We calculate the first four cumulants of the integrated current of the one dimensional symmetric simple exclusion process of N sites with open boundary conditions. For large system size N , the generating function of the integrated current depends on the densities ρ a and ρ b of the two reservoirs and on the fugacity z, the parameter conjugated to the integrated current, through a single parameter. Based on our expressions for these first four cumulants, we make a conjecture which leads to a prediction for all the higher cumulants. In the case ρ a = 1 and ρ b = 0, our conjecture gives the same universal distribution as the one obtained by Lee, Levitov and Yakovets for one dimensional quantum conductors in the metallic regime.

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The 1/2 power law is reported in a Rayleigh-Bénard experiment: Nu approximately Ra(1/2), where Ra and Nu are the Rayleigh and Nusselt numbers. This observation is coherent with the predictions of the ultimate convection regime, characterized by fully turbulent heat transfers. Ordered rough boundaries are used to cancel the correction due to the thickness variation of the viscous sublayer, and the observation of the asymptotic regime is therefore possible. This result supports the interpretation of a laminar-turbulent boundary-layer transition to account for the observation of Chavanne et al. of a new regime [X. Chavanne et al., Phys. Rev. Lett. 79, 3648 (1997)].

We present velocity spectra measured in three cryogenic liquid 4He steady flows: grid and wake flows in a pressurized wind tunnel capable of achieving mean velocities up to 5 m/s at temperatures above and below the superfluid transition, down to 1.7 K, and a "chunk" turbulence flow at 1.55 K, capable of sustaining mean superfluid velocities up to 1.3 m/s. Depending on the flows, the stagnation pressure probes used for anemometry are resolving from one to two decades of the inertial regime of the turbulent cascade. We do not find any evidence that the second order statistics of turbulence below the superfluid transition differ from the ones of classical turbulence, above the transition.Comment: 13 pages, 9 figure

In thei sol ated experi m entm enti oned above[ 1] ,a m i ni ature total -head tube was con gured to operate as an anem om eter i n a H e-II co-ow (or \bul k ow "), at 2: 08 and 1: 4K .In a two-ui d m odelpi cture,thi s probe senses a com bi nai son ofthe vel oci ti es ofthe super ui d and norm al com ponents. Its spati al and ti m e resol uti on (typical l y 2m m and 1kH z) enabl ed to resol ve one decade of power l aw scal i ng bel ow the i njecti on scal e. T hi s scal i ng wasfound to overl ap w i th the scal i ng i n the i nerti alrange of cl assi cal ow s. T hi s strong resul t suggests that the l argestscal esstructuresi n quantum turbul ence undergo a K ol m ogorov-type cascade.Second sound probes have a severaldecades hi story as an e ci ent tool to m easure quantum vorti ces l i ne densi ty (V LD ), i n parti cul ar i n turbul ent co-ow s (for i nstance [ 12{14] and references w i thi n) and counter-ow s (for i nstance [ 3{7]and references w i thi n). U nfortunatel y, the si ze of these sensors and thei r si dewal l posi ti onni ng m adei m possi bl e space and ti m e resol ved m easurem entsof ow uctuati ons. T he ai m ofthi s paper i s to report such a l ocal uctuati ons m easurem ent from a m i crom achi ned m i ni ature second sound resonator. T hi s probe therefore com pl etes the i nerti alrange characteri zati on w i th a ful l y super ui d observabl e,i ndependent ofthe earl i er vel oci ty m easurem ents.T he ow set-up.{ O ur ow i sa H e-IIl oop con ned i n a nearl y cyl i ndri calcryostatand conti nuousl y powered by a centri fugalpum p (see gure 1).Turbul ence i sprobed i n a = 23m m -di am eter, 250m m -l ong brass pi pe, l ocated upstream from the pum p . D ow nstream the pum p, the ui d returnsto the pi pe i nl et ow i ng al ong the outsi de ofi t. O n thi s return path,a 30m m -l ong 3m m -cel lhoneycom b breaks the spi n m oti on generated by the pum p. A s a test,another 20m m -l ong honeycom b has once been i nserted i n the pi pe i nl et w i thout noti ceabl e changes. A Pi tot tube i s l ocated 130m m before the pi pe outl et. It provi des a m easurem ent ofthe m ean vel oci ty by m ean of an i n-si tu capaci ti ve di erenti alpressure gauge. T he useful lrangeofvel oci ty i sV = 0: 3 1: 3m =s.A tl owervel ociti es ow i nstabi l i ti esare detected and athi ghervel oci ti es, typi cal l y at1: 5m =s,a cavi tati on threshol d i sencountered. From i n-si tu m easurem entsw i th a sem i conducti ng m i ni aturepressuresensors [ 16] ,weesti m atea typi cal35% vel oci ty turbul ence rati o i n the pi pe. W i th vel oci ty V and pi pe di am eter ,severalR eynol ds num bers can be de ned usi ng di erent denom i nators. T hi s m ul ti pl i ci ty resul t from the extra degrees offreedom ofquantum ui ds com pared to cl assi cal ui d. To assess the \i nstabi l i ty" ofthe superui d,a possi bl edenom i natori sthe quantum ofci rcul ati on = h=m ' 0: 997: 10 7 m 2 =s (h i s Pl anck constant and m i s the m ass ofthe 4-H e atom ) w hi ch i s the onl y avai l abl e

