Non-dissipative Fluid Research Articles

Matter–curvature effects upon the dissipative viscous collapse of massive stellar object

This paper investigates the evolutionary phases of a collapsing dissipative star cluster in the presence of dark matter. For this purpose, the minimal coupling model of [Formula: see text] gravity is used as a candidate for exotic matter in star cluster. The collapse equation is derived from generalized dynamical equations which show the total conservation of energy within the cluster. In this context, the approach of Misner and Sharp is applied to study the phenomenon and differentiate between homologous as well as non-homologous gravitational collapse. The generalized dynamical equations are also connected to modified heat transport equations related to heat flux, viscosity and shear, which deals with Israel–Stewart theory (without removing the thermodynamics heat/viscous coupling coefficients). It is found that shear-free and non-dissipative fluid give homologous collapse. The dissipation of collapsing star cluster provides a relation between tidal forces and density inhomogeneity. It is theoretically predicted that the presence of exotic matter controlled the collapsing mechanism.

Complexity of charged anisotropic spherically symmetric fluids in gravity

The previous ideology of complexity factor for the dynamical spheres [Herrera et al 2018, Phys. Rev. D, 98, 104059] is extended for the influence of charge. A dynamical spherically symmetric non-dissipative and dissipative self-gravitating structure is examined in the presence of Maxwell gravity to examine the complexity factor. The pattern of evolution is studied with the minimal complexity constraint. The complexity factor remains the same for the structure of fluid distribution, while we examine homologous constraints for the most basic evolution pattern. We calculate the structure scalars which play an important role in order to understand the fundamental properties of the system. The fluid is geodesic as well as shearing for the dissipative case and there is a large number of solutions. In the non-dissipative fluid distribution, a shear-free, homogeneous and isotropic, geodesic fluid correlates with the evolving homologous and vanishing complexity condition. The implication of the condition of vanishing complexity factor and stability are discussed at the end.

Dissipative unified dark fluid: Observational constraints

We adopt a standard FRW cosmology with a unified scenario, where the usual dark matter and dark energy sectors are replaced by a single dissipative unified dark fluid (DUDF). The equation of state of such fluid can asymptote between two power laws. As a result, it enables fluid to have a smooth transition from dust at early times to dark energy at late times. The dissipation is represented by a bulk viscosity with a constant coefficient, whereas shear viscosity is excluded due to the isotropy of the universe. We performed a likelihood analysis using recent observational datasets from local H0 measurements, Type Ia supernovae, observational Hubble data, baryon acoustic oscillations, and cosmic microwave background to put cosmological constraints on the model. The special case of the non-dissipative unified dark fluid (UDF) is also studied, while a similar analysis is implemented to the ΛCDM model for comparison. Our analysis revealed that between the three analyzed models, the DUDF has the lower χmin2-value. Based on model selection statistics in the form of the Akaike Information Criterion (AIC) and the Bayesian Information Criterion (BIC), we compared different models to select the favored one due to the observational data used. Our results revealed that the UDF model has the minimum AIC, whence, due to the AIC, it is the most favorable model for the data. ΔAIC values of models are, then, measured to this model. This difference indicated that the DUDF model is substantial on the level of empirical support. On the other hand, the BIC results still prefer the ΛCDM model. Our dark fluid also alleviates the tension in the Hubble parameter. We got an H0 value of 70.02 kms−1Mpc−1 for the DUDF model and 70.25 kms−1Mpc−1 for the UDF model. These results alleviate the tension to ∼2.2σ for the DUDF model and ∼2.1σ for the UDF model. In addition, we studied the evolution of the deceleration parameter, the effective equation of state parameter, and the density parameter. We also estimated a value for the viscosity of the cosmic fluid. We found that our unified fluid doesn't deviate from the standard ΛCDM model at early times, with the ability to play the role of the cosmological constant by accelerating the universe at late times.

Hydrodynamics of two-dimensional compressible fluid with broken parity: Variational principle and free surface dynamics in the absence of dissipation

We consider an isotropic compressible non-dissipative fluid with broken parity subject to free surface boundary conditions in two spatial dimensions. The hydrodynamic equations describing the bulk dynamics of the fluid as well as the free surface boundary conditions depend explicitly on the parity breaking non-dissipative odd viscosity term. We construct a variational principle in the form of an effective action which gives both bulk hydrodynamic equations and free surface boundary conditions. The free surface boundary conditions require an additional boundary term in the action which resembles a $1+1D$ chiral boson field coupled to the background geometry. We solve the linearized hydrodynamic equations for the deep water case and derive the dispersion of chiral surface waves. We show that in the long wavelength limit the flow profile exhibits an oscillating vortical boundary layer near the free surface. The thickness of the layer is controlled by the length scale given by the ratio of odd viscosity to the sound velocity $\delta \sim \nu_o/c_s$. In the incompressible limit, $c_s\to \infty$ the vortical boundary layer becomes singular with the vorticity within the layer diverging as $\omega \sim c_s$. The boundary layer is formed by odd viscosity coupling the divergence of velocity $\boldsymbol\nabla \cdot \boldsymbol{v}$ to vorticity $\boldsymbol\nabla \times \boldsymbol{v}$. It results in non-trivial chiral free surface dynamics even in the absence of external forces. The structure of the odd viscosity induced boundary layer is very different from the conventional free surface boundary layer associated with dissipative shear viscosity.

