Irrotational Research Articles

Geometrical Structure in a Perfect Fluid Spacetime with Conformal Ricci–Yamabe Soliton

The present paper aims to deliberate the geometric composition of a perfect fluid spacetime with torse-forming vector field ξ in connection with conformal Ricci–Yamabe metric and conformal η-Ricci–Yamabe metric. We delineate the conditions for conformal Ricci–Yamabe soliton to be expanding, steady or shrinking. We also discuss conformal Ricci–Yamabe soliton on some special types of perfect fluid spacetime such as dust fluid, dark fluid and radiation era. Furthermore, we design conformal η-Ricci–Yamabe soliton to find its characteristics in a perfect fluid spacetime and lastly acquired Laplace equation from conformal η-Ricci–Yamabe soliton equation when the potential vector field ξ of the soliton is of gradient type. Overall, the main novelty of the paper is to study the geometrical phenomena and characteristics of our newly introduced conformal Ricci–Yamabe and conformal η-Ricci–Yamabe solitons to apply their existence in a perfect fluid spacetime.

Lie Symmetries, Closed-Form Solutions, and Various Dynamical Profiles of Solitons for the Variable Coefficient (2+1)-Dimensional KP Equations

This investigation focuses on two novel Kadomtsev–Petviashvili (KP) equations with time-dependent variable coefficients that describe the nonlinear wave propagation of small-amplitude surface waves in narrow channels or large straits with slowly varying width and depth and non-vanishing vorticity. These two variable coefficients, Kadomtsev–Petviashvili (VCKP) equations in (2+1)-dimensions, are the main extensions of the KP equation. Applying the Lie symmetry technique, we carry out infinitesimal generators, potential vector fields, and various similarity reductions of the considered VCKP equations. These VCKP equations are converted into nonlinear ODEs via two similarity reductions. The closed-form analytic solutions are achieved, including in the shape of distinct complex wave structures of solitons, dark and bright soliton shapes, double W-shaped soliton shapes, multi-peakon shapes, curved-shaped multi-wave solitons, and novel solitary wave solitons. All the obtained solutions are verified and validated by using back substitution to the original equation through Wolfram Mathematica. We analyze the dynamical behaviors of these obtained solutions with some three-dimensional graphics via numerical simulation. The obtained variable coefficient solutions are more relevant and useful for understanding the dynamical structures of nonlinear KP equations and shallow water wave models.

A complex-analytic approach to kinetic energy properties of irrotational flows

Using methods from complex analysis we obtain some qualitative results for the kinetic energy of two-dimensional irrotational water flows (monotonicity of horizontal averages with depth, location of the extrema).

K-cosymplectic metric as an η-Ricci soliton

Let M be an almost cosymplectic manifold such that the Reeb vector field is Killing. In this paper, it is proved that if the metric of M satisfying the [Formula: see text]-Einstein condition is an [Formula: see text]-Ricci soliton, then either M is Ricci flat or the potential vector field is an infinitesimal contact transformation. Also, a concrete example of cosymplectic [Formula: see text]-manifold admitting non-trivial Ricci and [Formula: see text]-Ricci solitons is constructed.

The topological phase of bright solitons

We study the topological phase of bright soliton with arbitrary velocity under the self-steepening effect. Such topological phase can be described by the topological vector potential and effective magnetic field. We find that the point-like magnetic fields correspond to the density peak of such bright solitons, where each elementary magnetic flux is π. Furthermore, the topological phase of interactional two bright solitons is discussed. In particular, we show that interaction of two solitons can generate an additional topological field due to their nontrivial topological phase. Our research provided the possibility to use bright solitons to explore topological properties.

