Shell model of superfluid turbulence

Wacks, Daniel H.; Barenghi, Carlo F.

doi:10.1103/physrevb.84.184505

Cited by 26 publications

(26 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Competing methods, such as vortex filament simulations or the solution of the nonlinear Schrödinger equation, are extremely demanding computationally, having therefore a very short span of scales. Shell models offer an attractive alternative, as recently suggested by Wacks and Barenghi, 8 who proposed a two-fluid shell model for superfluid turbulence using a Gledzer-Ohkitani-Yamada (GOY) shell model 9,10 with additional coupling terms. While only 18 shells were used in Ref.…”

Section: Superfluid Energy Spectra In Shell Modelsmentioning

confidence: 97%

Energy spectra of superfluid turbulence in3He

et al. 2012

View full text Add to dashboard Cite

In superfluid 3 He-B, turbulence is carried predominantly by the superfluid component. To explore the statistical properties of this quantum turbulence and its differences from the classical counterpart, we adopt the time-honored approach of shell models. Using this approach, we provide numerical simulations of a Sabra shell model that allows us to uncover the nature of the energy spectrum in the relevant hydrodynamic regimes. These results are in qualitative agreement with analytical expressions for the superfluid turbulent energy spectra that were found using a differential approximation for the energy flux.

show abstract

Section: Superfluid Energy Spectra In Shell Modelsmentioning

confidence: 97%

Energy spectra of superfluid turbulence in3He

et al. 2012

View full text Add to dashboard Cite

show abstract

“…Such models probably underestimate friction dissipation, but the coupled motion of both fluids is computed self-consistently. Shell models of turbulence (52,53) and Leith models (54) are variants of the HVBK equations trading spatial information for that in the k-space.…”

Section: Theoretical Models Of Quantum Turbulencementioning

confidence: 99%

Introduction to quantum turbulence

Barenghi

Skrbek

Sreenivasan

2014

Proc. Natl. Acad. Sci. U.S.A.

271

255

View full text Add to dashboard Cite

The term quantum turbulence denotes the turbulent motion of quantum fluids, systems such as superfluid helium and atomic Bose-Einstein condensates, which are characterized by quantized vorticity, superfluidity, and, at finite temperatures, two-fluid behavior. This article introduces their basic properties, describes types and regimes of turbulence that have been observed, and highlights similarities and differences between quantum turbulence and classical turbulence in ordinary fluids. Our aim is also to link together the articles of this special issue and to provide a perspective of the future development of a subject that contains aspects of fluid mechanics, atomic physics, condensed matter, and low-temperature physics.Turbulence is a spatially and temporally complex state of fluid motion. Five centuries ago, Leonardo da Vinci noticed that water falling into a pond creates eddies of motion. Today, turbulence still provides physicists, applied mathematicians, and engineers with a continuing challenge. Leonardo realized that the motion of water shapes the landscape. Today's researchers appreciate that many physical processes, from the generation of the Galactic magnetic field to the efficiency of jet engines, depend on turbulence.The articles in this collection are devoted to a special form of turbulence known as quantum turbulence (1-3), which appears in quantum fluids. Quantum fluids differ from ordinary fluids in three respects: (i) they exhibit two-fluid behavior at nonzero temperature or in the presence of impurities, (ii) they can flow freely, without the dissipative effect of viscous forces, and (iii) their local rotation is constrained to discrete vortex lines of known strength (unlike the eddies in ordinary fluids, which are continuous and can have arbitrary size, shape, and strength). Superfluidity and quantized vorticity are extraordinary manifestations of quantum mechanics at macroscopiclength scales.Recent experiments have highlighted quantitative connections, as well as fundamental differences, between turbulence in quantum fluids and turbulence in ordinary fluids (classical turbulence). The relation between the two forms of turbulence is indeed a common theme in the articles collected here. Because different scientific communities (lowtemperature physics, condensed-matter physics, fluid dynamics, and atomic physics) have contributed to progress in quantum turbulence, † the aim of this article is to introduce the main ideas in a coherent way. Quantum FluidsIn this series of articles, we shall be concerned almost exclusively with superfluid 4 He, the B-phase of superfluid 3 He, and, to a lesser extent, with ultracold atomic gases. These systems exist as fluids at temperatures on the order of a Kelvin, milliKelvin, and microKelvin, respectively.‡ Their constituents are either bosons (such as 4 He atoms with zero spin) or fermions (such as 3 He atoms with spin 1/2). This difference is fundamental: the former obey Bose-Einstein statistics and the latter Fermi-Dirac quantum statistics.Let us consider an...

show abstract

“…In simulations we used ν s = 10 −12 and ν n = 10 −10 . The coupling terms F n,s m [8,9], given by Eq (3d), account for the mutual friction between normal and superfluid velocities. This dissipative force is proportional to parameters α s (T ) = α and α n (T ) = αρ s /ρ n .…”

mentioning

confidence: 99%

“…Shell models of superfluid turbulence [8,9] are simplified caricatures of the NavierStokes and Euler equations in k-representation:…”

mentioning

confidence: 99%

Enhancement of Intermittency in Superfluid Turbulence

et al. 2013

View full text Add to dashboard Cite

We consider the intermittent behavior of superfluid turbulence in 4 He. Due to the similarity in the nonlinear structure of the two-fluid model of superfluidity and the Euler and Navier-Stokes equations one expects the scaling exponents of the structure functions to be the same as in classical turbulence for temperatures close to the superfluid transition T λ and also for T T λ . This is not the case when mutual friction becomes important. Using shell model simulations, we propose that for an intermediate regime of temperatures, such that the density of normal and superfluid components are comparable to each other, there exists a range of scales in which the effective exponents indicate stronger intermittency. We offer a bridge relation between these effective and the classical scaling exponents. Since this effect occurs at accessible temperatures and Reynolds numbers, we propose that experiments should be conducted to further assess the validity and implications of this prediction.Introduction. Non-equilibrium systems are often characterized by relatively quiescent periods which are interrupted by rare but violent changes of the physical observables. This phenomenon which is referred to as "intermittency" is very generic as it appears in many different stationary random processes.It is believed [1], that highly excited hydrodynamic turbulence possesses universal statistics in the inertial interval of scales L r η. Here L is the of energy input scale, e.g. due to instabilities of high velocity flows, and η is the viscous energy dissipation scale. The intermittent behavior of space homogeneous fully developed turbulence of incompressible fluids can be studied in terms of the velocity structure functions [1]

show abstract

Shell model of superfluid turbulence

Cited by 26 publications

References 39 publications

Energy spectra of superfluid turbulence in3He

Energy spectra of superfluid turbulence in3He

Introduction to quantum turbulence

Enhancement of Intermittency in Superfluid Turbulence

Contact Info

Product

Resources

About