共查询到20条相似文献，搜索用时 296 毫秒
1.
R. R. Kerswell 《地球物理与天体物理流体动力学》2013,107(1-4):107-144
Abstract An explanation is put forward for the instability observed within a precessing, rotating spheroidal container. The constant vorticity solution for the flow suggested by Poincaré is found to be inertially unstable through the parametric coupling of two inertial waves by the underlying constant strain field. Such resonant couplings are due either to the elliptical or shearing strains present which elliptically distort the circular streamlines and shear their centres respectively. For the precessing Earth's outer core, the shearing of the streamlines and the ensuing shearing instability are the dominant features. The instability of some exact, linear solutions for finite precessional rates is established and used to corroborate the asymptotic analysis. A complementary unbounded analysis of a precessing, rotating fluid is also presented and used to deduce a likely upperbound on the growth rate of a small disturbance. Connection is made with past experimental studies. 相似文献
2.
Abstract The superconducting-gravimeter data of Melchior and Ducarme (1986) has been interpreted as internal motion in the Earth's core by Aldridge and Lumb (1987) using a Poincaré model. Several low-order modes with periods of 13–16 hours have been tentatively identified in the core which is taken to be an incompressible, homogeneous fluid within a rigid, rotating container. The identification is based on asymptotic values of the frequencies which change slowly with time while the modes decay with an e-folding time of about 280 days. The slow change in frequency with time implies a small temporal variation in the rotation rate of the core. This mean flow is a nonlinear effect often observed in laboratory experiments designed to excite Poincaré modes. Interaction among modes during free ringdown is also observed in those experiments and apparently in the data of Melchior et al. (1988) as well. Laboratory work thus provides the link to extend the Poincaré model to include viscous and nonlinear effects in order to interpret the gravimetric observations as core modes. 相似文献
3.
R. Smoluchowski 《Physics of the Earth and Planetary Interiors》1979,20(2-4):247-254
Recent observations and progress in the understanding of various requirements for the generation of magnetic fields permit much more definite conclusions to be drawn about the fields of the giant planets than was possible until quite recently. The Jovian magnetic field of about 4 gauss could be either of primordial origin or generated by a thermally driven dynamo. The expected Saturnian field of about 1 gauss can be similarly accounted for either by a thermally or by a precessionally driven dynamo. The presence of a field on Uranus of perhaps 0.1 gauss presents a problem because although it could be accounted for by a thermally driven dynamo operating in a highly conductive shell of hydrogen, the so far unobserved thermal flux and convection may be too low. If such a dynamo were to operate then one would expect the field to show seasonal variations. A precessional dynamo driven by Miranda seems to be marginally possible. On Neptune a conductive shell similar to that on Uranus appears to be much thinner, which perhaps explains the absence of an active dynamo driven either thermally or precessionally by Triton. It is, however, very likely that Neptune does have a magnetic field but that it is too weak to lead to observable electromagnetic radiations. 相似文献
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The differentially heated rotating annulus is a laboratory experiment historically designed for modelling large-scale features of the mid-latitude atmosphere. In the present study, we investigate a modified version of the classic baroclinic experiment in which a juxtaposition of convective and motionless stratified layers is created by introducing a vertical salt stratification. The thermal convective motions are suppressed in a central region at mid-depth of the rotating tank, therefore double-diffusive convection rolls can develop only in thin layers located at top and bottom, where the salt stratification is weakest. For high enough rotation rates, the baroclinic instability destabilises the flow in the top and the bottom shallow convective layers, generating cyclonic and anticyclonic eddies separated by the stable stratified layer. Thanks to this alternation of layers resembling the convective and radiative layers of stars, the planetary’s atmospheric troposphere and stratosphere or turbulent layers at the sea surface above stratified waters, this new laboratory setup is of interest for both astrophysics and geophysical sciences. More specifically, it allows to study the exchange of momentum and energy between the layers, primarily by the propagation of internal gravity waves (IGW). PIV velocity maps are used to describe the wavy flow pattern at different heights. Using a co-rotating laser and camera, the wave field is well resolved and different wave types can be found: baroclinic waves, Kelvin and Poincaré type waves. The signature of small-scale IGW can also be observed attached to the baroclinic jet. The baroclinic waves occur at the thin convectively active layer at the surface and the bottom of the tank, though decoupled they show different manifestation of nonlinear interactions. The inertial Kelvin and Poincaré waves seem to be mechanically forced. The small-scale wave trains attached to the meandering jet point to an imbalance of the large-scale flow. For the first time, the simultaneous occurrence of different wave types is reported in detail for a differentially heated rotating annulus experiment. 相似文献
6.
