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1.
In the Beltrami flow field, the rate of change of vorticity covariance has been discussed in the presence of magnetic field.  相似文献   

2.
The present paper deals with the turbulent flow of an incompressible viscous fluid which is isotropic and spatially homogeneous. The expression for the rate of change of vorticity covariance is derived. The derived result shows that the defining scalars (r, t) and (r,t) of the rate of change of vorticity covariance solely depend upon the defining scalarQ of the two-point velocity correlation.  相似文献   

3.
In this paper we are concerned with incompressible MHD turbulence in a rotating system and have derived an equation for the rate of change of vorticity covariance of MHD turbulent flow. The result derived shows that the defining scalars (r,t), (r,t), and (r,t) for the rate of change of vorticity covariance solely depend on the defining scalars of the tensorsW ij, Pik,j, Fkj,i, Tik,j, andR kj,ialready defined in the text.  相似文献   

4.
Two exact solutions of Einstein's field equations of vacuum are presented and investigated. We will regard the term vacuum fluid as the limiting case of scalar field with an almost constant potential. Considering the four velocity of this fluid we find, that in both solutions there is an anisotropic expansion of the cosmic fluid, but the fluid has vanishing vorticity.We investigate whether shear could prevent the transition into an inflationary era in these models, and the effect of shear on a scalar field is also considered. It is found that shear will speed up the rollover of the scalar field in some Bianchi type-VIII models.Possible initial conditions are discussed in light of the group structures of the models.  相似文献   

5.
The formation of structures in the universe is one of the most challenging problems of cosmology. In this paper, an attempt to explain the formation of galaxies through the generation of vortices (with dissipation) in an uniformly expanding perfect fluid is made. The equation governing the mean square vorticity for a turbulent (isotropic and homogeneous) fluid is derived. It is shown that the mechanism of stretching vortices could enhance the mean square vorticity as a function of time. However, ultimately expansion and dissipation dominate and the solution for the mean square vorticity reaches the prediction by linear theory.  相似文献   

6.
The excitation of spiral waves by an external perturbation in a disc deposits angular momentum in the vicinity of the corotation resonance (the radius where the speed of a rotating pattern matches the local rotation rate). We use matched asymptotic expansions to derive a reduced model that captures non-linear dynamics of the resulting torque and fluid motions. The model is similar to that derived for forced Rossby wave critical layers in geophysical fluid dynamics. Using the model we explore the saturation of the corotation torque, which occurs when the background potential (specific) vorticity is redistributed by the disturbance. We also consider the effects of dissipation. If there is a radial transport of potential vorticity, the corotation torque does not saturate. The main application is to the creation, growth and migration of protoplanets within discs like the primordial solar nebula. The disturbance also nucleates vortices in the vicinity of corotation, which may spark further epochs of planet formation.  相似文献   

7.
We study the Einstein-Maxwell equations for a tilted Bianchi type-II space-time. The matter content is a perfect fluid, with equation of statep=(γ?1)ε, (1≤γ≤2). The field equations are solved for all values of γ in the limiting case of small vorticity. The source of rotation is an electromagnetic field, which from observational requirements must be a small quantity at the present time.  相似文献   

8.
It is shown that the magnetic induction equation reduces to an autoregressive model equation. Assuming weakly ergodic field variations in steady mean plasma flow, this model permits the estimation of the mean flow deformation tensor, velocity divergence and kinetic vorticity from magnetic field time series. Applications, made to hourly-averaged, in-ecliptic interplanetary magnetic field (IMF) measurements from Ulysses spacecraft, showed that the direction of maximum deformation rate was, for most of the time, aligned to the mean field, while the vorticity tended to become perpendicular to the mean radial direction at large heliodistances.  相似文献   

9.
In mean‐field magnetohydrodynamics the mean electromotive force due to velocity and magnetic‐field fluctuations plays a crucial role. In general it consists of two parts, one independent of and another one proportional to the mean magnetic field. The first part may be nonzero only in the presence of mhd turbulence, maintained, e.g., by small‐scale dynamo action. It corresponds to a battery, which lets a mean magnetic field grow from zero to a finite value. The second part, which covers, e.g., the α effect, is important for large‐scale dynamos. Only a few examples of the aforementioned first part of the mean electromotive force have been discussed so far. It is shown that a mean electromotive force proportional to the mean fluid velocity, but independent of the mean magnetic field, may occur in an originally homogeneous isotropic mhd turbulence if there are nonzero correlations of velocity and electric current fluctuations or, what is equivalent, of vorticity and magnetic field fluctuations. This goes beyond the Yoshizawa effect, which consists in the occurrence of mean electromotive forces proportional to the mean vorticity or to the angular velocity defining the Coriolis force in a rotating frame and depends on the cross‐helicity defined by the velocity and magnetic field fluctuations. Contributions to the mean electromotive force due to inhomogeneity of the turbulence are also considered. Possible consequences of the above findings for the generation of magnetic fields in cosmic bodies are discussed (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

