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1.
Mean-field hydrodynamics advanced to clear explanations for the origin and properties of the global meridional flow in stellar convection zones. Qualitative arguments and analysis of basic equations both show that the meridional circulation is driven by non-conservative centrifugal and buoyancy forces and results from a slight disbalance between these two drivers. The deviations from the thermal wind balance are relatively large near the boundaries of convection zones. Accordingly, the meridional flow attains its largest velocities in the boundary layers and decreases inside the convection zone. This picture, however, is neither supported nor dismissed by the conflicting results of recent helioseismic soundings or 3D numerical experiments. The relevant physics of the differential temperature and its possible relation to the solar oblateness are briefly discussed.  相似文献   

2.
Abstract

Models of a differentially rotating compressible convection zone are calculated, considering the inertial forces in the poloidal components of the equations of motion. Two driving mechanisms have been considered: latitude dependent heat transport and anisotropic viscosity. In the former case a meridional circulation is induced initially which in turn generates differential rotation, whereas in the latter case differential rotation is directly driven by the anisotropic viscosity, and the meridional circulation is a secondary effect.

In the case of anisotropic viscosity the choice of boundary conditions has a big influence on the results: depending on whether or not the conditions of vanishing pressure perturbation are imposed at the bottom of the convection zone, one obtains differential rotation with a fast (≥ 10 ms?1) or a slow (～ 1 ms?1) circulation. In the latter case the rotation law is mainly a function of radius and the rotation rate increases inwards if the viscosity is larger in radial direction than in the horizontal directions.

The models with latitude dependent heat transport exhibit a strong dependence on the Prandtl number. For values of the Prandtl number less than 0.2 the pole-equator temperature difference and the surface velocity of the meridional circulation are compatible with observations. For sufficiently small values of the Prandtl number the convection zone becomes globally unstable like a layer of fluid for which the critical Rayleigh number is exceeded.  相似文献   

3.
Convection in a Boussinesq fluid in an annular channel rotating about a vertical axis with lateral rigid sidewalls, stress-free top and bottom, uniformly heated from below is investigated. The sidewalls are assumed to be either perfectly insulating or conducting. Three different types of convection are identified when the channel is rotating sufficiently fast: (i) global oscillatory convection preferred for small Prandtl numbers in channels with intermediate or large aspect ratios (width to height ratio), (ii) wall-localized oscillatory convection representing the most unstable mode for moderate or large Prandtl numbers in channels with intermediate or large aspect ratios and (iii) global stationary convection preferred in channels with sufficiently small aspect ratios regardless of the size of the Prandtl number. The corresponding weakly nonlinear problem describing differential rotation and meridional circulation is also examined, showing that geostrophic, multiple-peaked (two prograde and two retrograde) differential rotation can be maintained by the Reynolds stresses in wall-localized convective eddies in a rapidly rotating channel.  相似文献   

4.
— The mean zonal velocity in the atmosphere is taken as being created continually by the global scale Hadley circulation produced by the differential solar heating through the balance between the Coriolis effect and vertical diffusion, and not by conservation of absolute momentum. Hence a proper determination of the diffusion coefficient becomes the key to the solution of the zonal flow problem. In this study we take the flow field as composed of a primary global scale Hadley circulation, and a secondary flow created by the convergences of the eddy transports of heat and momentum and surface friction, which give rise to the classical three cell structure of the meridional circulation but which only modifies the zonal velocity distribution slightly.¶Finally, we use the equilibrium solution of the perturbation potential vorticity equation to obtain the eddy transports of momentum and heat, with the zonal velocity given by the primary Hadley flow as the basic flow, and we found that they are close to the statistically observed values, demonstrating that the system can maintain itself.  相似文献   

5.
Abstract

With the help of simplifying approximations, we have derived expressions for the non-diffusive fluxes of the angular momentum which are brought about by the action of Coriolis forces on the convective motion. The original turbulence, which is not perturbed by the Coriolis forces, is considered given and weakly anisotropic, the anisotropy having a preferred radial direction. The eddy viscosities are evaluated. Hence, a closed equation for the angular velocity is derived, and then solved for the case of slow rotation. It is shown that the differential rotation is generated most effectively in the case of moderate rotation when the Rossby number is of order unity. At small Rossby numbers, the rotation differentiality is inhibited. A negative eddy viscosity is suggested for the case of rapid rotation. Some implications for the Sun and other astrophysical objects are discussed.  相似文献   

