Gravitational Wave - Gauge Field Oscillations

Gravitational waves propagating through a stationary gauge field transform into gauge field waves and back again. When multiple families of flavor-space locked gauge fields are present, the gravitational and gauge field waves exhibit novel dynamics. At high frequencies, the system behaves like coupled oscillators in which the gravitational wave is the central pacemaker. Due to energy conservation and exchange among the oscillators, the wave amplitudes lie on a multidimensional sphere, reminiscent of neutrino flavor oscillations. This phenomenon has implications for cosmological scenarios based on flavor-space locked gauge fields.Comment: 4 pages, 3 figures, 1 animation; replacement matches published versio

Wave number selection under the action of accelerated rotation

Unsteady viscous incompressible flows in a spherical layer due to an increase in the rotation velocity of the inner sphere with constant acceleration are investigated. The acceleration starts at the Reynolds numbers Re corresponding to a stationary flow and ends at Re higher than the stability limit of the stationary flow, whereupon the rotation velocity of the inner sphere remains constant. The outer sphere is fixed and the spherical layer thickness is equal to the inner sphere radius. The inner sphere acceleration effect is studied on both the formation of one of two possible secondary-flow structures after the acceleration has been stopped, namely, traveling azimuthal waves with wavenumbers of 3 or 4, and on the change in the flow structure during the action of the acceleration. It is shown that not only an increase in the acceleration but also a decrease in Re corresponding to the acceleration onset can lead to an increase in the deviation of the instantaneous velocity profiles from their stationary values and can be accompanied by a variation in the secondary flow wavenumber.Peer reviewe

Excitation of non-radial stellar oscillations by gravitational waves: a first model

The excitation of solar and solar-like g modes in non-relativistic stars by arbitrary external gravitational wave fields is studied starting from the full field equations of general relativity. We develop a formalism that yields the mean-square amplitudes and surface velocities of global normal modes excited in such a way. The isotropic elastic sphere model of a star is adopted to demonstrate this formalism and for calculative simplicity. It is shown that gravitational waves solely couple to quadrupolar spheroidal eigenmodes and that normal modes are only sensitive to the spherical component of the gravitational waves having the same azimuthal order. The mean-square amplitudes in case of stationary external gravitational waves are given by a simple expression, a product of a factor depending on the resonant properties of the star and the power spectral density of the gravitational waves' spherical accelerations. Both mean-square amplitudes and surface velocities show a characteristic R^8-dependence (effective R^2-dependence) on the radius of the star. This finding increases the relevance of this excitation mechanism in case of stars larger than the Sun.Comment: 8 pages, to be published in MNRAS (in press); corrected typo

General Classical Electrodynamics

Maxwell’s Classical Electrodynamics (MCED) suffers several inconsistencies: (1) the Lorentz force law of MCED violates Newton’s Third Law of Motion (N3LM) in case of stationary and divergent or convergent current distributions; (2) the general Jefimenko electric field solution of MCED shows two longitudinal far fields that are not waves; (3) the ratio of the electrodynamic energy-momentum of a charged sphere in uniform motion has an incorrect factor of 4/3. A consistent General Classical Electrodynamics (GCED) is presented that is based on Whittaker’s reciprocal force law that satisfies N3LM. The Whittaker force is expressed as a scalar magnetic field force, added to the Lorentz force. GCED is consistent only if it is assumed that the electric potential velocity in vacuum, ’a’, is much greater than ’c’ (a ≫ c); GCED reduces to MCED, in case we assume a = c. Longitudinal electromagnetic waves and superluminal longitudinal electric potential waves are predicted. This theory has been verified by seemingly unrelated experiments, such as the detection of superluminal Coulomb fields and longitudinal Ampère forces, and has a wide range of electrical engineering applications

Linearly forced fluid flow on a rotating sphere

We investigate generalized Navier-Stokes (GNS) equations that couple nonlinear advection with a generic linear instability. This analytically tractable minimal model for fluid flows driven by internal active stresses has recently been shown to permit exact solutions on a stationary two-dimensional sphere. Here, we extend the analysis to linearly driven flows on rotating spheres. We derive exact solutions of the GNS equations corresponding to time-independent zonal jets and superposed westward-propagating Rossby waves, qualitatively similar to those seen in planetary atmospheres. Direct numerical simulations with large rotation rates obtain statistically stationary states close to these exact solutions. The measured phase speeds of waves in the GNS simulations agree with analytical predictions for Rossby waves.Comment: 13 pages, 6 figure

Perturbation Analysis of the Kuramoto Phase Diffusion Equation Subject to Quenched Frequency Disorder

