Fluid Dynamics / Hydrodynamics  

In General > s.a. history of physics; physics teaching; sound [including differential geometry viewpoint]; symmetry breaking [history].
* History: It is the field in which people have been working for the longest time with the most meagre results; The problem is that at the basic level it involves an infinite number of ordinary differential equations, and we know that even a finite number of ordinary differential equations have a peculiar behaviour, like strange attractors; We can understand this mathematically from the fact that the Euler equation came from an approximation of the fluid by small fluid elements.
* And fundamental physics: In principle one would start from the Boltzmann equation and derive from it the Navier-Stokes equation.
* Formalism: The motion of a Newtonian incompressible fluid is described by the Navier-Stokes equations of momentum conservation and the continuity equation, in the absence of density variations, magnetic fields and heat sources; To solve them, usually one assumes a finite volume V, and prescribes the velocity vector u on ∂V.
* Status: 1987, In the compressible fluid case, not even the 1D problem is understood.
* Decomposition: Motion of a continuous fluid can be decomposed into an "incompressible" rearrangement which preserves volumes (described by the Euler equation), and a gradient map that transfers fluid elements in a way unaffected by any pressure or elasticity (described by the Zel'dovich approximation, used to model the motion of a self-gravitating fluid in cosmology).
* Hydrodynamical approach: It works for Δt \(\gg\) collision time and lengths Δx \(\gg\) collision length.
@ Books: Goldstein 60; Von Mises & Friedrichs 71; Marchioro & Pulvirenti 94; Massey 06; Kambe 07; Buresti 12; in Thorne & Blandford 15; Bernard 15; Regev et al 16 [in physics and astrophysics].
@ Geometric: de Montigny JPA(03); Kambe 09 [and dynamical systems]; Gawlik et al PhyD(11)-a1010 [variational discretizations of complex-fluid dynamics].
@ General references: issue JMP(07)#6 [mathematical aspects]; García-Colín et al PRP(08) [beyond the Navier-Stokes equation, Burnett hydrodynamics]; López-Arias EJP(12)-a1103 [Thomas Young and the behavior of air streams]; Sasa PRL(14) [hydrodynamics from the Hamiltonian description of particle systems]; Dostoglou et al JMS(15)-a1406 [in the limit of infinitely-many particles]; > s.a. computational physics.
@ Equation of state: Friedman et al PRL(89) [and astrophysics]; Eliezer et al 02; Silbergleit ap/02 [Klein-Gordon field in cosmology].
> Other general topics: see Continuous Media; Emergence [vs molecular dynamics]; fluctuations; Navier-Stokes Equation and Euler Equations.
> Online resources: see Wikipedia page.

Relativistic Hydrodynamics
@ General references: in Dixon 78; Geroch et al JMP(01)gq [Lagrange formulation]; Sklarz & Horwitz FP(01) [continuous media, including viscosity]; Ivanov a0905-conf [geometrical modeling]; Chen & Spiegel CQG(11)-a1107 [causal]; Kovtun JPA(12) [hydrodynamic fluctuations]; Rezzolla & Zanotti 13; Disconzi Nonlin(14)-a1310 [viscous]; García-Perciante et al JSP(15)-a1406 [stability]; Christodoulou & Lisibach a1411 [self-gravitating, phase transition]; Jensen et al a1701 [effective field theory, superspace formalism]; > s.a. computational physics; gravitating matter [fluid spheres]; Maxwell-Lorentz Equations; solution methods for einstein's equation [fluid-gravity correspondence]; time in gravity.
@ Dissipative: in Dixon 78; Geroch & Lindblom PRD(90), AP(91); Geroch JMP(95); Kreiss et al JMP(97)gq; Anile et al gq/98; Calzetta & Thibeault PRD(01) [interacting with scalar field]; Geroch gq/01 [re hyperbolic theories of dissipation]; Silva et al GRG(02)gq [evolution]; Molnár et al EPJC(10)-a0907 [numerical methods]; Andersson & Comer CQG(15)-a1306 [covariant action principle]; Disconzi et al IJMPD-a1510 [first-order formulation, and cosmology]; Crossley et al a1511 [in curved spacetime, effective field theory]; Pimentel et al GRG(16)-a1604 [energy-momentum tensor].
@ In curved spacetimes: Duggal JMP(89); Krisch & Glass JMP(02)gq/01, PRD(09)-a0908 [anisotropic]; Love & Cianci PTRS(11)-a1208 [using the Chapman-Enskog procedure]; Bemfica et al a1708 [viscous, coupled to gravity]; Van den Bergh a1710 [rotating and twisting]; > s.a. FLRW spacetimes.

