On the Closure Problem of the Coarse-Grained Hydrodynamics of Turbulent Superfluids

Nemirovskii, Sergey K.

doi:10.1007/s10909-020-02483-6

Cited by 14 publications

(15 citation statements)

References 49 publications

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“…The information needed to close the system is a model for the average dynamics of the quantized vortices [41], which can be specified by assuming a phenomenological relation of the type u…”

Section: Closure Of the Macroscopic Model: The Dynamics Of Vorticesmentioning

confidence: 99%

“…where f n ν is the macroscopic mutual friction. In the absence of turbulence, it is natural to identify the left-hand side with the Magnus force per unit volume (i.e., the Magnus force on a single vortex times the vortex density) and the right-hand side with some drag force per unit volume, see e.g., [9,14,27,41].…”

Section: The Argument For the Absence Of The Generalised Iordanskii Forcementioning

confidence: 99%

See 1 more Smart Citation

Superfluid Dynamics in Neutron Star Crusts: The Iordanskii Force and Chemical Gauge Covariance

Gavassino¹,

Antonelli²,

Haskell³

2021

Universe

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We present a geometrical derivation of the relativistic dynamics of the superfluid inner crust of a neutron star. The resulting model is analogous to the Hall-Vinen-Bekarevich-Khalatnikov hydrodynamics for a single-component superfluid at finite temperature, but particular attention should be paid to the fact that some fraction of the neutrons is locked to the motion of the protons in nuclei. This gives rise to an ambiguity in the definition of the two currents (the normal and the superfluid one) on which the model is built, a problem that manifests itself as a chemical gauge freedom of the theory. To ensure chemical gauge covariance of the hydrodynamic model, the phenomenological equation of motion for a quantized vortex should contain an extra transverse force, that is the relativistic version of the Iordanskii force discussed in the context of superfluid Helium. Hence, we extend the mutual friction model of Langlois et al. (1998) to account for the possible presence of this Iordanskii-like force. Furthermore, we propose that a better understanding of the (still not completely settled) controversy around the presence of the Iordanskii force in superfluid Helium, as well as in neutron stars, may be achieved by considering that the different incompatible results present in the literature pertain to two, opposite, dynamical regimes of the fluid system.

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“…The information needed to close the system is a model for the average dynamics of the quantized vortices [41], which can be specified by assuming a phenomenological relation of the type u…”

Section: Closure Of the Macroscopic Model: The Dynamics Of Vorticesmentioning

confidence: 99%

Section: The Argument For the Absence Of The Generalised Iordanskii Forcementioning

confidence: 99%

Superfluid Dynamics in Neutron Star Crusts: The Iordanskii Force and Chemical Gauge Covariance

Gavassino¹,

Antonelli²,

Haskell³

2021

Universe

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show abstract

“…Proton, neutron and energy-momentum conservation produce 6 equations of motion, so that 3 additional equations are needed. The information needed to close the system is a model for the average dynamics of the quantized vortices [40], which can be specified by assuming a phenomenological relation of the type u…”

Section: Closure Of the Macroscopic Model: The Dynamics Of Vorticesmentioning

confidence: 99%

“…The pre-factors z (j) are kinetic coefficients which encode the microphysics into the PEVM, namely equation (39). We remark that the decomposition (40) is not an expansion of the total force f on a basis (for which just 4 linearly independent vectors would be enough, e.g. f (1) , f (3) , f (5) , f (7) ) but it is a subdivision of the total force into the elementary parts that the most generic microscopic model is expected to produce.…”

Section: Formulation Of the Phenomenological Equation Of Vortex Motio...mentioning

confidence: 99%

Superfluid dynamics in neutron star crusts: the Iordanskii force and chemical gauge covariance

Gavassino,

Antonelli,

Haskell

2020

Preprint

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We present a geometrical derivation of the relativistic dynamics of the superfluid inner crust of a neutron star. The resulting model is analogous to the Hall-Vinen-Bekarevich-Khalatnikov hydrodynamics for a single-component superfluid at finite temperature, but particular attention should be paid to the fact that some fraction of the neutrons are locked to the motion of the protons in nuclei. This gives rise to an ambiguity in the definition of the two currents (the normal and the superfluid one) on which the model is built, a problem that manifests itself as a chemical gauge freedom of the theory. To ensure chemical gauge covariance of the hydrodynamic model, the phenomenological equation of motion for a quantized vortex should contain an extra transverse force, that is the relativistic version of the Iordanskii force discussed in the context of superfluid Helium. Hence, we extend the mutual friction model of Langlois et al. (1998) to account for the possible presence of this Iordanskii-like force. Furthermore, we propose that a better understanding of the (still not completely settled) controversy around the presence of the Iordanskii force in superfluid Helium, as well as in neutron stars, may be achieved by considering that the different incompatible results present in the literature pertain to two, opposite, dynamical regimes of the fluid system.

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“…The observed temperature-independence of spectra is thus constraining for the delicate modeling of the small scales of quantum turbulence, in particular to develop mathematical closures for the continuous description of He-II (eg. see [31]).…”

mentioning

confidence: 96%

Local measurement of vortex statistics in quantum turbulence

Woillez

Valentin

Roche

2021

EPL

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The density fluctuations of quantum vortex lines are measured in a turbulent flow of superfluid He, at temperatures corresponding to superfluid fractions of 16%, 47% and 81%. The probe is a micro-fabricated second sound resonator allowing for local and small-scale measurements in the core of the flow, downstream a grid at a 10-mesh size. Remarkably, all the vortex power spectra collapse on a single master curve, independently from the superfluid fraction and the mean velocity. By contrast with previous measurements, we report a peculiar shape of the power spectra. The vortex density probability distributions are found to be strongly skewed, similarly to the vorticity distributions observed in classical turbulence. Implications of those results are discussed.

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On the Closure Problem of the Coarse-Grained Hydrodynamics of Turbulent Superfluids

Cited by 14 publications

References 49 publications

Superfluid Dynamics in Neutron Star Crusts: The Iordanskii Force and Chemical Gauge Covariance

Superfluid Dynamics in Neutron Star Crusts: The Iordanskii Force and Chemical Gauge Covariance

Superfluid dynamics in neutron star crusts: the Iordanskii force and chemical gauge covariance

Local measurement of vortex statistics in quantum turbulence

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