10.
This paper explores the dynamics of Gödel-type geometry for tilted and non-tilted congruences. The kinematical as well as dynamical quantities are investigated for both congruences with non-vanishing nature of vorticity vector. The obtained vorticity is of kinematical type, i.e., not produced by a circular flow of superenergy on the plane orthogonal to the vorticity vector. We conclude that super-Poynting vector is non-zero for the tilted congruence linked with heat flux of fluid distribution while it vanishes in non-tilted case.  相似文献   

11.
We have measured the internal velocity field in jovian synoptic-scale cyclones and anticyclones by tracking cloud elements in very high spatial resolution images obtained by the Voyager 1 and 2 (in 1979) and Galileo (1996-2000) spacecrafts. In total we have studied 24 different closed vortices (6 cyclones, 18 anticyclones) spanning a latitude range from ∼60° N to 60° S and with East-West sizes larger than ∼2000 km. The tangential component of the velocity as a function of the distance to the vortex center and position angle is used to retrieve the vorticity field. We find that the velocity increases in all the vortices from a nearly quiescent center to a maximum at the vortex periphery, with a record of about 180 m s−1 for the GRS. The vorticity of cyclones and anticyclones increases in general toward their periphery with absolute values in the range from ∼2-14×10−5 s−1. There is a marked tendency to increase the vortices vorticity with their latitude location. However the vorticity does not depend on the vortex size, circulation sense, or ambient background meridional wind shear. The vortex Rossby number ranges from ∼0.2 to 0.5. A study of the interaction between the Great Red Spot with other vortices show that the GRS does not change its vorticity upon their absorption. The two White Ovals mergers showed contradictory results, with greater vorticity in the case of BE, but lower vorticity in the case of BA, although data are poorer for this last case. We present the case of a short lived but large coherent cyclone at −59° that was embedded in a weakly anticyclone wind shear domain. We show that jovian vortices do not follow the simple Kida vortex relationship between vorticity and aspect ratio as it has been previously suggested.  相似文献   

12.
In addition to the scalar Shakura–Sunyaev α ss turbulent viscosity transport term used in simple analytic accretion disc modelling, a pseudo-scalar transport term also arises. The essence of this term can be captured even in simple models for which vertical averaging is interpreted as integration over a half-thickness and each hemisphere is separately studied. The additional term highlights a complementarity between mean field magnetic dynamo theory and accretion disc theory treated as a mean field theory. Such pseudo-scalar terms have been studied, and can lead to large-scale magnetic field and vorticity growth. Here it is shown that vorticity can grow even in the simplest azimuthal and half-height integrated disc model, for which mean quantities depend only on radius. The simplest vorticity growth solutions seem to have scales and vortex survival times consistent with those required for facilitating planet formation. In addition, it is shown that, when the magnetic back-reaction is included to lowest order, the pseudo-scalar driving the magnetic field growth and that driving the vorticity growth will behave differently with respect to shearing and non-shearing flows: the former pseudo‐scalar can more easily reverse sign in the two cases.  相似文献   

13.
A combined BCDE (Brans-Dicke and Einstein-Cartan) theory with lambda-term is developed through Raychaudhuri’s equation, for inflationary scenario. It involves a variable cosmological constant, which decreases with time, jointly with energy density, cosmic pressure, shear, vorticity, and Hubble’s parameter, while the scale factor, total spin and scalar field increase exponentially. The post-inflationary fluid resembles a perfect one, though total spin grows, but the angular speed does not (Astrophys. Space Sci. 312: 275, 2007d).   相似文献   

14.
We consider a spherical, solid planet surrounded by a thin layer of an incompressible, inviscid fluid. The planet rotates with constant angular velocityWe study the vortex motion within this rotating ocean. For this purpose, we obtain a linearized version of the Navier-Stokes equation and adopt it as our ocean model; next, we prove analytically that a certain function of vorticity is an invariant of motion.Using this ocean model and this invariant property of vorticity, we are able to establish a general equation governing the motion of vortices within a fluid shell: it is a nonlinear partial differential equation of the third order for the stream function of motion.We finally examine some particular solutions of this vorticity equation that represent solitary waves of permanent form and decay within a finite distance. These solutions have been represented in terms of quadratic, exponential, and hyperbolic functions.The question whether these vortices that propagate as solitary waves could be solitons depends on their behavior when they collide with each other; this has not yet been resolved.Retired, U.S. Naval Research Laboratory, Washington, D.C., U.S.A.  相似文献   

15.
We consider a spherical, solid planet surrounded by a thin layer of an incompressible, inviscid fluid. The planet rotates with constant angular velocity about a fixed axis. The motion imparted by this planetary rotation upon the fluid particles of the ocean has been assumed to be governed by a linear version of the Navier-Stokes equation.We study the vortex motion within this rotating ocean and establish that the propagation of vortices depends on a third-order partial differential equation for the stream function. We prove that, in the most general case, this vorticity equation cannot generate any solitary waves; however, should the vertical component of vorticity satisfy a certain functional relationship, then we have obtained a family of solitary waves of permanent form.Retired, U.S. Naval Research Laboratory, Washington, D.C., U.S.A.  相似文献   