Inertio–elastic instability of a vortex column

We analyse the instability of a vortex column in a dilute polymer solution at large ${{Re}}$ and ${{De}}$ with ${{El}} = {{De}}/{{Re}}$ , the elasticity number, being finite. Here, ${{Re}} = \varOmega _0 a^2/\nu$ and ${{De}} = \varOmega _0 \tau$ are, respectively, the Reynolds and Deborah numbers based on the core angular velocity ( $\varOmega _0$ ), the radius of the column ( $a$ ), the total (solvent plus polymer) kinematic viscosity ( $\nu = (\mu _s +\mu _p)/\rho$ with $\mu _s$ and $\mu _p$ being the solvent and polymer contributions to the viscosity) and the polymeric relaxation time ( $\tau$ ). The stability of small-amplitude perturbations in this distinguished limit is governed by the elastic Rayleigh equation whose spectrum is parameterized by ${E} = {{El}}(1-\beta )$ , $\beta$ being the ratio of the solvent to the solution viscosity. The neglect of the relaxation terms, in the said limit, implies that the polymer solution supports undamped elastic shear waves propagating relative to the base-state flow. Unlike the neutrally stable inviscid case, an instability of the vortex column arises for finite ${E}$ due to a pair of elastic shear waves being driven into a resonant interaction under the differential convection by the irrotational shearing flow outside the core. An asymptotic analysis for the Rankine profile shows the absence of an elastic threshold for this instability. The growth rate is $O(\varOmega _0)$ for order unity $E$ , although it becomes transcendentally small for ${E} \ll 1$ , being $O(\varOmega _0 {E}^2{\rm e}^{-1/{E}^{{1}/{2}}})$ . An accompanying numerical investigation shows that the instability persists for smooth monotonically decreasing vorticity profiles, provided the radial extent of the transition region (from the rotational core to the irrotational exterior) is less than a certain ${E}$ -dependent threshold.

A numerical approach for coupled analysis of the seismic response of a cable-moored submerged floating tunnel

A submerged floating tunnel (SFT) is propounded as an efficacious alternative to conventional bridges and underground/submerged tunnels for crossing deep waterways. SFT designers must ensure safe margins and develop approaches to prevail a wide range of plausible situations related to transport, wave, natural vibrations etc. to evaluate the structural stability. To date, only limited researches on this field have been performed to illustrate the significance of seaquake analyses and their effects have been underlined. The present paper intends at numerically simulating a two-dimensional (2D) fluid-structure interaction (FSI) problem in order to scrutinize the dynamic response of an SFT system under bidirectional earthquake actions. Hydrodynamic Pressure due to seismic base excitation is considered as independent nodal variables to represent the gravity influenced inviscid, compressible and irrotational fluid flow effects and the tunnel shell is considered as flexible. This work exposes the importance of the input seismic excitation characteristics that governs the distribution of the induced internal acceleration/force around the lining of the tunnel. Numerical results indicate that the increment rate of the internal acceleration in high SFT caused by vertical ground motion is nearly by 200% when compared to the low-laying tunnel. It is confirmed that long-period record may amplify the overall response of the SFT (up to 80%) when the tunnel approaches the ocean surface, as well as the mooring tensile force to a lesser extent. Finally the proposed coupled numerical procedure suggests that earthquake response spectrum in various intensity levels has an influential role in the response of long-span SFTs and special attention should be paid to the seismic design of such structures.

Transport coefficients for modeling fission dynamics

Transport coefficients are important ingredients in dynamical investigations of a nuclear fission process, which determine the dynamical evolution of the fissioning system. The inertia (mass) and friction (dissipation) tensors influence substantially on different observables. The proper calculation of these tensors is a necessary condition for correct modeling of the fission process. The calculation of the inertia and friction tensors is presented for a large variety of nuclear shapes generated by a {c,h,α} parametrization. The inertia tensor is calculated within the Werner-Wheeler approximation for incompressible irrotational flow. The friction tensor is calculated within the one-body and two-body mechanisms of nuclear dissipation. A numerical code is made available, which calculates all these quantities. Program summaryProgram Title: Mass_DissCPC Library link to program files:https://doi.org/10.17632/rcndf6sbns.1Licensing provisions: CC BY NC 3.0Programming language: C++Nature of problem: The modeling of the nuclear fission within dynamical consideration requires calculation of the inertia and friction coefficients. This calculation should be performed for a large variety of the nuclear shapes, which describe the evolution of the shape of compound nucleus from the ground state till the separated fission fragments.Solution method: The inertia tensor is calculated within the Werner-Wheeler approximation for incompressible irrotational flow. The friction tensor is calculated within the one-body and two-body mechanisms of the nuclear dissipation. The shape of the fissioning nucleus is described by the {c,h,α} parametrization. This parametrization determines the axially symmetric shapes in cylindrical coordinates. The inertia and friction tensors are calculated using numerical integration procedure as a function of the three shape parameters. All subroutines, which define the nuclear shape, are separated from the code, which calculates the inertia and friction tensors. Thus, the program could be adopted for any other shape parameterization in case if it is given in cylindrical coordinates.

