Related papers: Ray helicity: a geometric invariant for multi-dime…
Helicity, a measure of the linkage of flux lines, has subtle and largely unknown effects upon dynamics. Both magnetic and hydrodynamic helicity are conserved for ideal systems and could suppress nonlinear dynamics. What actually happens is…
Based on the invariance of the phase of waves, plane waves was shown to propagate with negative frequencies in a medium which moves at superluminal speeds opposite to the propagation direction of plane waves. The validity of the invariance…
Even when neglecting diffraction effects, the well-known equations of geometrical optics (GO) are not entirely accurate. Traditional GO treats wave rays as classical particles, which are completely described by their coordinates and…
Fully developed homogeneous isotropic turbulence in 2D is fundamentally different from 3D. In 2D, the simultaneous conservation of both energy and enstrophy in the inertial ranges of scales leads to a forward cascade of enstrophy and a…
We consider a two-layer fluid with a depth-dependent upper-layer current (e.g. a river inflow, an exchange flow in a strait, or a wind-generated current). In the rigid-lid approximation, we find the necessary singular solution of the…
According to the principle of relativity, the equations describing the laws of physics should have the same forms in all admissible frames of reference, i.e., form-invariance is an intrinsic property of correct wave equations. However, so…
By considering the irreducible representations of the Lorentz group, an analysis of the different spin-2 waves is presented. In particular, the question of the helicity is discussed. It is concluded that, although from the point of view of…
The relativistic two-body problem is considered for spinless particles subject to an external macroscopic electromagnetic field. When this field is made of the monochromatic superposition of two counter-propagating plane waves (and provided…
This short note is concerned with the rotational invariance of the stored energy density in continuum physics as a scalar function of a few vectors. A simple derivation is presented for the determination of the general form of the energy…
We calculate the helicity and chirality effects experienced by a spin-1/2 particle subjected to classical electromagnetic and gravitational fields. The helicity evolution is then determined in the non-relativistic, relativistic, and…
Helicity is a fundamental conserved quantity in physical systems governed by vector fields whose evolution is described by volume-preserving transformations on a three-manifold. Notable examples include inviscid, incompressible fluid flows,…
The topological underpinning of magnetic fields connected to a planar boundary is naturally described by field line winding. This observation leads to the definition of winding helicity, which is closely related to the more commonly…
Decaying magnetohydrodynamic (MHD) turbulence is important in various astrophysical contexts, including early universe magnetic fields, star formation, turbulence in galaxy clusters, magnetospheres and solar corona. Previously known in the…
Plane-symmetric gravitational waves are considered as gravitational lenses. Numbers of images, frequency shifts, mutual angles, and image distortion parameters are computed exactly in essentially all non-singular plane wave spacetimes. For…
Magnetic fields of laboratory, planetary, stellar, and galactic plasmas commonly exhibit significant order on large temporal or spatial scales compared to the otherwise random motions within the hosting system. Such ordered fields can be…
Although gauge invariance preserves the values of physical observables, a gauge transformation can introduce important alterations of physical interpretations. To understand this, it is first shown that a gauge transformation is not, in…
We construct small-amplitude periodic water waves with multiple critical layers. In addition to waves with arbitrarily many critical layers and a single crest in each period, two-dimensional sets of waves with several crests and troughs in…
Refraction is the predominant mechanism causing spatially inhomogeneous surface gravity wave fields. However, the complex interplay between depth- and current-induced wave refraction remains poorly understood. Assuming weak currents and…
It is shown that the helicity amplitudes can be used to describe and analyze the properties of the electromagnetic field in classical and in quantum theory. On the one hand they embody the relativistic content of electromagnetic theory. On…
We study the evolution of kinetic and magnetic energy spectra in magnetohydrodynamic flows in the presence of strong cross helicity. For forced turbulence, we find weak inverse transfer of kinetic energy toward the smallest wavenumber. This…