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1.
The turbulent diffusion tensor describing the evolution of the mean concentration of a passive scalar is investigated for non-helically forced turbulence in the presence of rotation or a magnetic field. With rotation, the Coriolis force causes a sideways deflection of the flux of mean concentration. Within the magnetohydrodynamics approximation there is no analogous effect from the magnetic field because the effects on the flow do not depend on the sign of the field. Both rotation and magnetic fields tend to suppress turbulent transport, but this suppression is weaker in the direction along the magnetic field. Turbulent transport along the rotation axis is not strongly affected by rotation, except on shorter length-scales, i.e. when the scale of the variation of the mean field becomes comparable with the scale of the energy-carrying eddies. These results are discussed in the context of anisotropic convective energy transport in the Sun.  相似文献   

2.
Homogeneous anisotropic turbulence simulations are used to determine off-diagonal components of the Reynolds stress tensor and its parameterization in terms of turbulent viscosity and Λ-effect. The turbulence is forced in an anisotropic fashion by enhancing the strength of the forcing in the vertical direction. The Coriolis force is included with a rotation axis inclined relative to the vertical direction. The system studied here is significantly simpler than that of turbulent stratified convection which has often been used to study Reynolds stresses. Certain puzzling features of the results for convection, such as sign changes or highly concentrated latitude distributions, are not present in the simpler system considered here. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

3.
Small levels of turbulence can be present in stellar radiative interiors due to, e.g., the instability of rotational shear. In this paper we estimate turbulent transport coefficients for stably stratified rotating stellar radiation zones. Stable stratification induces strong anisotropy with a very small ratio of radial‐to‐horizontal turbulence intensities. Angular momentum is transported mainly due to the correlation between azimuthal and radial turbulent motions induced by the Coriolis force. This non‐diffusive transport known as the Λ‐effect has outward direction in radius and is much more efficient compared to the effect of radial eddy viscosity. Chemical species are transported by small radial diffusion only. This result is confirmed using direct numerical simulations combined with the test‐scalar method. As a consequence of the non‐diffusive transport of angular momentum, the estimated characteristic time of rotational coupling (≲100 Myr) between radiative core and convective envelope in young solar‐type stars is much shorter compared to the time‐scale of Lithium depletion (∼1 Gyr) (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

4.
We excite an epicyclic motion, the amplitude of which depends on the vertical position, z , in a simulation of a turbulent accretion disc. An epicyclic motion of this kind may be caused by a warping of the disc. By studying how the epicyclic motion decays, we can obtain information about the interaction between the warp and the disc turbulence. A high-amplitude epicyclic motion decays first by exciting inertial waves through a parametric instability, but its subsequent exponential damping may be reproduced by a turbulent viscosity. We estimate the effective viscosity parameter, α v, pertaining to such a vertical shear. We also gain new information on the properties of the disc turbulence in general, and measure the usual viscosity parameter, α h, pertaining to a horizontal (Keplerian) shear. We find that, as is often assumed in theoretical studies, α v is approximately equal to α h and both are much less than unity, for the field strengths achieved in our local box calculations of turbulence. In view of the smallness (∼0.01) of α v and α h we conclude that for β p gas p mag∼10 the time-scale for diffusion or damping of a warp is much shorter than the usual viscous time-scale. Finally, we review the astrophysical implications.  相似文献   

5.
K. Petrovay 《Solar physics》2003,215(1):17-30
The first consistent model for the turbulent tachocline is presented, with the turbulent diffusivity computed within the model instead of being specified arbitrarily. For the origin of the 3D turbulence a new mechanism is proposed. Owing to the strongly stable stratification, the mean radial shear is stable, while the horizontal shear is expected to drive predominantly horizontal, quasi-2D motions in thin slabs. Here I suggest that a major source of 3D overturning turbulent motions in the tachocline is the secondary shear instability due to the strong, random vertical shear arising between the uncorrelated horizontal flows in neighboring slabs. A formula for the vertical diffusivity due to this turbulence, Equation (9), is derived and applied in a simplified 1D model of the tachocline. It is found that Maxwell stresses due to an oscillatory poloidal magnetic field of a few hundred gauss are able to confine the tachocline to a thickness less than 5 Mm. The integral scale of the 3D overturning turbulence is the buoyancy scale, on the order of 10 km, and its velocity amplitude is a few m s–1, yielding a vertical turbulent diffusivity on the order of 108 cm2 s–1.  相似文献   