Other Types > s.a. condensed matter [liquids]; gas; membranes; molecular physics [polymer fluids]; perfect fluid; superfluids; Viscoelasticity.
* Incompressible: A fluid with equation of state ρ = constant.
* Non-perfect fluids: There are heat-conducting, viscous, particle-creating, and/or anisotropic ones.
* Complex fluids: Binary mixtures in which two phases coexist; Examples are solid–liquid (suspensions or solutions of macromolecules such as polymers), solid-gas (granular), liquid-gas (foams) and liquid-liquid (emulsions); They exhibit unusual mechanical responses to applied stress or strain, including transitions between solid-like and fluid-like behavior, due to the geometrical constraints that the phase coexistence imposes and characteristics such as high disorder, caging, and clustering on multiple length scales; > s.a. Wikipedia page.
* Lattice gas models: Computer simulations (notably 2D hexagonal lattice).
@ Dissipative: Rajeev JPCS(13)-a1004 [geometric formulation]; Andersson & Comer CQG(06) [and superfluid neutron stars]; Glorioso et al a1701 [effective field theory].
@ Hyperfluids: Obukhov & Tresguerres PLA(93)gq/00; Obukhov PLA(96)gq/00.
@ Complex fluids: Gast & Russel PT(98)dec; Shen & Cheung PT(10)sep.
@ Quantum fluids: Tsubota et al PRP(13) [rev]; Gripaios & Sutherland PRL(15)-a1406; Suto JMP(15)-a1504 [probability distribution of the total momentum]; > s.a. bose-einstein condensation; condensed matter; gas; ideal gas; superfluids.
@ Related topics: Roberts CEJP(11)ht/04 [fluid-like generalization of membranes]; Rajeev IJMPA(08)-a0705 [with short-distance cutoff, non-commutative]; Doering et al JMP(12)#11 [incompressible, turbulence and mixing].

Related Concepts and Phenomenology > s.a. Bernoulli Equation; Continuity Equation; Circulation Theorem; critical phenomena; Equation of State.
* Plateau-Rayleigh instability: A fluid cylinder longer than its circumference in energetically unstable to breakup.
@ Stability: Plateau 1873, Rayleigh PLMS(1878); Chandrasekhar PRS(64) [liquid drops]; Joseph 76; > s.a. Instabilities.
@ Ordinary physics: Burgess et al PRL(01) + pn(00)dec [dripping]; Lohse PT(03)feb [bubbles].
@ Microscale description: Celani et al PRL(12) [failure of the overdamped approximation and entropic anomaly].
@ Smooth Particle Hydrodynamics: Inutsuka JCP(02)ap; Cossins PhD(10)-a1007 [rev]; Price JCP(11)-a1012 [and magnetohydrodynamics]; Springel ARAA(10)-a1109 [in astrophysics]; Chiaki & Yoshida MNRAS(15)-a1504 [particle splitting based on Voronoi diagrams]; Price et al a1702 [in astrophysics].
@ Cosmology, structure formation: Bouchet ap/96-ln [perturbations]; Gibson JFE(00)ap [turbulence, viscosity, etc]; Mohayaee & Sobolevskii PhyD(08)-a0712; Cervantes-Cota & Klapp a1306-ch [rev].
@ Astrophysics emphasis: Thompson 06; Ogilvie JPP(16)-a1604-ln [and magnetohydrodynamics].
@ Astrophysics, instabilities: Hartle & Sharp ApJ(67); Friedman & Schutz ApJ(75); Bardeen et al ApJ(77); Friedman CMP(78); Hiscock & Lindblom AP(83), PRD(85); Semelin et al PRD(01)ap/99.
> Other phenomenology: see chaos; dark energy; electromagnetism with matter; Floating; Flux [flow rate]; Froude Number; gravitational collapse; magnetism [magnetohydrodynamics]; meta-materials [suspensions]; phase transitions; Pressure; relativistic cosmology; Rheology; thermodynamics; turbulence [including Magnus, Reynolds Number, examples]; viscosity [including bound]; wave phenomena.
> Other related topics: see Adiabatic Transformation; bianchi I models [effects]; energy-momentum tensor; Enstrophy; knots; Knudsen Number.

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