The Kuramoto phase diffusion equation is a nonlinear partial differential equation which describes the spatio-temporal evolution of a phase variable in an oscillatory reaction diffusion system. Synchronization manifests itself in a stationary phase gradient where all phases throughout a system evolve with the same velocity, the synchronization frequency. The formation of concentric waves can be explained by local impurities of higher frequency which can entrain their surroundings. Concentric waves in synchronization also occur in heterogeneous systems, where the local frequencies are distributed randomly. We present a perturbation analysis of the synchronization frequency where the perturbation is given by the heterogeneity of natural frequencies in the system. The nonlinearity in form of dispersion, leads to an overall acceleration of the oscillation for which the expected value can be calculated from the second order perturbation terms. We apply the theory to simple topologies, like a line or the sphere, and deduce the dependence of the synchronization frequency on the size and the dimension of the oscillatory medium. We show that our theory can be extended to include rotating waves in a medium with periodic boundary conditions. By changing a system parameter the synchronized state may become quasi degenerate. We demonstrate how perturbation theory fails at such a critical point.Comment: 22 pages, 5 figure

Wave number selection under the action of accelerated rotation

Unsteady viscous incompressible flows in a spherical layer due to an increase in the rotation velocity of the inner sphere with constant acceleration are investigated. The acceleration starts at the Reynolds numbers Re corresponding to a stationary flow and ends at Re higher than the stability limit of the stationary flow, whereupon the rotation velocity of the inner sphere remains constant. The outer sphere is fixed and the spherical layer thickness is equal to the inner sphere radius. The inner sphere acceleration effect is studied on both the formation of one of two possible secondary-flow structures after the acceleration has been stopped, namely, traveling azimuthal waves with wavenumbers of 3 or 4, and on the change in the flow structure during the action of the acceleration. It is shown that not only an increase in the acceleration but also a decrease in Re corresponding to the acceleration onset can lead to an increase in the deviation of the instantaneous velocity profiles from their stationary values and can be accompanied by a variation in the secondary flow wavenumber. © Published under licence by IOP Publishing Ltd.This work was supported by the Russian Foundation for Basic Research Project No. 16-05-00004 and 18-08-00074. MG acknowledges,in part, support from the ERC Advanced Grant No. 320773. Research at the Ural Federal University is supported by the Act 211 of the Government of the Russian Federation, agreement No 02.A03.21.0006

Wave and Vortex Dynamics on the Surface of a Sphere

Motivated by the observed potential vorticity structure of the stratospheric polar vortex, we study the dynamics of linear and nonlinear waves on a zonal vorticity interface in a two-dimensional barotropic flow on the surface of a sphere (interfacial Rossby waves). After reviewing the linear problem, we determine, with the help of an iterative scheme, the shapes of steadily propagating nonlinear waves; a stability analysis reveals that they are (nonlinearly) stable up to very large amplitude. We also consider multi-vortex equilibria on a sphere: we extend the results of Thompson (1883) and show that a (latitudinal) ring of point vortices is more unstable on the sphere than in the plane; notably, no more than three point vortices on the equator can be stable. We also determine the shapes of finite-area multi-vortex equilibria, and reveal additional modes of instability feeding off shape deformations which ultimately result in the complex merger of some or all of the vortices. We discuss two specific applications to geophysical flows: for conditions similar to those of the wintertime terrestrial stratosphere, we show that perturbations to a polar vortex with azimuthal wavenumber 3 are close to being stationary, and hence are likely to be resonant with the tropospheric wave forcing; this is often observed in high-resolution numerical simulations as well as in the ozone data. Secondly, we show that the linear dispersion relation for interfacial Rossby waves yields a good fit to the phase velocity of the waves observed on Saturn’s ‘ribbon’

Wave and Vortex Dynamics on the Surface of a Sphere

Motivated by the observed potential vorticity structure of the stratospheric polar vortex, we study the dynamics of linear and nonlinear waves on a zonal vorticity interface in a two-dimensional barotropic flow on the surface of a sphere (interfacial Rossby waves). After reviewing the linear problem, we determine, with the help of an iterative scheme, the shapes of steadily propagating nonlinear waves; a stability analysis reveals that they are (nonlinearly) stable up to very large amplitude. We also consider multi-vortex equilibria on a sphere: we extend the results of Thompson (1883) and show that a (latitudinal) ring of point vortices is more unstable on the sphere than in the plane; notably, no more than three point vortices on the equator can be stable. We also determine the shapes of finite-area multi-vortex equilibria, and reveal additional modes of instability feeding off shape deformations which ultimately result in the complex merger of some or all of the vortices. We discuss two specific applications to geophysical flows: for conditions similar to those of the wintertime terrestrial stratosphere, we show that perturbations to a polar vortex with azimuthal wavenumber 3 are close to being stationary, and hence are likely to be resonant with the tropospheric wave forcing; this is often observed in high-resolution numerical simulations as well as in the ozone data. Secondly, we show that the linear dispersion relation for interfacial Rossby waves yields a good fit to the phase velocity of the waves observed on Saturn’s ‘ribbon’