6.
The instability of a stratified layer of a self-gravitating plasma has been studied to include jointly the effects of viscosity, Coriolis forces and the finite Larmor radius (FLR). For a plasma permeated by a uniform horizontal magnetic field, the stability analysis has been carried out for a transverse mode of wave propagation. The solution has been obtained through variational methods for the case when the direction of axis of rotation is along the magnetic field. The analysis for the case when the direction of rotation is transverse to the magnetic field has also been considered and the solutions for this case have been obtained through integral approach. The dispersion relations have been derived in both the cases and solved numerically. It is found that both the viscous and FLR effects have a stabilizing influence on the growth rate of the unstable mode of disturbance. Coriolis forces are found to have stabilizing influence for small wave numbers and destabilizing for large wave numbers.  相似文献   

7.
The aim of this work is to present a transport process which is likely to have a great importance for the internal constitution of the stars. In order to set the problem, we first give a short presentation of the physical properties of the Sun and stars, described usually under the names of `Standard Solar Model' or `Standard Stellar Models' (SSM). Next we show that an important question about SSM is that they do not explain the age dependance of lithium deficiency of stars of known age: stars of galactic clusters and the Sun. It has been suggested a long time ago to assume the presence of a macrosocpic diffusion process in the radiative zone, below the surface convective zone of solar like stars. It is then possible for the lithium present in the convective zone to be carried to the thermonuclear burning level below the convective zone. The first assumption was that differential rotation generates turbulence and therefore that a turbulent diffusion process takes place. However, this model predicts a lithium abundance which is strongly rotation dependant, contrary to the observations. Furthermore, the diffusion coefficient being large all over the radiative zone, it prevents the possibility of gravitational separation by diffusion and consequently leads to an impossibility of explaining the difference of helium abundance between the surface and the center of the Sun. The consequence is obviously that we need to take into account another physical process. Stars having a mass M < 1.3 M ⊙ have a convective zone which begins close to the stellar surface and extends down to a depth which is an appreciable fraction of stellar radius. In the convective zone, strong stochastic motions take care, at least partially, of heat transfer. These motions do not vanish at the lower boundary and generate internal waves into the radiative zone. These random internal waves are at the origin of a diffusion process which can be considered as responsible of the diffusive transport of lithium down to the lithium burning level. This is certainly not the only physical process responsible of lithium deficiency in main sequence stars, but its properties open the way to a completely consistent analysis of lithium deficiency. The model of generation of gravity waves is based on a model of heat transport in the convective zone by diving plumes. The horizontal component of the turbulent motion at the boundary of the convective zone is supposed to generate the horizontal motion of internal waves. The result is a large horizontal component of the diffusion coefficient, which produces in a short time an horizontal uniform chemical composition. It is known that gravity waves, in the absence of any dissipative process, cannot generate vertical mixing. Therefore, the vertical component of the diffusion coefficient is entirely dependant of radiative damping. It decreases quickly in the radiative zone, but is large enough to be responsible of lithium burning. Due to the radial dependance of velocity amplitude, the diffusion coeficient increases when approaching the stellar center. However, very close to the center, non-linear dissipative and radiative damping of internal waves become large and the diffusion coefficient vanishes at the very center. The development of this abstract can be found in E. Schatzman (1996, J. Fluid Mech. 322, 355). This revised version was published online in July 2006 with corrections to the Cover Date.  相似文献   

8.
A model is presented for an accretion disc with turbulent viscosity and a magnetically influenced wind. The magnetic field is generated by a dynamo in the disc, involving the turbulence and radial shear. Disc-wind solutions are found for which the wind mass flux is sufficient to play a major part in driving an imposed steady inflow, but small enough for most material to be accreted on to the central object. Constraints arise for the magnetic Reynolds and Prandtl numbers in terms of the turbulent Mach number and vertical length-scale of the disc's horizontal magnetic field. It is shown that the imposition of a stellar boundary condition enhances the wind mass flux in the very inner region of the disc and may result in jet formation.  相似文献   

9.
In this paper considering the turbulent dusty flow of an incompressible viscous fluid which is nearly isotropic and spatially homogeneous with an extra vector argument (rotation symmetry) the expression for acceleration covariance in the presence of the Coriolis force has been derived and solution has been obtained in terms of defining scalars.  相似文献   

10.
The hydromagnetic instability of a self-gravitating, incompressible rotating plasma of variable density has been examined in the presence of Hall currents. The system is assumed to be permeated by a variable horizontal magnetic field. The solution of the relevant linearized perturbation equations has been obtained by the normal mode technique through a variational principle which is shown to characterize the problem. Proper solutions have been obtained for a semi-infinite plasma having exponential density stratification along the vertical. The dispersion relation has been derived and solved numerically for different values of the physical parameters involved. It is found that Hall currents and Coriolis forces have both destabilizing influence as the growth rate of the unstable modes is found to increase with the increase of both Hall currents and Coriolis forces.  相似文献   