Selfsimilar Hessian manifolds

A selfsimilar manifold is a Riemannian manifold (M,g) endowed with a homothetic vector field ξ. We characterize global selfsimilar manifolds and describe the structure of local selfsimilar manifolds. We prove that any selfsimilar manifold with a potential homothetic vector field is a conical Riemannian manifold or a Euclidean space. A radiant Hessian manifold is a selfsimilar Hessian manifold (M,∇,g,ξ) such that ∇ξ=λId, where λ is a constant. We prove that any selfsimilar Hessian manifold with a potential homothetic vector field is locally isomorphic to a product of radiant Hessian manifolds and describe the local structure of radiant selfsimilar Hessian manifolds.

∗-η-Ricci Soliton and Gradient Almost ∗-η-Ricci Soliton Within the Framework of Para-Kenmotsu Manifolds

The goal of the present study is to study the ∗-η-Ricci soliton and gradient almost ∗-η-Ricci soliton within the framework of para-Kenmotsu manifolds as a characterization of Einstein metrics. We demonstrate that a para-Kenmotsu metric as a ∗-η-Ricci soliton is an Einstein metric if the soliton vector field is contact. Next, we discuss the nature of the soliton and discover the scalar curvature when the manifold admits a ∗-η-Ricci soliton on a para-Kenmotsu manifold. After that, we expand the characterization of the vector field when the manifold satisfies the ∗-η-Ricci soliton. Furthermore, we characterize the para-Kenmotsu manifold or the nature of the potential vector field when the manifold satisfies the gradient almost ∗-η-Ricci soliton.

Almost Kenmotsu 3-h-metric as a cotton soliton

PurposeCotton soliton is a newly introduced notion in the field of Riemannian manifolds. The object of this article is to study the properties of this soliton on certain contact metric manifolds.Design/methodology/approachThe authors consider the notion of Cotton soliton on almost Kenmotsu 3-manifolds. The authors use a local basis of the manifold that helps to study this notion in terms of partial differential equations.FindingsFirst the authors consider that the potential vector field is pointwise collinear with the Reeb vector field and prove a non-existence of such Cotton soliton. Next the authors assume that the potential vector field is orthogonal to the Reeb vector field. It is proved that such a Cotton soliton on a non-Kenmotsu almost Kenmotsu 3-h-manifold such that the Reeb vector field is an eigen vector of the Ricci operator is steady and the manifold is locally isometric to.Originality/valueThe results of this paper are new and interesting. Also, the Proposition 3.2 will be helpful in further study of this space.

Convective Velocity Perturbations and Excess Gain in Flame Response as a Result of Flame-Flow Feedback

Convective velocity perturbations (CVPs) are known to play an important role in the response of flames to acoustic perturbations and in thermoacoustic combustion instabilities. In order to elucidate the flow-physical origin of CVPs, the present study models the response of laminar premixed slit flames to low amplitude perturbations of the upstream flow velocity with a reduced order flow decomposition approach: A linearized G-equation represents the shape and heat release rate of the perturbed flame, while the velocity perturbation field is decomposed into irrotational and solenoidal contributions. The former are determined with a conformal mapping from geometry and boundary conditions, whereas the latter are governed by flame front curvature and flow expansion across the flame, which generates baroclinic vorticity. High-resolution CFD analysis provides values of model parameters and confirms the plausibility of model results. This flow decomposition approach makes it possible to explicitly evaluate and analyze the respective contributions of irrotational and solenoidal flows to the flame response, and conversely the effect of flame perturbations on the flow. The use of the popular ad hoc hypothesis of convected velocity perturbation is avoided. It is found that convected velocity perturbations do not result from immediate acoustic-to-hydrodynamic mode conversion, but are generated by flame-flow feedback. In this sense, models for flame dynamics that rely on ad-hoc models for CVPs do not respect causality. Furthermore, analysis of the flame impulse response reveals that for the configuration investigated, flame-flow feedback is also responsible for “excess gain” of the flame response, that is, the magnitude of the flame frequency response above unity.