6.
The generation and evolution of the Sun’s magnetic field and other stars is usually related to the dynamo mechanism. This mechanism is based on the consideration of the joint influence of the α effect and differential rotation. Dynamo sources can be located at different depths of the convection zone and can have different intensities. Based on such a system, the dynamical system in the case of the stellar dynamo in a two-layer medium has been constructed with regard to meridional fluxes in order to model the double cycle that corresponds to the simultaneous presence of 22-year and quasi-biennial magnetic field oscillations. It has been indicated that the regime of mixed oscillations can originate because a dynamo wave moves oppositely to the meridional flows in the upper layer of the convection zone. This results in the deceleration of the toroidal field propagation and in the generation of slow oscillations. In deeper layers, the directions of a dynamo wave and meridional flows coincide with each other, as a result of which fast magnetic fields originate. Therefore, the total contribution of two oscillations with different frequencies corresponds to the appearance of quasi-biennial cycles against 22-year cycles. It has been indicated that the beating regime, which can be related to the secular oscillations of solar magnetic activity, originates in the system when the meridional flows are weak.  相似文献   

7.
The flow structure induced by thermal convection in a rotating spherical shell with viscous boundary conditions is considered under the assumption that the differential rotation of the core relative to the mantle is absent. The radial, azimuthal, and meridional components of the flow’s velocity and helicity are studied. With the magnetic field assumed to be frozen into a liquid (frozen-flux hypothesis), it is shown that the numerical results fit the observations of the geomagnetic field variations close to the pole.  相似文献   

8.
Abstract

Coriolis forces stimulate dynamo action in a rapidly-rotating fluid by promoting complexities in the pattern of fluid motions, notably departures from symmetry about the axis of rotation. This pattern and its time variations determine the instantaneous form and temporal behaviour of the magnetic field so produced. Instantaneous magnetic fields will usually exhibit in their broad-scale features approximate alignment with the rotation axis. This is borne out by observations of the magnetic fields of the Earth, Jupiter and Saturn, and it is likely on general grounds that Neptune will be found to have an aligned magnetic field. But, as is shown by laboratory and theoretical studies of thermal convection in rapidly-rotating fluids, for some ranges of rotation speed, rate of heating, etc. certain patterns can occur which in electrically-conducting fluids would produce magnetic fields exhibiting departures from alignment with the rotation axis, which instantaneously could be quite pronounced but would average out to very small values over sufficiently long periods of time. These findings indicate obvious strategies for theoretical studies towards the interpretation of Uranus's eccentric magnetic field (which need not invoke departures from axial symmetry in the thermal, mechanical or electrical boundary conditions of the dynamo region within the planet) and for further observational studies.  相似文献   

9.
Abstract

The annulus model considers convection between concentric cylinders with sloping endwalls. It is used as a simplified model of convection in a rapidly rotating sphere. Large azimuthal wavenumbers are preferred in this problem, and this has been exploited to develop an asymptotic approach to nonlinear convection in the annulus. The problem is further reduced because the Taylor-Proudman constraint simplifies the dependence in the direction of the rotation vector, so that a nonlinear system dependent only on the radial variable and time results. As Rayleigh number is increased a sequence of bifurcations is found, from steady solutions to periodic solutions and 2-tori, typically ending in chaotic behaviour. Both the magnetic (MHD convection) and non-magnetic problem has been considered, and in the non-magnetic case our bifurcation sequence can be compared with those found by previous two-dimensional numerical simulations.  相似文献   

10.
Abstract

The onset of convection in a cylindrical fluid annulus is analyzed in the case when the cylindrical walls are rotating differentially, a temperature gradient in the radial direction is applied, and the centrifugal force dominates over gravity. The small gap approximation is used and no-slip conditions on the cylindrical walls are assumed. It is found that over a considerable range of the parameter space either convection rolls aligned with the axis of rotation or rolls in the perpendicular (azimuthal) direction are preferred. It is shown that by a suitable redefinition of parameters, results for finite amplitude Taylor vortices and for convection rolls in the presence of shear can be applied to the present problem. Weakly nonlinear results for transverse rolls in a Couette flow indicate the possibility of subcritical bifurcation for Prandtl numbers P less than 0.82. Heat and momentum transports are derived as functions of P and the problem of interaction between transverse and longitudinal rolls is considered. The relevance of the analysis for problems of convection in planetary and stellar atmospheres is briefly discussed.  相似文献   