11.
Instability of a horizontal rotating layer of a self-gravitating electrically conducting fluid has been studied to simultaneously, include the effects of Hall currents and magnetic resistivity. The prevailing magnetic field is uniform and acts along the vertical direction along which the fluid has a one-dimensional density gradient. The solution has been obtained through the variational methods. The dispersion relation obtained has been solved numerically and it is found that Hall currents as well as magnetic resistivity have a destabilizing influence. Coriolis forces, however, have a stabilizing influence.  相似文献   

12.
The instability in a horizontal layer of stratified compressible isotropic and anisotropic plasmas has been studied to include simultaneously the effects of Coriolis forces and the finiteness of the ion Larmor radius. Using an integral approach, the dispersion relation has been derived in both cases for plasmas having density stratified exponentially along the vertical. The dispersion, relation has been solved numerically and it is found that both the FLR and Coriolis forces have stabilizing influence on the instability in the isotropic plasmas. The same result is obtained for the case of anisotropic plasmas where also the dispersion relation has been evaluated numerically.  相似文献   

13.
If the solar dynamo operates at the bottom of the convection zone, then the magnetic flux created there has to rise to the surface. When the convection zone is regarded as passive, the rising flux is deflected by the Coriolis force to emerge at rather high latitudes, poleward of typical sunspot zones (Choudhuri and Gilman, 1987; Choudhuri, 1989). Choudhuri and D'Silva (1990) included the effects of convective turbulence on the rising flux through (a) giant cell drag and (b) momentum exchange by small-scale turbulence. The momentum exchange mechanism could enable flux tubes of radii not more than a few hundred km to emerge radially at low latitudes, but the giant cell drag mechanism required unrealistically small flux tube radii (a few meters for a reasonable giant cell upflow) to counteract the Coriolis force. We now include the additional effect of Kelvin-Helmholtz instability in a symmetrical flux ring caused by the azimuthal flow induced during its rise. The azimuthal flow crosses the threshold for the instability only if there is a giant cell upflow to drag the flux tubes appreciably. In the absence of such a drag, as in the case of a passive convection zone or in the case of momentum exchange by small-scale turbulence, the azimuthal velocity never becomes large enough to cause the instability, leaving the results of the previous calculations unaltered. The giant cell drag, aided by Kelvin-Helmholtz instability, however, becomes now a viable mechanism for curbing the Coriolis force - 104 G flux tubes with radii of a few hundred km being dragged radially by upflows of 70 m s-1.  相似文献   

14.
Two comments are prompted by the recent paper of Quiroga (1983). First, it is pointed out that Quiroga's identification of two distinct types of motion (hydrodynamic and turbulent) within the galactic disk supports the suggestion that turbulent motions in the Galaxy are generated by the shearig action of differential galactic rotation. Secondly, as a result of these turbulent motions dominating the systematic hydrodynamics of galactic rotation at scale sizes below 100–300 pc, it appears that some process(es) associated with interstellar turbulence rather than with galactic rotation should play a dominant role in the establishment of the angular momentum of interstellar material.  相似文献   

15.
The problem of the influence of vortex helicity on the synergic structuring of cosmic matter in it, as well as the appearance of the effect of negative viscosity in three-dimensional gyrotropic turbulence, were studied in the framework of the fundamental problem of simulating the evolution of a rotating astrophysical nonmagnetic disk—in particular, the accretion disk—surrounding the Sun at the early stage of its existence. The evolution equations for averaged vorticity and vortex helicity, as well as rheological relations for the turbulent flow of heat and asymmetrical tensor of the turbulent stress in helical turbulence, were obtained. The demonstrative dependence of helicity on the rotation velocity, density (temperature) gradients, and turbulent energy of the disk gas was established. The role of helicity in the appearance of the inverse Richardson-Kolmogorov energy cascade from small vortices to larger ones and the related process of the generation of the power-consuming macroscale coherent vortex formations appearing in gyrotropic turbulence at high Reynolds number were discussed. The results of the numerical experiments confirming the real existence of the inverse energy cascade in helical turbulence were analyzed. It was assumed that the relatively long-term decay of turbulence in the solar protoplanet cloud can be due to the absence of the reflective symmetry of the anisotropic field of the turbulent velocities with respect to its equatorial plane. As the concept of the inverse energy cascade in three-dimensional helical turbulence is more and more reliably confirmed in numerical experiments, accounting for this effect affecting the structure and dynamics of the astrophysical nonmagnetic disk becomes important during its simulation.  相似文献   