Turbulence in superfluid helium is unusual and presents a challenge to fluid dynamicists because it consists of two coupled, interpenetrating turbulent fluids: the first is inviscid with quantized vorticity, and the second is viscous with continuous vorticity. Despite this double nature, the observed spectra of the superfluid turbulent velocity at sufficiently large length scales are similar to those of ordinary turbulence. We present experimental, numerical, and theoretical results that explain these similarities, and illustrate the limits of our present understanding of superfluid turbulence at smaller scales. He.) Besides the lack of viscosity, another major difference from ordinary (classical) fluids such as water or air is that, in helium, vorticity is constrained to vortex line singularities of fixed circulation κ = h=M, where h is Planck's constant, and M is the mass of the relevant boson (M = m 4 , the mass of He, the vortex core radius ξ ≈ 10 −10 m is comparable to the interatomic distance. Thus, quantization of circulation results in the appearance of another characteristic length scale: the mean separation between vortex lines, ℓ. In typical experiments (both in 4 He and 3 He), ℓ is orders of magnitude smaller than the scale D of the largest eddies but is also orders of magnitudes larger than ξ.There is a growing consensus (2) that superfluid turbulence at large scales R ℓ is similar to classical turbulence if excited similarly, for example by a moving grid. The idea is that motions at scales R ℓ should involve at least a partial polarization (3-5) of vortex lines and their organization into vortex bundles that, at such large scales, should mimic continuous hydrodynamic eddies. Therefore, one expects a classical Richardson-Kolmogorov energy cascade, with larger "eddies" breaking into smaller ones. The spectral signature of this classical cascade is indeed observed experimentally in superfluid helium. In the absence of viscosity, in superfluid turbulence the kinetic energy should cascade downscale without loss, until it reaches scales R ∼ ℓ, where the discreteness becomes important. It is also believed that the energy is further transferred downscales by the interacting Kelvin waves (helical perturbation of the individual vortex lines) where it is radiated away by thermal quasiparticles (phonons and rotons in 4 He). Although this scenario seems reasonable, crucial details are yet to be established. Our understanding of superfluid turbulence at scales of the order of ℓ is still at infancy stage, and what happens at scales below ℓ is a question of intensive debates. The "quasiclassical" region of scales, R ℓ, is better understood, but still less than classical hydrodynamic turbulence. The main reason is that at nonzero temperatures (but still below the critical temperature), superfluid helium is a two-fluid system. According to the theory of Landau and Tisza (6), it consists of two interpenetrating components: the inviscid superfluid, of density ρ s and velocity u s (associated to the quantum ground stat...

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Hydrodynamic aspects of superfluidity; quantum fluids PACS 67.57.De -Superflow and hydrodynamics PACS 67.25.dk -Vortices and turbulenceAbstract -The 4/5-law of turbulence, which characterizes the energy cascade from large to smallsized eddies at high Reynolds numbers in classical fluids, is verified experimentally in a superfluid 4 He wind tunnel, operated down to 1.56 K and up to R λ ≈ 1640. The result is corroborated by high-resolution simulations of Landau-Tisza's two-fluid model down to 1.15 K, corresponding to a residual normal fluid concentration below 3 % but with a lower Reynolds number of order R λ ≈ 100. Although the Kármán-Howarth equation (including a viscous term) is not valid a priori in a superfluid, it is found that it provides an empirical description of the deviation from the ideal 4/5-law at small scales and allows us to identify an effective viscosity for the superfluid, whose value matches the kinematic viscosity of the normal fluid regardless of its concentration.