

Methods of the Lagrangian and Hamiltonian Mechanics in Aeroacoustics Problems

It is well known that a sound source related to nonstationary motion of vortices at small Mach numbers can be obtained in the incompressible inviscid fluid approximation. In this study, it is proposed to describe the perturbation dynamics of an incompressible ideal fluid using the Lagrangian and Hamiltonian formalism with the displacement field and momentum density perturbation as canonical variables. Based on Noether’s theorem, the conditions of quadrupole moment conservation in the evolution of small perturbations of stationary flows have been formulated. It has been shown that these conditions are always satisfied for perturbations of uniform jet flows. The obtained results not only yield a solution to the general mechanics problem on motion integrals; they are also significant in aeroacoustics because the quadrupole moment of a vortex flow is the principal term of sound source expansion in the Mach number.

I-RheoGT: Transforming from Time to Frequency Domain without Artifacts

We present a new analytical tool for educing the frequency-dependent complex shear modulus of materials from computer-aided numerical simulations of their time-dependent shear relaxation modulus, without the need of preconceived models. The rheological tool is presented in the form of an open access executable named “i-Rheo GT”, enabling its use to a broad scientific community. Its effectiveness is corroborated by analyzing the dynamics of ideal single mode Maxwell fluids and by means of a direct comparison with both bulk-rheology measurements and coarse-grained molecular dynamics simulations data transformed via a generalized Maxwell model. When adopted to transform atomistic molecular dynamics simulations data, the unbiased nature of the tool reveals new insights into the materials’ linear viscoelastic properties, especially at high frequencies, where conventional tools struggle to interpret the data and molecular dynamics simulations actually provide their most statistically accurate predictions. The w...

Exegesis of Sect. III.B from “Fundamentals of the Mechanics of Continua” by E. Hellinger

AbstractThis is our third and last exegetic essay on the fundamental review article DIE ALLGEMEINEN ANSÄTZE DER MECHANIK DER KONTINUA in the Encyklopädie der mathematischen Wissenschaften mit Einschluss ihrer Anwendungen, Bd. IV‐4, Hft. 5 (1913) by Ernst Hellinger which contains the translation and the commentary of the remaining text starting from p. 663. The six subsections, No. 9–15, deal with the applications of the previously developed conceptual tools to formulate: an effective theory of elasticity, the dynamics of ideal fluids, models for internal friction and elastic hysteresis, a theory of capillarity, optics, the fundamental equations of electrodynamics, an introduction of the thermodynamical foundations and the relationship between the theory of continua and the theory of relativity. Hellinger refers to relevant literature while consolidating in an effective way the contemporary knowledge in 1913. Considering notational differences as being irrelevant for the characterization of the presented scientific content, Hellinger's article shows that an effective compendium of a large part of the insights given in Truesdell and Toupin and Truesdell and Noll has already been available in 1913. We include in this paper an assessment of the different roles played by pioneers, who are innovating their scientific discipline, and by erudite scholars whose role consists in re‐ordering existent knowledge and advertising to a wider audience the most important technical results already obtained in a given discipline.

Knotted solutions for linear and nonlinear theories: Electromagnetism and fluid dynamics

We examine knotted solutions, the most simple of which is the “Hopfion”, from the point of view of relations between electromagnetism and ideal fluid dynamics. A map between fluid dynamics and electromagnetism works for initial conditions or for linear perturbations, allowing us to find new knotted fluid solutions. Knotted solutions are also found to be solutions of nonlinear generalizations of electromagnetism, and of quantum-corrected actions for electromagnetism coupled to other modes. For null configurations, electromagnetism can be described as a null pressureless fluid, for which we can find solutions from the knotted solutions of electromagnetism. We also map them to solutions of Euler's equations, obtained from a type of nonrelativistic reduction of the relativistic fluid equations.

A Numerical Scheme for the Compressible Low-Mach Number Regime of Ideal Fluid Dynamics

Based on the Roe solver a new technique that allows to correctly represent low Mach number flows with a discretization of the compressible Euler equations was proposed in Miczek et al. (Astron Astrophys 576:A50, 2015). We analyze properties of this scheme and demonstrate that its limit yields a discretization of the continuous limit system. Furthermore we perform a linear stability analysis for the case of explicit time integration and study the performance of the scheme under implicit time integration via the evolution of its condition number. A numerical implementation demonstrates the capabilities of the scheme on the example of the Gresho vortex which can be accurately followed down to Mach numbers of $${\sim }10^{-10}$$ .