16.
As was demonstrated in earlier studies, turbulence can result in a negative contribution to the effective mean magnetic pressure, which, in turn, can cause a large‐scale instability. In this study, hydromagnetic mean‐field modelling is performed for an isothermally stratified layer in the presence of a horizontal magnetic field. The negative effective magnetic pressure instability (NEMPI) is comprehensively investigated. It is shown that, if the effect of turbulence on the mean magnetic tension force vanishes, which is consistent with results from direct numerical simulations of forced turbulence, the fastest growing eigenmodes of NEMPI are two‐dimensional. The growth rate is found to depend on a parameter β* characterizing the turbulent contribution of the effective mean magnetic pressure for moderately strong mean magnetic fields. A fit formula is proposed that gives the growth rate as a function of turbulent kinematic viscosity, turbulent magnetic diffusivity, the density scale height, and the parameter β*. The strength of the imposed magnetic field does not explicitly enter provided the location of the vertical boundaries are chosen such that the maximum of the eigenmode of NEMPI fits into the domain. The formation of sunspots and solar active regions is discussed as possible applications of NEMPI (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

17.
It is shown that the phase difference between the horizontal components of the wind velocity induced by the first diurnal propagating tidal mode between 90 and 100 km altitude is modified by turbulent diffusion. Experimental data are compared with calculations made by two different methods. The calculated results agree well with the data for a coefficient of eddy diffusion K = 5 × 106 cm2 s−1 which is a realistic one at this altitude. Incidentally, it is shown that some measurements which have been interpreted as a presence of evanescent modes are probably due to an increase in vertical wavelength of the first propagating diurnal mode due to turbulent diffusion.  相似文献   

18.
In this paper we make an effort to understand the interaction of turbulence generated by the magnetorotational instability (MRI) with turbulence from other sources, such as supernova explosions (SNe) in galactic disks. First we perform a linear stability analysis (LSA) of non‐ideal MRI to derive the limiting value of Ohmic diffusion that is needed to inhibit the growth of the instability for different types of rotation laws. With the help of a simple analytical expression derived under first‐order smoothing approximation (FOSA), an estimate of the limiting turbulence level and hence the turbulent diffusion needed to damp the MRI is derived. Secondly, we perform numerical simulations in local cubes of isothermal nonstratified gas with external forcing of varying strength to see whether the linear result holds for more complex systems. Purely hydrodynamic calculations with forcing, rotation and shear are made for reference purposes, and as expected, non‐zero Reynolds stresses are found. In the magnetohydrodynamic calculations, therefore, the total stresses generated are a sum of the forcing and MRI contributions. To separate these contributions, we perform reference runs with MRI‐stable shear profiles (angular velocity increasing outwards), which suggest that the MRI‐generated stresses indeed become strongly suppressed as function of the forcing. The Maxwell to Reynolds stress ratio is observed to decrease by an order of magnitude as the turbulence level due to external forcing exceeds the predicted limiting value, which we interpret as a sign of MRI suppression. Finally, we apply these results to estimate the limiting radius inside of which the SN activity can suppress the MRI, arriving at a value of 14 kpc (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

19.
Instability in a horizontal layer of a stratified rotating self-gravitating plasma is studied to include simultaneously the effects of Hall currents and the finiteness of the ion Larmor radius. Proper solutions have been obtained through the variational methods for a semi-infinite plasma in which the density has an exponential gradient along the vertical. The dispersion relation obtained has been solved numerically and it is found that the growth rate of the unstable perturbations decreases with both coriolis forces and gyroviscous effects. The influence of the effects of gyroviscosity as well as of Coriolis forces is consequently stabilizing. Hall currents are found to have a destabilizing influence as the growth rate is found to increase with this effect.  相似文献   

20.
We study the turbulent behaviour induced by the magnetic shear instability for a magnetized, incompressible fluid in a spherical shell. A differential rotation that is decreasing outwards but hydrodynamically stable according to the Rayleigh criterion is prescribed, and an external, uniform magnetic field is imposed parallel to the rotation axis. Our main concern in this paper is the fully global treatment of this magnetohydrodynamical system, so we focus particular attention on the influence of the boundary conditions. Non-linear, steady solutions are presented for stress-free as well as for rigid boundary conditions for one specific model with a fixed strength of the external magnetic field and a fixed differential rotation rate. We calculate the eddy viscosity νT and the viscosity alpha αSS resulting from the total stress tensor. These turbulence parameters turn out to differ drastically depending on the boundary conditions for the flow. An investigation of the radial structure of the viscosity alpha (whilst varying the differential rotation law) shows that the enhanced generation of turbulence takes place mainly in the boundary layers of the shell.  相似文献   

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