Radio pulsars provide us with some of the most stable clocks in the universe. Nevertheless several pulsars exhibit sudden spin-up events, known as glitches. More than forty years after their first discovery, the exact origin of these phenomena is still open to debate. It is generally thought that they are observational manifestation of a superfluid component in the stellar interior and provide an insight into the dynamics of matter at extreme densities. In recent years, there have been several advances on both the theoretical and observational side, that have provided significant steps forward in our understanding of neutron star interior dynamics and possible glitch mechanisms. In this article we review the main glitch models that have been proposed and discuss our understanding, in the light of current observations.

Models of pulsar glitches

Radio pulsars provide us with some of the most stable clocks in the universe. Nevertheless several pulsars exhibit sudden spin-up events, known as glitches. More than forty years after their first discovery, the exact origin of these phenomena is still open to debate. It is generally thought that they an observational manifestation of a superfluid component in the stellar interior and provide an insight into the dynamics of matter at extreme densities. In recent years there have been several advances on both the theoretical and observational side, that have provided significant steps forward in our understanding of neutron star interior dynamics and possible glitch mechanisms. In this article we review the main glitch models that have been proposed and discuss our understanding, in the light of current observations.

Models of Pulsar Glitches

papers which should have been cited have come to our attention. It appears that our effort to write a relatively complete chronology of thought about heat waves fell somewhat short of the mark. We thought it would be useful to correct the more serious omissions in that chronology in this addendum, and not to try to list all the papers which bear on one or another aspect of the subject. The literature on heat waves is still a manageable one, the subject is still active, but not explosively so. It seems to us that nearly the whole of the literature is covered in our review, in the various summaries of results on propagation of waves in liquid helium, and in the recent review of Jou, Casas-Vázquez and Lebon [1988] which give some references missed by us, and

Reviews of Modern Physics: Addendum to the Paper "Heat Waves"

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.

https://www.pnas.org/content/pnas/111/Supplement_1/4683.full.pdf

Experimental, numerical, and analytical velocity spectra in turbulent quantum fluid

Recent experiments have shown that the high Reynolds number turbulent flow of superfluid helium is similar to classical turbulence. To understand this evidence we have developed an idealized model of normal fluid turbulence which is based on vorticity tubes and we have studied numerically the behavior of superfluid quantized vortex lines in this model of turbulent normal flow. We have found that the vortex lines form ordered superfluid vortex bundles in regions of high normal fluid vorticity. A vortex wave instability and mutual friction are responsible for generating a high density of vortex lines such that the resulting macroscopic superfluid vorticity and the driving normal fluid vorticity patterns match. The results are discussed from the point of view of the idea, put forward to explain experiments, that in the isothermal, turbulent flow of He II a high density of vortex lines locks the two fluid components together and the resulting turbulent flow is that of a classical Navier–Stokes fluid.

Superfluid vortex lines in a model of turbulent flow

There are two well known theories to describe the motion and thermodynamics of superfluids when a large number of quantized vortex lines are present and when the phenomena under study are on scales large compared with the vortex line spacing. These works have been criticised on the grounds that their governing equations for the smoothly varying, spatially averaged, fields do not satisfy the accepted invariance principles basic to modern continuum mechanics. This paper demonstrates one way in which such theories can arise from a properly invariant continuum approach and indicates the presence of hitherto unconsidered terms that bring them closer to the generally accepted microscopic picture. The resulting theory has applications both to rotating helium II in the laboratory, and to rotating neutron stars (pulsars).

Superfluid mechanics for a high density of vortex lines

In this note we consider the question of continuous dependence upon the initial data for solutions of the equations governing the motion of a linearly viscous compressible fluid. In particular, we show that provided the base flow lies in a certain class ~r and the perturbed flow in a class , / / then the solutions depend Hflder continuously on the initial data in the sense of F. JOHN [1]. The precise definition of the classes dr and ~ is given in (9) and (10). To establish this result we employ the weighted energy arguments of MURRAY & PROa~rrR [2] and MURRAY [3]. The uniqueness of the solutions is, of course, implied by the continuous dependence result. An earlier proof of the uniqueness was given by SERRIN [4] using a conventional energy approach. We assume that the fluid occupies a bounded region D of three space with a boundary dD which is smooth enough to allow applications of the divergence theorem. The density p, the components of the velocity v1 and the temperature T are well known to satisfy the system of equations

Continuous dependence for the compressible linearly viscous fluid

Uniqueness, stability and nonexistence are discussed for the null solution to the equations governing the behavior of materials associated with nonlinear theories of continuum mechanics. The technique employed is a variant of the weighted energy argument.

Qualitative Results for a Class of General Materials

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0080454100009584

R. N. Hills

Papers

Superfluid mechanics for a high density of vortex lines

Continuous dependence for the compressible linearly viscous fluid

Qualitative Results for a Class of General Materials

19.—Concavity and the Evolutionary Properties of a Class of General Materials

Evolutionary properties of elastodynamic solutions for non-negative and indefinite strain energies