Scattering cross-section of a cylindrical conducting particle illuminated by electromagnetic plane waves near a conducting quarter-space

The study of the electromagnetic scattering by a particle located near a perfectly conducting corner is a fundamental topic in radar imaging, communications, remote sensing and other applications. In earlier works, the analytical modeling considered the linear field and its scattering properties. Nonetheless, energy efficiencies (or cross-sections) are meaningful fundamental physical observables connected with quadratic quantities of the linear field, which reveal additional properties of the scatterer not obtained from the linear scattered field. The aim of this work is therefore directed toward developing an improved analytical formalism for the energy efficiency factors (or cross-sections) of a cylindrical conducting particle, illuminated by electromagnetic plane waves, and located near a perfectly conducting corner-space. Incident plane progressive waves with an arbitrary angle of incidence are considered in a homogeneous, non-dissipative and non-magnetic fluid. The multiple scattering effects occurring between the electrically-conducting cylindrical particle and corner are described rigorously using the modal expansion method in cylindrical coordinates, the classical method of images and the translational addition theorem. Exact closed-form series expansions are derived and numerical examples illustrate the analysis with particular emphases on the distances from the corner-space, particle size and polarization of the incident field. The results are useful to predict the energetic scattering for various applications, and can serve to validate the results of purely numerical methods in experimental design. Some analogies with the acoustical cross-section theory are also noted.

Shear-free axial system and f (G) gravity

This paper investigates the influences of dark sources on the evolution of shear-free axially symmetric dissipative fluid in f (G) gravity. Matter contents (energy terms of the system), corresponding dynamical variables as well as scalar functions are derived in the presence of dark sources. The dark terms appear as one of the sources producing pressure anisotropy and heat dissipation. We then study non-geodesic and geodesic fluids with and without dissipation under shear-free condition. The non-geodesic (non-dissipative) fluid gives inhomogeneous expansion while the geodesic fluid makes the system either vorticity-free or expansion-free. The vorticity-free non-dissipative geodesic fluid reduces the axial system to FRW model in the presence of homogeneous distribution of dark sources while the expansion-free geodesic fluid does not exist even in the presence of dark sources.

An equivalent system of Einstein Equations

We provide the full set of equations governing the evolution of self-gravitating systems by using a tetrad formalism in General Relativity and the orthogonal splitting of the Riemann tensor. We apply this formalism to spherical case and found that: the only static solution with homogeneous energy density, under the physical reasonable considerations, is the Schwarzchild solution; the conditions under which a non-dissipative fluid is static and finally that shear-free and isotropic pressure conditions are equivalent, for non-dissipative fluids with homogeneous energy density.

Dynamical instability of shear-free collapsing star in extended teleparallel gravity

We study the spherically symmetric collapsing star in terms of dynamical instability. We take the framework of extended teleparallel gravity with non-diagonal tetrad, power-law form of model presenting torsion and matter distribution as non-dissipative anisotropic fluid. The vanishing shear scalar condition is adopted to search the insights of collapsing star. We apply first order linear perturbation scheme to metric, matter and $f(T)$ functions. The dynamical equations are formulated under this perturbation scheme to develop collapsing equation for finding dynamical instability limits in two regimes such as Newtonian and post-Newtonian. We obtain constraint free solution of perturbed time dependent part with the help of vanishing shear scalar. The adiabatic index exhibits the instability ranges through second dynamical equation which depend on physical quantities such as density, pressure components, perturbed parts of symmetry of star, etc. We also develop some constraints on positivity of these quantities and obtain instability ranges to satisfy the dynamical instability condition.

First principles approach to the Abraham–Minkowski controversy for the momentum of light in general linear non-dispersive media

We study the problem of the definition of the energy–momentum tensor of light in general moving non-dispersive media with linear constitutive law. Using the basic principles of classical field theory, we show that for the correct understanding of the problem, one needs to carefully distinguish situations when the material medium is modeled either as a background on which light propagates or as a dynamical part of the total system. In the former case, we prove that the (generalized) Belinfante–Rosenfeld (BR) tensor for the electromagnetic field coincides with the Minkowski tensor. We derive a complete set of balance equations for this open system and show that the symmetries of the background medium are directly related to the conservation of the Minkowski quantities. In particular, for isotropic media, the angular momentum of light is conserved despite of the fact that the Minkowski tensor is non-symmetric. For the closed system of light interacting with matter, we model the material medium as a relativistic non-dissipative fluid and we prove that it is always possible to express the total BR tensor of the closed system either in the Abraham or in the Minkowski separation. However, in the case of dynamical media, the balance equations have a particularly convenient form in terms of the Abraham tensor. Our results generalize previous attempts and provide a first principles basis for a unified understanding of the long-standing Abraham–Minkowski controversy without ad hoc arguments.

