Turbulence |

**In General** > s.a. chaos; Reynolds Number.

* __Idea__: An eddy-like
state of fluid motion where the inertial-vortex forces of the eddies are larger
than any of the other forces that tend to damp
the
eddies out; Characteristics are the apparently
random local eddies and whirlpools, diffusion, and dissipation.

* __History__: The first
serious study began with Reynolds, who proposed that its onset is due to instabilities
in the laminar flow, that can be characterized
(in a classical fluid) by the Reynolds number; This is now thought to be too
simplistic; Reaching the critical value for *R* is only a sufficient
condition, and there are some flows that do not have a critical Reynolds number;
Very little is understood from first principles, and it has famously been called the last great unsolved problem of classical physics.

* __Goal__: There is no consensus
even on what finding a solution to the problem means; According to engineers,
finding mean velocity profiles, wall stresses,
and *p* gradients (use statistical theory, from O Reynolds on), and
the motivation is reducing the energy spent in overcoming the drag caused by
turbulence; For physicists,
the goal is understanding the non-linear processes and the details of motions
at various scales.

* __Basic concepts__: Randomness, eddy viscosity, cascade, scaling.

* __And chaos__: The approach
to turbulence has been shown to be chaotic for certain systems, following the
predictions of Ruelle & Takens (1971),
and contrary to the Landau-Hopf theory; Turbulent flow itself is thought to
be chaotic, but this cannot be experimentally tested.

> __Online resources__: see Wikipedia page.

**Related Topics** > s.a. approaches to quantum gravity; magnetism [megnetohydrodynamics]; Scale Invariance; sound [analog
metric viewpoint]; Transport.

* __Superfluid turbulence__: Shows quantized vortices (& Onsager,
Feynman).

* __Magnus effect__: A turbulence
and viscosity effect; For a moving ball, a region of turbulence develops downstream;
If the ball spins, the region is
asymmetric, more on the side of the trailing edge, and exerts a force on
the ball in the same direction as the Bernoulli effect; __Applications__:
Golf balls, it explains why dimples are effective.

@ __Superfluid turbulence__: Donnelly SA(88)nov; > s.a. Superfluids.

@ __Magnus effect__: Nathan AJP(08)feb [and flight of baseball].

@ __Applications__: Leung & Gibson CJOL(04)ap/03
[in geophysics and astrophysics]; Ghosh et al PRS(05)
[enhancing particle coalescence].

@ __Quantum fluids__: Fisher & Pickett pw(06)apr;
Vinen & Donnelly PT(07)apr;
Tsubota CP(09) [superfluid helium and Bose-Einstein condensates]; Nemirovskii PRP(13) [rev].

@ __Numerical simulations__: Smits & Marusic PT(13)sep [wall-bounded]; > s.a. computational physics.

@ __Other approaches__: Canuto & Dubovikov IJMPA(97);
Kozyrev TMP(08)
[ultrametric theory]; Jejjala ert al IJMPD(10)-a1005-GRF [string theory].

@ __And chaos__: Ruelle 95; Li a1306 [Reynolds number and the distinction between turbulence and chaos].

@ __In astrophysics and cosmology__:
Low ap/03-in;
Leubner et al AiG-ap/06 [plasma
fluctuations,
non-extensive entropy]; Esquivel & Lazarian ApJ(10)-a0905 [Tsallis
statistics approach]; Gaite a1202 [cosmic structure]; > s.a. black-hole phenomenology; interstellar matter; Intergalactic Matter.

@ __Other topics__: Gurarie ht/95 [and
statistical physics, field theory]; Gotoh & Nakano JSP(03)
[role of pressure]; Galanti & Tsinober
PLA(04)
[ergodicity]; Choi et al mp/04 [wave
turbulence, rev]; Lück et al PLA(06)
[coherence length]; Hof et al PRL(08)
[evidence for transient nature of all turbulence].

**References**

@ __Historical__: Reynolds PTRS(1883); Darrigol HSPBS(02) [XIX century];
Eyink & Sreenivasan RMP(06) [Onsager]; Bodenschatz & Eckert in(11)-a1107 [Prandtl].

@ __Intros, reviews__: Deissler RMP(84);
Dwoyer et al ed-85; Frisch & Orszag PT(90)jan;
Kadanoff PT(95)sep;
L'vov & Procaccia
PW(96); Gawedzki cd/96 [intro];
Gibson AMR(96)ap/99 [review];
Nelkin AJP(00)apr [RL];
Bernard cm/00-ln;
Tabeling PRP(02)
[2D]; Barenghi pw(04)dec;
Falkovich & Sreenivasan PT(06)apr
[universal properties].

@ __Texts__: Mathieu & Scott 00; Davidson 04 [r PT(05)oct].

@ __General references__: Muriel PhyA(09)
[proposed definitions]; Benzi & Biferale JSP(09)
[and the Parisi-Frisch multifractal conjecture]; Eling et al CP(11)-a1004 [geometrization]; Smart PT(11)jan; Bardos & Titi JoT(13)-a1301-conf [mathematical tools].

@ __Statistical approach__: Ruelle JSP(14) [non-equilibrium statistical mechanics]; Leschziner 15 [graduate text].

@ __Scaling__: Gawedzki ht/97;
Falkovich et al RMP(01);
Carbone et al RNC(04);
Bershadskii JSP(07)
[finite-size corrections]; Flandoli et al CMP(08); Renner & Peinke JSP(12) [scaling models].

@ __Other systems__: Naulin et al PLA(04)
[plasma, statistical]; Zakharov et al
PRP(04)
[1D waves]; Wyngaard 10 [Earth's atmosphere, r PT(11)jan, PRS(11)]; news Phy(12)jul [droplets throwing out a fine spray as they hit a liquid surface]; Green et al PRX(14) [turbulence and the gravity-fluid correspondence].

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