Decay of vorticity in homogeneous turbulence

Smith, Michael R.; Donnelly, Russell J.; Goldenfeld, Nigel; Vinen, W. F.

doi:10.1103/physrevlett.71.2583

Cited by 204 publications

(167 citation statements)

References 10 publications

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“…These include windtunnel experiments downstream of a grid [3] and flow behind a towed grid in a stationary channel filled with Helium II [4]. However, unambiguous statements can still not be made about the dependence of the decay of fluid turbulence on the initial conditions.…”

Section: Introductionmentioning

confidence: 99%

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Decay of magnetohydrodynamic turbulence from power-law initial conditions

Kalelkar

Pandit

2004

Phys. Rev. E

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We derive relations for the decay of the kinetic and magnetic energies and the growth of the Taylor and integral scales in unforced, incompressible, homogeneous and isotropic three-dimensional magnetohydrodynamic (3DMHD) turbulence with power-law initial energy spectra. We also derive bounds for the decay of the cross-and magnetic helicities. We then present results from systematic numerical studies of such decay both within the context of an MHD shell model and direct numerical simulations (DNS) of 3DMHD. We show explicitly that our results about the power-law decay of the energies hold for times t < t * , where t * is the time at which the integral scales become comparable to the system size. For t < t * , our numerical results are consistent with those predicted by the principle of 'permanence of large eddies'.

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Section: Introductionmentioning

confidence: 99%

“…The decay of homogeneous and isotropic, fluid turbulence has been the subject of extensive theoretical [1,2] and experimental [3,4,5] studies. These include windtunnel experiments downstream of a grid [3] and flow behind a towed grid in a stationary channel filled with Helium II [4].…”

Section: Introductionmentioning

confidence: 99%

Decay of magnetohydrodynamic turbulence from power-law initial conditions

Kalelkar

Pandit

2004

Phys. Rev. E

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“…The superfluid experiments measure the decay of vortex line length, with the first measurements at relatively high temperatures [3] and recent confirmation at lower temperatures. These experiments include 3 He for T < 0.2T c [4], where T c ≤ 2.2mK, and more recent measurements in 4 He at T ≤ 0.5K [5].…”

mentioning

confidence: 99%

“…For the cases here, this length is the order of the vortex diameter and does not grow. A better approach is to to mimic experimental measurements of line length that are based upon the scattering of beams of several types by the zero density vortex cores [3][4][5]. A suitable diagnostic for the length is obtained by counting the number of boxes where ρ < ρ c ≈ 0, giving a volume, then dividing by the core cross-section for a p = 1 profile.…”

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confidence: 99%

Vortex Stretching as a Mechanism for Quantum Kinetic Energy Decay

Kerr

2011

Phys. Rev. Lett.

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A pair of perturbed anti-parallel quantum vortices, simulated using the three-dimensional GrossPitaevskii equations, is shown to be unstable to vortex stretching. This results in kinetic energy K ∇ψ being converted into interaction energy EI and eventually local kinetic energy depletion that is similar to energy decay in a classical fluid, even though the governing equations are Hamiltonian and energy conserving. The intermediate stages include: the generation of vortex waves, their deepening, multiple reconnections, the emission of vortex rings and phonons and the creation of an approximately -5/3 kinetic energy spectrum at high wavenumbers. All the wave generation and reconnection steps follow from interactions between the two original vortices, unlike the selfinteractions in vortex wave models. A four vortex example is given to demonstrate that some of these steps might be general. . These results imply that the effect could be a property of the ideal, inviscid equations for a pure superfluid or quantum gas, so that coupling to the viscous normal fluid component is not required to get decay.

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“…Maurer and Tabeling measured local pressure fluctuations in helium flows driven by two counter-rotating disks in a range of temperature between 1.4 and 2.3 K and obtained the Kolmogorov spectrum above and below T λ [26]. A group at the University of Oregon reported in a series of papers [27,28,29,30] the observed attenuation of second sound behind a grid that moved steadily through helium II at temperatures above 1 K. Among these works, Stalp et al measured the decay of grid turbulence in helium II and showed that the experimental results were consistent with a classical model of energy spectrum that included the Kolmogorov law [28]. Then, Vinen analyzed the similarity between superfluid turbulence and classical turbulence [24] and showed the importance of length scales for understanding the energy of the velocity field.…”

Section: B Recent Studies On Superfluid Turbulencementioning

confidence: 99%

Dynamics of Quantized Vortices in Superfluid Helium and Rotating Bose-Einstein Condensates

Tsubota

Kasamatsu

2005

J Low Temp Phys

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In this article, we review the research on the dynamics of quantized vortices in superfluid helium and rotating Bose-Einstein condensates with emphasis on the recent research done by our group. A quantized vortex is a topological defect that arises from the order parameter in Bose-Einstein condensation in which frictionless superfluid flows with quantized circulation around each vortex.A quantized vortex was both predicted and discovered first in superfluid 4 He which was the first example of a Bose-Einstein condensate. Quantized vortices have been thoroughly studied in superfluid 4 He; one of the principal problems was the superfluid turbulent state consisting of a tangle of quantized vortices in thermal counterflow. More recently, the interest has shifted to the nature of superfluid turbulence, apart from the case of counterflow. After briefly reviewing the earlier research and describing the current problems, we focus our review on superfluid turbulence and vortex filament dynamics. One of the important problems is how superfluid turbulence relates to classical turbulence. Superfluid turbulence was recently shown to have an energy spectrum consistent with the Kolmogorov law, which is an important statistical law in fully developed classical turbulence. We also describe the diffusion of an inhomogeneous vortex tangle with relation to the observed decay of vortices at very low temperatures where the normal fluid component is so negligible that the usual mutual friction does not work as a decay mechanism. In connection to the above discussion of groups of vortices, we describe the vortex states that appear in a rotating channel with counterflow. Rotational effects cause the vortices to form ordered arrays, whereas counterflow effects tend to cause disordered vortex tangles; the competition of these two effects makes a new state of "a polarized vortex tangle" which opens up superfluid phase diagrams as a new area of study.In the specific field of atomic-gas Bose-Einstein condensation, we discuss recent numerical analysis of the Gross-Pitaevskii equation that describes the structure and dynamics of the order parameter. Consistent with observations, the simulated condensate starts an elliptic oscillation after the rotation is turned on, which induces the surface-mode excitations. The vortices develop from these surface excitations and then enter the bulk condensate, eventually forming a vortex lattice. When a condensate is held in a quadratic-plus-quartic combined potential, the fast rotation makes "a giant vortex" in which most vortices are absorbed into a central hole around which the superflow circulates.

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Decay of vorticity in homogeneous turbulence

Cited by 204 publications

References 10 publications

Decay of magnetohydrodynamic turbulence from power-law initial conditions

Decay of magnetohydrodynamic turbulence from power-law initial conditions

Vortex Stretching as a Mechanism for Quantum Kinetic Energy Decay

Dynamics of Quantized Vortices in Superfluid Helium and Rotating Bose-Einstein Condensates

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