Smith AJ 《Ground water》2008,46(2):228-238
Published frequency-domain solutions of periodic flow in aquifers apply strictly to mathematically linear systems that arise when aquifer diffusivity is assumed constant in space and time. This assumption can be invalid in phreatic aquifers that experience spatiotemporal variation in the free surface position and consequent variation in saturated thickness. A weakly nonlinear approach to formulating and solving periodic flow problems in the frequency domain can be applied in situations where conventional linearized approximations break down. The weakly nonlinear equations provide robust approximations of the true nonlinear response and require much less computational effort and time to solve than the full nonlinear problem. Nondimensional rules of thumb are presented for choosing between linear, weakly nonlinear and nonlinear solution strategies. 相似文献
7.
Lee-Or Merkine 《地球物理与天体物理流体动力学》2013,107(1-2):25-37
Abstract The mutual interaction of fields induced by spatially separated potential vorticity sources in a quasi-geostrophic barotropic flow is investigated using the weakly nonlinear approach. It is found that a powerful nonlinear response can be triggered by Rossby lee waves. This resonance phenomenon which dominates all other nonlinear corrections depends on certain global resonance conditions and on the change in the phase of the Rossby lee wave across the distance separating the sources. The response is particularly strong for topographic forcing possessing δ-function characterisitics. 相似文献
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We present a theoretical weakly nonlinear analysis of the dynamics of an inviscid flow submitted to both rotation and precession of an unbounded cylindrical container, by considering the coupling of two Kelvin (inertial) waves. The parametric centrifugal instability known for this system is shown to saturate when one expands the Navier–Stokes equation to higher order in the assumed small precession parameter (ratio of precession to rotation frequencies) with the derivation of two coupled Landau equations suitable to describe the dynamics of the modes. It is shown that an azimuthal mean flow with differential rotation is generated by this modes coupling. The time evolution of the associated dynamical system is studied. These theoretical results can be compared with water experiments and also to some numerical simulations where viscosity and finite length effects cannot be neglected. 相似文献
10.
An idealized model of tidal dynamics in the North Sea: resonance properties and response to large-scale changes 总被引：3，自引：1，他引：2
Pieter C. Roos Jorick J. Velema Suzanne J. M. H. Hulscher Ad Stolk 《Ocean Dynamics》2011,61(12):2019-2035
An idealized process-based model is developed to investigate tidal dynamics in the North Sea. The model geometry consists
of a sequence of different rectangular compartments of uniform depth, thus, accounting for width and depth variations in a
stepwise manner. This schematization allows for a quick and transparent solution procedure. The solution, forced by incoming
Kelvin waves at the open boundaries and satisfying the linear shallow water equations on the f plane with bottom friction, is in each compartment written as a superposition of eigenmodes, i.e. Kelvin and Poincaré waves.
A collocation method is employed to satisfy boundary and matching conditions. First, the general resonance properties of a
strongly simplified geometry with two compartments, representing the Northern North Sea and Southern Bight, are studied. Varying
the forcing frequency while neglecting bottom friction reveals Kelvin and Poincaré resonance. These resonances continue to
exist (but with lower amplification and a modified spatial structure) when adding the Dover Strait as a third compartment
and separating the solutions due to forcing from either the north or the south only. Including bottom friction dampens the
peaks. Next, comparison with tide observations along the North Sea coast shows remarkable agreement for both semi-diurnal
and diurnal tides. This result is achieved with a more detailed geometry consisting of 12 compartments fitted to the coastline
of the North Sea. Further simulations emphasize the importance of Dover Strait and bottom friction. Finally, it is found that
a sea level rise of 1 m, uniformly applied to the entire North Sea, amplifies the M2-elevation amplitudes almost everywhere
along the coast, with an increase of up to 8 cm in Dover Strait. Bed level changes of ±1 m, uniformly applied to the Southern
Bight only, imply weaker changes, with changes in coastal M2-elevation amplitudes below 5 cm. 相似文献
11.