Dynamical Instability of Expansion-Free Collapse in f(T) Gravity

In this paper, we analyze the dynamical instability of a spherically symmetric collapsing star in the context of f(T) gravity. For this purpose, we assume power-law f(T) model with non-dissipative anisotropic fluid distribution under expansion-free condition. The perturbation scheme is applied to all matter, metric and f(T) functions. We formulate dynamical equations using contracted Bianchi identities to investigate dynamical instability ranges in Newtonian and post-Newtonian regimes. It is found that the instability ranges of expansion-free fluid are independent of adiabatic index but depend on radial density profile, anisotropic pressure and torsion terms.

Effects of some physical factors on the inhomogeneity in planar symmetry

This paper is devoted to identify some physical causes of energy density inhomogeneity and stability of self-gravitating relativistic fluids in plane symmetry such as Weyl tensor, local anisotropy, dissipative terms and their specific combination. We first develop a relationship between matter variables and the Weyl tensor and then formulate dynamical equations using Bianchi identities. For the non-dissipative dust fluid, we conclude that the system will remain homogeneous if and only if it is conformally flat which implies the shear-free condition. However, the converse is not true for the non-dissipative isotropic fluid. For non-dissipative anisotropic fluid, the inhomogeneity factor is identified to be one of the structure scalars. A particular case of geodesic with dissipation is also discussed.

Dynamical instability of spherical collapse in f舁(T) gravity

We study the dynamical instability of a spherically symmetric collapsing star in the context of f (T) gravity. For this purpose, we assume power-law f (T) model with non-dissipative anisotropic fluid distribution and find the dynamical equations which are used to construct collapse equation. The perturbation scheme is applied to all matter, metric and f (T) functions. We formulate the collapse equation under perturbation to investigate dynamical instability ranges in Newtonian as well as post-Newtonian regimes. It is found that these ranges depend on structural quantities of the collapsing star through adiabatic index. Finally, we develop some constraints on positivity of these quantities to meet the dynamical instability condition.

Viscoelastic tidal dissipation in giant planets and formation of hot Jupiters through high-eccentricity migration

We study the possibility of tidal dissipation in the solid cores of giant planets and its implication for the formation of hot Jupiters through high-eccentricity migration. We present a general framework by which the tidal evolution of planetary systems can be computed for any form of tidal dissipation, characterized by the imaginary part of the complex tidal Love number, ${\rm Im}[{\tilde k}_2(\omega)]$, as a function of the forcing frequency $\omega$. Using the simplest viscoelastic dissipation model (the Maxwell model) for the rocky core and including the effect of a nondissipative fluid envelope, we show that with reasonable (but uncertain) physical parameters for the core (size, viscosity and shear modulus), tidal dissipation in the core can accommodate the tidal-Q constraint of the Solar system gas giants and at the same time allows exoplanetary hot Jupiters to form via tidal circularization in the high-e migration scenario. By contrast, the often-used weak friction theory of equilibrium tide would lead to a discrepancy between the Solar system constraint and the amount of dissipation necessary for high-e migration. We also show that tidal heating in the rocky core can lead to modest radius inflation of the planets, particularly when the planets are in the high-eccentricity phase ($e\sim 0.6$) during their high-e migration. Finally, as an interesting by-product of our study, we note that for a generic tidal response function ${\rm Im}[{\tilde k}_2(\omega)]$, it is possible that spin equilibrium (zero torque) can be achieved for multiple spin frequencies (at a given $e$), and the actual pseudo-synchronized spin rate depends on the evolutionary history of the system.

Ballooning theory of the second kind—two dimensional tokamak modes

The 2-D ballooning transform, devised to study local high toroidal number (n) fluctuations in axisymmetric toroidal system (like tokamaks), yields a well-defined partial differential equation for the linear eigenmodes. In this paper, such a ballooning equation of the second kind is set up for ion temperature gradient driven modes pertinent to a 2-D non-dissipative fluid plasma; the resulting partial differential equation is numerically solved, to calculate the global eigenvalues, and the 2-D mode structure is presented graphically along with analytical companions. The radial localization of the mode results from translational symmetry breaking for growing modes and is a vivid manifestation of spontaneous symmetry breaking in tokamak physics. The eigenmode, poloidally ballooned at ϑ=±π/2, is radially shifted from associated rational surface. The global eigenvalue is found to be very close to the value obtained in 1-D parameterized (λ=∓π/2) case. The 2-D eigenmode theory is applied to estimate the toroidal ...