Asymptotic Modeling of a Viscous Laminar Flow Around Thin Airfoils: Resolution and Experimental Treatment in Case of Supersonic Flow

In this paper, starting from the conservation equations in a 2D orthogonal curvilinear coordinate system, an approached asymptotic model for perturbed potential flow equation is established. The study considers a high-speed steady laminar irrotational flow of a compressible and viscous fluid, over thin airfoils at low incidence in the standard atmosphere. This study is aimed to contribute to developing a fully two-dimensional general model that is efficiently applicable to industrial scale and scientific research, in a laminar flow, defined on thin geometries as it takes into consideration both compressibility and viscous effects. The singular perturbation model is solved in case of supersonic viscous flow, based on asymptotic and singular perturbation methods. Asymptotic matching of different layers is done through the triple deck theory. Experimental measurements have been conducted, with the AF300 supersonic wind tunnel, on a NACA 43013 airfoil model fitted with two pressure taps. The comparison of the local Mach numbers between the asymptotic model and the experimentation shows the accuracy of the model in case of laminar flow but diverge relatively as the flow becomes turbulent towards the trailing edge.

Closed-form invariant solutions from the Lie symmetry analysis and dynamics of solitonic profiles for (2 + 1)-dimensional modified Heisenberg ferromagnetic system

This paper studies the ([Formula: see text])-dimensional modified Heisenberg ferromagnetic (MHF) system, which describes the different nonlinear dynamical structures for long water-waves of small amplitude with weakly nonlinear restoring forces and high-frequency dispersion. This MHF system arises in the propagation of the magnetization vector of the isotropic ferromagnet and biological pattern formation. By employing the Lie symmetry analysis method, infinitesimal generators, Lie point symmetries, potential vector fields, commutation relations of infinitesimal vectors, and attractive symmetry reductions are derived. Based on the two phases of Lie similarity reductions, ([Formula: see text])-dimensional MHF system is reduced to various nonlinear ordinary differential equations (ODEs). Afterwards, with the help of symbolic computation, we solve the acquired ODEs and obtain a variety of exact closed-form solutions involving arbitrary independent functions and other constant parameters. The physical features of the obtained multi-wave soliton solutions are demonstrated to analyze the impact of the involved arbitrary independent functions on the dynamics of the solitary wave solutions via three-dimensional graphics. These exact solutions are accomplished in the shapes of single solitons, doubly solitons, multi-wave solitons, elastic behavior of multisoliton, oscillating multi-solitons, curved-shaped periodic solitons, and kink-type solitons, and so on. The newly constructed results show the trustworthiness, reliability, and efficiency of the Lie symmetry technique for obtaining the invariant closed-form solutions to nonlinear governing model. Moreover, conservation laws and self-adjoint systems have been obtained by implementing Noether’s technique. By using Lie symmetry analysis, the achieved outcomes might be helpful to understand the physical formation of this model and confirm the effectiveness and authenticity of the mentioned method.

Turbulent entrainment in viscoelastic fluids

Direct numerical simulations (DNS) of turbulent fronts spreading into an irrotational flow region are used to analyse the turbulent entrainment mechanism for viscoelastic fluids. The simulations use the FENE-P fluid model and are initiated from DNS of isotropic turbulence with Weissenberg and turbulence Reynolds numbers varying in the ranges $1.30 \le Wi \le 3.46$ and $206 \le Re_{\lambda }^{0} \le 404$, respectively. The enstrophy dynamics near the turbulent/non-turbulent interface (TNTI) layer, that separates regions of turbulent and irrotational flow, includes a new mechanism – the viscoelastic production – caused by the interaction between the vorticity field and the polymer stresses. This term can be a sink or a source of enstrophy in the turbulent core region of the flow, depending on the Weissenberg number, and contributes to the initial growth of the enstrophy in the viscous superlayer, together with the viscous diffusion, which is the only mechanism present for Newtonian fluids. For low and moderate Weissenberg numbers the scaling of the TNTI layer is similar to the scaling of TNTI layers for Newtonian fluids, but this is no longer the case at high Weissenberg numbers where the enstrophy tends to be concentrated into thin vortex sheets instead of vortex tubes. Finally, it is shown that the substantial decrease of the entrainment rates observed in turbulent flows of viscoelastic fluids, compared with Newtonian fluids, is caused by a reduction of the surface area and fractal dimension of the irrotational boundary, originated by the depletion of ‘active’ scales of motion in the fluid solvent caused by the viscoelasticity.