11.
A three-dimensional, hydrostatic, primitive equation numerical model with modern turbulence closures is used to explore lateral circulation and the associated transport of sediments in idealized, moderately to highly stratified estuaries. The model results suggest that boundary mixing on a sloping bottom can drive a significant amount of lateral circulation. This mechanism has received little attention to date in the estuarine literature. Good agreement with an analytical solution and similar vertical structures of lateral flows to observations from the Hudson River estuary support the importance of the boundary mixing mechanism. Boundary mixing is at least as important as differential advection for the modeled scenarios, when the two mechanisms are evaluated using the salt balance equation for model runs without rotation. Linearly superposing analytical solutions for lagged boundary mixing lateral flow and Ekman-forced lateral flow yields a good representation of the near-bottom lateral flow from the model with rotation. The 2 h lag required for the boundary mixing solution is roughly equal to the vertical diffusion time scale, indicating that lateral flow adjustment depends on development of a bottom mixed layer. Sediment dynamics at cross sections seaward and landward of the salt intrusion are very different. Seaward of the salt intrusion, sediments are eroded in the channel and preferentially deposited on the right slope (looking seaward), mainly due to the combination of high sediment concentration in the channel during flood with strong up-slope transport on that side (tidal pumping). Lateral sediment re-distribution landward of the salt intrusion is negligible due to weak residual lateral circulation.  相似文献   

12.
We investigate numerically kinematic dynamos driven by flow of electrically conducting fluid in the shell between two concentric differentially rotating spheres, a configuration normally referred to as spherical Couette flow. We compare between axisymmetric (2D) and fully 3D flows, between low and high global rotation rates, between prograde and retrograde differential rotations, between weak and strong nonlinear inertial forces, between insulating and conducting boundaries and between two aspect ratios. The main results are as follows. Azimuthally drifting Rossby waves arising from the destabilisation of the Stewartson shear layer are crucial to dynamo action. Differential rotation and helical Rossby waves combine to contribute to the spherical Couette dynamo. At a slow global rotation rate, the direction of differential rotation plays an important role in the dynamo because of different patterns of Rossby waves in prograde and retrograde flows. At a rapid global rotation rate, stronger flow supercriticality (namely the difference between the differential rotation rate of the flow and its critical value for the onset of nonaxisymmetric instability) facilitates the onset of dynamo action. A conducting magnetic boundary condition and a larger aspect ratio both favour dynamo action.  相似文献   

13.
Abstract

A meridional circulation of sunspots has been measured through the digital analysis of the Meudon spectroheliograms from 1978 to 1983. Old and young sunspots follow a zonal meridional circulation, in several bands of latitude, in which two adjacent bands have opposite motions. This meridional circulation pattern is time-dependent. Using the H α filaments as magnetic field tracers, a large-scale magnetic pattern has been found that was also obtained independently by direct measurement of the magnetic field (Hoeksema, 1988).

The coincidence of a large-scale magnetic pattern with a zonal meridional circulation suggests the existence of azimuthal rolls below the surface, and these azimuthal rolls can explain a number of properties of the solar cycle. New rolls occur with increasing proximity to the Equator, thereby indicating the direction of propagation of the dynamo wave. The occurrence of rolls is very favorable to the emergence of the magnetic regions. The rolls also influence the magnetic complexity of the active regions. They modulate the surface rotation through the Coriolis force, which accelerates or decelerates the fluid particles. They therefore offer a plausible explanation of the torsional oscillation pattern.

There are a number of problems raised by such an unexpected circulation pattern: for example, the coexistence of axisymmeric rolls with hypothetical giant cells, the location of the dynamo source below or within the convective zone, and the coupling of the radiative interior and the convective layers. To resolve these important issues, continuous observational studies are needed of the manifestation of solar activity, as well as of radius and luminosity variations. So, we have aimed our paper at an audience of theoreticians in the hope that they take up the challenges we describe.  相似文献   

14.
Abstract

Convection in a rotating spherical shell has wide application for understanding the dynamics of the atmospheres and interiors of many celestial bodies. In this paper we review linear results for convection in a shell of finite depth at substantial but not asymptotically large Taylor numbers, present nonlinear multimode calculations for similar conditions, and discuss the model and results in the context of the problem of solar convection and differential rotation. Detailed nonlinear calculations are presented for Taylor number T = 105, Prandtl number P = 1, and Rayleigh number R between 1 |MX 104 and 4 |MX 104 (which is between about 4 and 16 times critical) for a shell of depth 20% of the outer radius. Sixteen longitudinal wave numbers are usually included (all even wave numbers m between 0 and 30) the amplitudes of which are computed on a staggered grid in the meridian plane.