16.
R. Komm  R. Howe  F. Hill 《Solar physics》2012,277(2):205-226
We study the temporal variation of the vorticity of subsurface flows of 828 active regions and 977 quiet regions. The vorticity of these flows is derived from measured subsurface velocities. The horizontal flows are determined by analyzing high-resolution Global Oscillation Network Group Doppler data with ring-diagram analysis covering a range of depths from the surface to about 16 Mm. The vertical velocity component is derived from the divergence of the measured horizontal flows using mass conservation. We determine the change in unsigned magnetic flux density during the disk passage of each active region using Michelson Doppler Imager (MDI) magnetograms binned to the ring-diagram grid with centers spaced by 7.5° ranging ± 52.5° in latitude and central meridian distance with an effective diameter of 15° after apodization. We then sort the data by their flux change from decaying to emerging flux and divide the data into five subsets of equal size. We find that the vorticity of subsurface flows increases during flux emergence and decreases when active regions decay. For flux emergence, the absolute values of the zonal and meridional vorticity components show the most coherent variation with activity, while for flux decrease the strongest signature is in the absolute values of the meridional and vertical vorticity components. The temporal variation of the enstrophy (residual vorticity squared) is thus a good indicator for either flux increase or decrease. There are some indications that the increase in vorticity during flux emergence happens about a day later at depths below about 8 Mm compared to layers shallower than about 4 Mm. This timing difference might imply that the vorticity signal analyzed here is caused by the interaction between magnetic flux and turbulent flows near the solar surface. There are also hints that the vorticity decrease during flux decay begins about a day earlier at layers deeper than about 8 Mm compared to shallower ones. However, the timing difference between the change at different depths is comparable to the time step of the analysis.  相似文献   

17.
R. E. Falco 《Solar physics》2006,234(2):213-242
We offer a new viewpoint that can explain some of the recently obtained high-resolution observations of granules and faculae. Examining the data of Scharmer, Gudiksen, Kiselman et al. (2002) we observe many granules undergo an evolution that results in faculae emerging from within their boundaries, and moving towards and into intergranular lanes. These faculae have a characteristic hairpin substructure. The evolving morphology can be closely described by a fluid dynamic instability we call the “vortex/shear layer” (VSL) interaction. It occurs in all granules whose underlying structure has vorticity when they emerge into the photosphere through the sub-photospheric turbulent boundary layer (SPTBL). The VSL results in the creation of vortices from the distributed vorticity of the SPTBL. The subsequent stretching of these vortices results in high amplification of vorticity, and the concurrent high amplification of the background magnetic field. Magnetic field lines spiral around the vortices, as well as being stretched along their axis. Thus, the VSL is also the origin of a coherent local dynamo. The spiral sheathing of high magnetic flux results in a simple explanation for the “hot wall” effect. The VSL also creates the “dark lanes” observed by Lites, Scharmer, Berger et al. (2004) and groupings of bright hairpins/vortex sheet ensembles, which look like the ribbon faculae (Berger, Rouppe van der Voort, Lofdahl et al., 2004). The SPTBL results in emerging tilted granules, which when combined with the VSL create the three-dimensionality which Lites, Scharmer, Berger et al. (2004), also observed. Both the VSL and the SPTBL result, on average, in a west side bias of hairpin faculae and granular three-dimensionality. An erratum to this article is available at .  相似文献   

18.
The instability of axisymmetric flows of inviscid compressible fluid with respect to two-dimensional infinitesimal perturbations with the nonconservation of angular momentum is investigated by numerically integrating the differential equations of hydrodynamics. The compressibility is taken into account for a homentropic flow with an adiabatic index varying over a wide range. The problem has been solved for two angular velocity profiles of an initial axisymmetric flow. In the first case, a power-law rotation profile with a finite enthalpy gradient at the flow edges has been specified. For this angular velocity profile, we show that the instability of sonic and surface gravity modes in a nearly Keplerian flow, when a radially variable vorticity exists in the main flow, can be explained by the combined action of the Landau mechanism and mode coupling. We also show that including a radially variable vorticity makes the limiting exponent in the rotation law at which the unstable surface gravity modes vanish dependent on the fluid compressibility. In the second case, a Keplerian rotation law with a quasi-sinusoidal deviation has been specified in such a way that the enthalpy gradient vanished at the flow edges. We have found than the sonic modes are then stabilized and the flow is unstable only with respect to the perturbations that also exist in an incompressible fluid.  相似文献   

19.
We find a solution for exponential inflation in Brans–Dicke cosmology endowed with a cosmological term, which includes time-varying shear and vorticity. We find that the scalar field and the scale factor increase exponentialy while shear, vorticity, energy density, cosmic pressure and the cosmological term decay exponentialy for negative beta, where beta is defined in the text.  相似文献   

20.
The Sen equations with a source term given by the energy-momentum tensor of a one component perfect fluid valid in arbitrary gauge are presented. Obtained equations are constructed from Lyra tensors. The consequences of the gauge covariance are briefly analysed.  相似文献   

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