Compressible helical flows

Morgulis, Andrey; Yudovich, V. I.; Zaslavsky, G. M.

doi:10.1002/cpa.3160480505

Cited by 28 publications

(23 citation statements)

References 6 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Finally, compressible quasisymmetric flows were considered in Ref. [7], whereas a general outlook on order and disorder in fluid motion can be found in the experiments of Gollub [8].In this letter we shall see that a discrete restricted spectral scenario can be displayed by means of impulsive waves in hydrodynamic quasicrystals, where we observe Bloch-like surface waves. The waves are generated at the frequencies corresponding to the Fourier components of the quasiperiodic structure at the dominant diffraction spots.…”

mentioning

confidence: 75%

See 1 more Smart Citation

Quasiperiodic Bloch-Like States in a Surface-Wave Experiment

et al. 2003

View full text Add to dashboard Cite

Bloch-like surface waves associated with a quasiperiodic structure are observed in a classic wave propagation experiment which consists of pulse propagation with a shallow fluid covering a quasiperiodically drilled bottom. We show that a transversal pulse propagates as a plane wave with quasiperiodic modulation, displaying the characteristic undulatory propagation in this quasiperiodic system and reinforcing the idea that analogous concepts to Bloch functions can be applied to quasicrystals under certain circumstances.PACS numbers: 47.35.+i, 47.54.+r, 71.23.Ft The main difficulty towards the development of a systematic analytic approach to the transport properties of quasiperiodic systems has been the absence of an analogous Bloch theorem approach as used in the periodic case. In the first efforts to apply a modified version of the Bloch theorem, it was noticed that the dense spectrum of quasiperiodic systems is dominated by only a few special reciprocal lattice points that may be taken to construct a quasi-Brillouin zone [1]. Thus, by considering only the dominant Fourier components, the atomic distribution can be expanded in terms of a discrete aperiodic lattice. Wave functions of the form Ψ k = u k (r)e ik·r will therefore solve the Schrodinger equation. In this case u k is quasiperiodic and should formally be defined on a countable dense set of reciprocal lattice vectors. But, by the above considerations, this expansion is useful since the Fourier development of the modulation function u k can be restricted to the few special reciprocal vectors that dominate the spectra. Thus, Bloch-like states could describe the plane wave propagation in so schematized quasicrystals and free-electron-like bands are expected. Recently this idea was experimentally tested showing that analogous concepts to Bloch functions can be applied to quasicrystals [2].The classic wave propagation in quasicrystalline systems was addressed in a first seminal acoustic experiment of He and Maynard [3] by the feature that acoustical waves are ideal tools to investigate formally similar * Electronic address: manolo@iec.csic.es † Electronic address: aragon@fata.unam.mx quantum propagation effects [4]. On the other hand, appearance of the quasicrystalline symmetry in fluids dynamics was firstly predicted theoretically by Zaslavsky and co-workers [5] and a simulation similar to the conditions of the present experiments was reported in Ref. [6]. Finally, compressible quasisymmetric flows were considered in Ref. [7], whereas a general outlook on order and disorder in fluid motion can be found in the experiments of Gollub [8].In this letter we shall see that a discrete restricted spectral scenario can be displayed by means of impulsive waves in hydrodynamic quasicrystals, where we observe Bloch-like surface waves. The waves are generated at the frequencies corresponding to the Fourier components of the quasiperiodic structure at the dominant diffraction spots. The observed Bloch-like waves are plane waves with quasiperiodic modulation generated ...

show abstract

mentioning

confidence: 75%

“…Finally, compressible quasisymmetric flows were considered in Ref. [7], whereas a general outlook on order and disorder in fluid motion can be found in the experiments of Gollub [8].…”

mentioning

confidence: 99%

Quasiperiodic Bloch-Like States in a Surface-Wave Experiment

et al. 2003

View full text Add to dashboard Cite

show abstract

“…The properties of these were studied in [15,16]. More solutions were found in [17][18][19]. A map of magnetohydrodynamics to just fluid dynamics was used extensively (for instance, [20][21][22]), and one also was able to show that in magnetohydrodynamics a defined "velocity of lines of force" v p = ( E × H)/H 2 [23] can be measured, and in some cases ("frozen field condition") coincides with the velocity of the fluid transporting it (see for instance [22,24], the last also considering transporting the electromagnetic Hopfion).…”

Section: Introductionmentioning

confidence: 99%

Knotted solutions for linear and nonlinear theories: Electromagnetism and fluid dynamics

et al. 2017

View full text Add to dashboard Cite

We examine knotted solutions, the most simple of which is the "Hopfion", from the point of view of relations between electromagnetism and ideal fluid dynamics. A map between fluid dynamics and electromagnetism works for initial conditions or for linear perturbations, allowing us to find new knotted fluid solutions. Knotted solutions are also found to to be solutions of nonlinear generalizations of electromagnetism, and of quantum-corrected actions for electromagnetism coupled to other modes. For null configurations, electromagnetism can be described as a null pressureless fluid, for which we can find solutions from the knotted solutions of electromagnetism. We also map them to solutions of Euler's equations, obtained from a type of nonrelativistic reduction of the relativistic fluid equations.

show abstract

“…The existence of two local invariants suggests a description of Beltrami flows in terms of Nambu brackets [26]. We also find that, if the Beltrami field is solenoidal, the proportionality factor is a function of the local invariants, giving an explanation of the helical flow paradox [27]. In addition, Theorem 1 naturally leads to the following method for the construction of Beltrami fields with given proportionality factor α, i.e.…”

Section: Introductionmentioning

confidence: 68%

Local representation and construction of Beltrami fields

Sato

Yamada

2019

Physica D: Nonlinear Phenomena

View full text Add to dashboard Cite

A Beltrami field is an eigenvector of the curl operator. Beltrami fields describe steady flows in fluid dynamics and force free magnetic fields in plasma turbulence. By application of the Lie-Darboux theorem of differential geoemtry, we prove a local representation theorem for Beltrami fields. We find that, locally, a Beltrami field has a standard form amenable to an Arnold-Beltrami-Childress flow with two of the parameters set to zero. Furthermore, a Beltrami flow admits two local invariants, a coordinate representing the physical plane of the flow, and an angular momentum-like quantity in the direction across the plane. As a consequence of the theorem, we derive a method to construct Beltrami fields with given proportionality factor. This method, based on the solution of the eikonal equation, guarantees the existence of Beltrami fields for any orthogonal coordinate system such that at least two scale factors are equal. We construct several solenoidal and nonsolenoidal Beltrami fields with both homogeneous and inhomogeneous proportionality factors. arXiv:1809.03136v1 [math-ph]

show abstract

Compressible helical flows

Cited by 28 publications

References 6 publications

Quasiperiodic Bloch-Like States in a Surface-Wave Experiment

Quasiperiodic Bloch-Like States in a Surface-Wave Experiment

Knotted solutions for linear and nonlinear theories: Electromagnetism and fluid dynamics

Local representation and construction of Beltrami fields

Contact Info

Product

Resources

About