Effects of electromagnetic field on energy density inhomogeneity in self-gravitating fluids

This paper is devoted to study the effects of electromagnetic field on the energy density inhomogeneity in the relativistic self-gravitating fluids for spherically symmetric spacetime. Two important equations of the Weyl tensor are formulated which help to analyze the energy density inhomogeneity in this scenario. We investigate two types of fluids, i.e., non-dissipative and dissipative. The non-dissipative fluid further includes dust, locally isotropic, and locally anisotropic charged fluids. We explore the effects of different factors on energy density inhomogeneity in all these cases, in particular, the effect of charge.

Interacting Wave Fronts and Rarefaction Waves in a Second Order Model of Nonlinear Thermoviscous Fluids

A wave equation including nonlinear terms up to the second order for a thermoviscous Newtonian fluid is proposed. In the lossless case this equation results from an expansion to third order of the Lagrangian for the fundamental non-dissipative fluid dynamical equations. Thus it preserves the Hamiltonian structure, in contrast to the Kuznetsov equation, a model often used in nonlinear acoustics. An exact traveling wave front solution is derived from a generalized traveling wave assumption for the velocity potential. Numerical studies of the evolution of a number of arbitrary initial conditions as well as head-on colliding and confluent wave fronts exhibit several nonlinear interaction phenomena. These include wave fronts of changed velocity and amplitude along with the emergence of rarefaction waves. An analysis using the continuity of the solutions as well as the boundary conditions is proposed. The dynamics of the rarefaction wave is approximated by a collective coordinate approach in the energy balance equation.

Continuous compression waves in the two-dimensional Riemann problem

The interaction between a plane shock wave in a plate and a wedge is considered within the framework of the nondissipative compressible fluid dynamic equations. The wedge is filled with a material that may differ from that of the plate. Based on the numerical solution of the original equations, self-similar solutions are obtained for several versions of the problem with an iron plate and a wedge filled with aluminum and for the interaction of a shock wave in air with a rigid wedge. The behavior of the solids at high pressures is approximately described by a two-term equation of state. In all the problems, a two-dimensional continuous compression wave develops as a wave reflected from the wedge or as a wave adjacent to the reflected shock. In contrast to a gradient catastrophe typical of one-dimensional continuous compression waves, the spatial gradient of a two-dimensional compression wave decreases over time due to the self-similarity of the solution. It is conjectured that a phenomenon opposite to the gradient catastrophe can occur in an actual flow with dissipative processes like viscosity and heat conduction. Specifically, an initial shock wave is transformed over time into a continuous compression wave of the same amplitude.

Expansion-free evolving spheres must have inhomogeneous energy density distributions

In a recent paper a systematic study on shearing expansion-free spherically symmetric distributions was presented. As a particular case of such systems, the Skripkin model was mentioned, which corresponds to a nondissipative perfect fluid with a constant energy density. Here we show that such a model is inconsistent with junction conditions. It is shown that in general for any nondissipative fluid distribution, the expansion-free condition requires the energy density to be inhomogeneous. As an example we consider the case of dust, which allows for a complete integration.

Solar wind flow past Venus and its implications for the occurrence of the Kelvin–Helmholtz instability

In this paper, the solar wind flow around Venus is modeled as a nondissipative fluid which obeys the ideal magnetohydrodynamic equations extended for mass loading processes. The mass loading parameter is calculated for four different cases, corresponding to solar minimum and maximum XUV flux and to nominal and low solar wind velocity. We get smooth profiles of the field and plasma parameters in the magnetosheath. Based on the results of this flow model, we investigate the occurrence of the Kelvin–Helmholtz (K–H) instability at the equatorial flanks of the ionopause of Venus. By comparing the instability growth time with the propagation time of the K–H wave, we find that the K–H instability can evolve at the ionopause for all four solar wind conditions.

Practical use of a Lie algebra structure in non-dissipative fluid and plasma models

A class of Hamiltonian models is considered that both includes many important examples from fluid and plasma theory and admits an elementary and simple abstract formulation. The formalism is illustrated by explicit expressions for both incompressible and compressible ideal magnetohydrodynamics, including a Coriolis force term and, in the incompressible case, allowing for a sharp ideally conducting boundary. The small-amplitude expansion is studied for a general background state, and the abstract setting gives much control of the usually messy algebra. One result is a new general and surprisingly simple symmetric expression for the coupling strength in the resonant three-wave interaction process. It may provide a convenient starting point for wave coupling calculations and seems suitable for the use in conjunction with computer algebra when various concrete models are considered.