The kinetic energy spectrum shows a peak in the wave number range m = 12–18 at R = 104, which straddles the critical wave number m = 14 predicted by linear theory. These are modes which peak near the equator. The spectrum shows a second strong peak at m = 0, which represents the differential rotation driven by the peak convective modes. As R is increased, the amplitude of low wave numbers increases relative to high wave numbers as convection fills in in high and middle latitudes, and as the longitudinal scale of equatorial convection grows. By R = 3 |MX 104, m = 8 is the peak convective mode. There is a clear minimum in the total kinetic energy at middle latitudes relative to low and high, well into the nonlinear regime, representing the continued dominance of equatorial and polar modes found in the linear case. The kinetic energy spectrum for m > 0 is maintained primarily by buoyancy work in each mode, but with substantial nonlinear transfer of kinetic energy from the peak modes to both lower and higher wave numbers.

For R = 1 to 2 |MX 104, the differential rotation takes the form of an equatorial acceleration, with angular velocity generally decreasing with latitude away from the equator (as on the sun) and decreasing inwards. By R = 4 |MX 104, this equatorial profile has completely reversed, with angular velocity increasing with depth and latitude. Also, a polar vortex which has positive rotation relative to the reference frame (no evidence of which has been seen on the sun) builds up as soon as polar modes become important. Meridional circulation is quite weak relative to differential rotation at R = 104, but grows relative to it as R is increased. This circulation takes the farm of a single cell of large latitudinal extent in equatorial regions, with upward flow near the equator, together with a series of narrower cells in high latitudes. It is maintained primarily by axisymmetric buoyancy forces. The differential rotation is maintained at all R primarily by Reynolds stresses, rather than meridional circulation. Angular momentum transport toward the equator for R = 1–2 |MX 104 maintains the equatorial acceleration while radially inward transport maintains the opposite profile at R = 4 |MX 104.

The total heat flux out the top of the convective shell always shows two peaks for the range of R studied, one at the equator and the other near the poles (no significant variation with latitude is seen on the sun), while heat flux in at the bottom shows only a polar peak at large R. The meridional circulation and convective cells transport heat toward the equator to maintain this difference.

The helicity of the convection plus the differential rotation produced by it suggest the system may be capable of driving a field reversing dynamo, but the toroidal field may migrate with lime in each cycle toward the poles and equator, rather than just toward the equator as apparently occurs on the sun.

We finally outline additions to the physics of the model to make it more realistic for solar application.  相似文献   

15.
为探索驱动地球系统差异旋转的力源,选择整个地球作为研究对象,应用经典电磁学理论,分析地球固体介质中的电荷在地球主磁场中的运动特点,发现存在一个与地球自转方向相反的切向洛伦兹力.通过电荷与介质间的相互作用,切向洛伦兹力传递至介质迫使介质西漂.为探索地球差异旋转的规律,建立了地球薄圆筒圈层模型.应用经典物理学理论和方法推导出了地球主磁场电磁转矩及其产生的角加速度公式.研究得到四点主要结论:1)作用于半径不同的地球薄圆筒圈层的地球主磁场电磁转矩及其产生的角加速度绝对值不同:地轴及赤道附近圈层的小,其自转相对较快;半径等于3～(1/2)倍地球半径的薄圆筒圈层及其相邻圈层的大,其自转相对较慢.2)同一薄圆筒圈层中的差异旋转缘于介质的介电常数、阻力系数及质量密度的差异.3)地球差异旋转缘于地球的自转、正负电荷的非对等分布及介质的介电常数、阻力系数、质量密度的差异.4)地球差异旋转导致地壳运动,孕育地震,地球主磁场是地球差异旋转和地震孕育的敏感因子.  相似文献   

16.
Abstract

The flow properties of an homogeneous fluid which is bounded by two concentric spheres and two meridional planes which intersect along a diameter of the spheres are investigated. The spheres rotate about this diameter with slightly different angular velocities. As in the axisymmetric case studied by Proudman (1956) and Stewartson (1966) the viscous terms in the equations of motion are important only in boundary layers on the spheres and on the cylinder C which circumscribes the inner sphere and which has generators parallel to the axis of rotation, provided the Ekman number E is small. In the inviscid region the velocities are independent of the coordinate measuring distance along the axis of rotation and are much weaker, by a factor 0(E ½), than the velocities in the Ekman layer on the driving surface (outer sphere). (It is assumed that the reference frame is fixed in the slower rotating inner sphere.) If the separation of the spheres is small compared to their radii then the asymmetric circulation inside C is characterized by an intense jet along the western wall. Loss of fluid from this jet sustains the eastward and northward flow in the inviscid interior where motion is driven by the suction of the Ekman layer on the outer sphere. (Geophysical conventions have been adopted.) Outside C an intense current is present on the eastern, not western, wall while motion in the inviscid region is westward, and away from the axis of rotation. Though there is no transport across C in the inviscid region, the meridional transport of the Ekman layer on the outer sphere is continuous across C and increases, through suction, as the equator is approached until it drains into an eastward flowing equatorial current of width 0(E 1/7). The eastern boundary current outside C and shear layers on C carry this fluid to the intersection of C and the western wall where it feeds the western boundary current inside C.