Locally homogeneous non-gradient quasi-Einstein 3-manifolds

Abstract In this paper, we classify the compact locally homogeneous non-gradient m-quasi Einstein 3- manifolds. Along the way, we also prove that given a compact quotient of a Lie group of any dimension that is m-quasi Einstein, the potential vector field X must be left invariant and Killing. We also classify the nontrivial m-quasi Einstein metrics that are a compact quotient of the product of two Einstein metrics. We also show that S1 is the only compact manifold of any dimension which admits a metric which is nontrivially m-quasi Einstein and Einstein.

Ricci solitons on pseudo–Riemannian hypersurfaces of 4–dimensional Minkowski space

In this paper, we get classification theorems for Ricci solitons on pseudo–Riemannian hypersurfaces of a Minkowski space E14 by taking the potential vector field as the tangent component of the position vector of the pseudo–Riemannian hypersurfaces. First, we obtain the necessary and sufficient condition for a pseudo–Riemannian hypersurface in E14 which admits such a Ricci soliton. According to the forms of the shape operator of a pseudo–Riemannian hypersurface, we obtain characterization results about Ricci solitons on the pseudo–Riemannian hypersurfaces in E14. More precisely, we show that totally umbilical isoparametric hypersurfaces, hyperbolic and a pseudo–spherical cylinder in E14 admit shrinking Ricci solitons whose potential vector fields are the tangent part of the position vectors in E14. Furthermore, we also get that a generalized umbilical Lorentzian hypersurface in E14 admits a shrinking Ricci soliton. Finally, we obtain that there do not exist Ricci solitons on the Lorentzian hypersurfaces in E14 whose minimal polynomials have complex roots or real roots with multiplicity three.

A weakly nonlinear wave equation for damped acoustic waves with thermodynamic non-equilibrium effects

The problem of propagating nonlinear acoustic waves is considered; the solution to which, both with and without damping, having been obtained to-date starting from the Navier–Stokes–Duhem equations together with the continuity and thermal conduction equation. The novel approach reported here adopts instead, a discontinuous Lagrangian approach, i.e. from Hamilton’s principle together with a discontinuous Lagrangian for the case of a general viscous flow. It is shown that ensemble averaging of the equation of motion resulting from the Euler–Lagrange equations, under the assumption of irrotational flow, leads to a weakly nonlinear wave equation for the velocity potential: in effect a generalisation of Kuznetsov’s well known equation with an additional term due to thermodynamic non-equilibrium effects.

Generalized m-quasi-Einstein metric on certain almost contact manifolds

In this paper, we study the generalized m-quasi-Einstein metric in the context of contact geometry. First, we prove if an H-contact manifold admits a generalized m-quasi-Einstein metric with non-zero potential vector field V collinear with ?, then M is K-contact and ?-Einstein. Moreover, it is also true when H-contactness is replaced by completeness under certain conditions. Next, we prove that if a complete K-contact manifold admits a closed generalized m-quasi-Einstein metric whose potential vector field is contact thenMis compact, Einstein and Sasakian. Finally, we obtain some results on a 3-dimensional normal almost contact manifold admitting generalized m-quasi-Einstein metric.

Geometric solitons in a D-homothetically deformed Kenmotsu manifold

We consider almost Riemann and almost Ricci solitons in a D-homothetically deformed Kenmotsu manifold having as potential vector field a gradient vector field, a solenoidal vector field or the Reeb vector field of the deformed structure, and explicitly obtain the Ricci and scalar curvatures for some cases. We also provide a lower bound for the Ricci curvature of the initial Kenmotsu manifold when the deformed manifold admits a gradient almost Riemann or almost Ricci soliton.