The relation between this study and the experiments of Baker and Robinson (1970) is discussed.  相似文献   

17.
The Loop Current of the Gulf of Mexico is simulated in the laboratory. A circular tank is filled with water and is placed off-center on a rotating table and the flow field is generated by injecting and withdrawing water at two openings on the wall. The free surface becomes parabolic due to balance of gravitational and centrifugal forces, simulating the latitudinal change of the Coriolis parameter (-effect) in the ocean. The flow characteristics depend on the influx and the rate of rotation and can be classified according to non-dimensional parameters (Rossby, Ekman and Froude numbers denoted byR 0,E andF, respectively). When the influx is small and the rotation rate is large (smallR 0,E andF) the flow will be almost linear, and the fluid flows along the side-wall boundary layer under constraint of the -effect. For a very large influx (largeR 0 andE) inertial forces become very large compared to the Coriolis force and the flow behaves like a potential flow. The flow studied had characteristics between these two extreme cases and hasR 0 andF similar to the Gulf circulation, though similarity inE is ambiguous. Photographs of the flow indicate that the inflow penetrates further into the interior when the rotation rate is increased while the influx is kept constant. The numerical analysis of the non-linear vorticity equation confirms this for the parameters corresponding to the experiment. In addition, the photographs reveal eddies embedded on both sides of the main stream, particularly near the inflow region. These eddies are intensified and become uniform in size as the influx increases. It is pointed out that such eddies were actually observed near the Loop Current north of the Yucatan Straits.  相似文献   

18.
Summary The zonally asymmetric stationary component of the general circulation is studied for small Rossby number without the beta-plane approximation. The equations for this component are linearized about a mean flow. An analytic solution for the meridional wind is found when the zonal wind and static stability of the mean flow are independent of the vertical coordinate. The solution is used to compute the transports of angular momentum and heat. The angular momentum transports give rise to a net convergence of the order of Rossby number and are balanced by the zonal mean Coriolis torque. However, the heat transports vanish at this order of magnitude.  相似文献   

19.
The observed plate velocities contain two types of motions. The poloidal component is related to the formation of ridges and subduction zones and the toroidal field expresses the shearing of surface plates. One very important consideration in modeling flow in the earth's mantle is the existence and motion of the lithospheric plates. The motion of plates represents a large-scale circulation with strong viscous coupling to the mantle underneath. The mantle flow probably is neither a purely free convection driven by buoyancy forces due to nonadiabatic temperature gradients in the mantle nor a forced convection generated by boundary forces, but a mixed convection that combines the effects of boundary and buoyancy forces. We present, in this paper, the mixed convection model resulting in a surface velocity field that contains both the observed poloidal and toroidal components.  相似文献   

20.
Abstract

An inviscid, electrically conducting fluid is contained between two rigid horizontal planes and bounded laterally by two vertical walls. The fluid is permeated by a strong uniform horizontal magnetic field aligned with the side wall boundaries and the entire system rotates rapidly about a vertical axis. The ratio of the magnitudes of the Lorentz and Coriolis forces is characterized by the Elsasser number, A, and the ratio of the thermal and magnetic diffusivities, q. By heating the fluid from below and cooling from above the system becomes unstable to small perturbations when the adverse density gradient as measured by the Rayleigh number, R, is sufficiently large.

With the viscosity ignored the geostrophic velocity, U, which is aligned with the applied magnetic field, is independent of the coordinate parallel to the rotation axis but is an arbitrary function of the horizontal cross-stream coordinate. At the onset of instability the value of U taken ensures that Taylor's condition is met. Specifically the Lorentz force, which results from marginal convection must not cause any acceleration of the geostrophic flow. It is found that the critical Rayleigh number characterising the onset of instability is generally close to the corresponding value for the usual linear problem, in which Taylor's condition is ignored and U is chosen to vanish. Significant differences can occur when q is small owing to a complicated flow structure. There is a central interior region in which the local magnetic Reynolds number, Rm , based on U is small of order q and on exterior region in which Rm is of order unity.  相似文献   

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