V. A. Zheligovsky 《Izvestiya Physics of the Solid Earth》2006,42(12):1051-1067
The problem of weakly nonlinear stability with respect to large-scale perturbations in 3-D convective magnetohydrodynamic (MHD) states in which the α-effect is absent or insignificant (e.g., because the system has symmetry relative to a center or a vertical axis) is examined. It is assumed that the MHD state whose stability is studied is free from large spatiotemporal scales and is insensitive to perturbations with the same small spatial scale as in the state under study. The equations for mean perturbation fields derived by asymptotic methods generalize the standard equations of magnetohydrodynamics (the Navier-Stokes and magnetic induction equations). A combined eddy diffusion operator, generally anisotropic and not necessarily negative definite, and additional quadratic terms similar to advective terms arise in the inferred generalized equations. 相似文献
12.
The role of inertial waves in the dynamies of the Earth's fluid core has been investigated through laboratory experiments on a spheroidal shell of rotating fluid. In these experiments inertial waves of azimuthal wavenumber 1, Ekman number 0(10?5), Rossby number 0(10?1) were excited by precession of an inner spheroidal body. Proximity to resonance was achieved by adjusting the ratio of the frequency of precession of the inner body to the rotational speed of the container to be near the eigenfrequency of the inertial wave mode being studied. Once the system was near resonance the perturbation was stopped and ringdown records were obtained. Amplitude, eigenfrequency and decay rate were recovered simultaneously for the principal and neighbouring modes excited using an iterative linearized least squares procedure.The recovery of complex eigenfrequencies for non-axisymmetric inertial waves in this shell geometry has given experimental verification of their existence. For those waves of azimuthal wavenumber one, a significant nonlinear interaction among modes is inferred from the simultaneous recovery of neighbouring modes. Other non linear effects include a mean azimuthal flow which appears to be stable for the low spatial order modes studied. These results contrast with highly unstable mean flow found experimentally in similar experiments carried out in cylindrical geometry. 相似文献
13.
CHAO JiPing & LIU Fei National Marine Environmental Forecasting Center Beijing China The First Institute of Oceanography SOA Qingdao China Key Laboratory Regional Climate-Environment for Temperate East Asia Institute of Atmospheric Physics Chinese Academy of Sciences Beijing China Graduate University of Chinese Academy of Sciences Beijing China 《中国科学D辑(英文版)》2007,50(1):153-160
Based on the developed Anderson and Moore's theory about cross-equatorial inertial jets and a nonlinear equivalence shallow water model, new universal functions are determined by the characters of the vortical large-scale air flow (atmosphere) or ocean current (ocean) related to the jet, then the potential vorticity and energy conservation equations along the streamline in the cross-equatorial in-ertial jets can be obtained. Because the governing equations are nonlinear, some limited multiple equi-libria of cross-equatorial inertial jets may exist. According to the character of large-scale air flow or ocean current outside the jets, the existent criterion for multiple eqnilibria in cross-equatorial inertial jets is discussed, and two examples for multiple equilibia of nonlinear governing equations are given. 相似文献
14.
We study solute transport in a periodic channel with a sinusoidal wavy boundary when inertial flow effects are sufficiently large to be important, but do not give rise to turbulence. This configuration and setup are known to result in large recirculation zones that can act as traps for solutes; these traps can significantly affect dispersion of the solute as it moves through the domain. Previous studies have considered the effect of inertia on asymptotic dispersion in such geometries. Here we develop an effective spatial Markov model that aims to describe transport all the way from preasymptotic to asymptotic times. In particular we demonstrate that correlation effects must be included in such an effective model when Péclet numbers are larger than O(100) in order to reliably predict observed breakthrough curves and the temporal evolution of second centered moments. For smaller Péclet numbers correlation effects, while present, are weak and do not appear to play a significant role. For many systems of practical interest, if Reynolds numbers are large, it may be typical that Péclet numbers are large also given that Schmidt numbers for typical fluids and solutes can vary between 1 and 500. This suggests that when Reynolds numbers are large, any effective theories of transport should incorporate correlation as part of the upscaling procedure, which many conventional approaches currently do not do. We define a novel parameter to quantify the importance of this correlation. Next, using the theory of CTRWs we explain a to date unexplained phenomenon of why dispersion coefficients for a fixed Péclet number increase with increasing Reynolds number, but saturate above a certain value. Finally we also demonstrate that effective preasymptotic models that do not adequately account for velocity correlations will also not predict asymptotic dispersion coefficients correctly. 相似文献
15.
According to the data of the IMAGE network of magnetometers the latitudinal profile of the amplitude of the Pc5 geomagnetic
pulsations is constructed, which are excited in the Earth’s magnetosphere in the form of the resonance Alfvén magnetohydrodynamic
pulsations. The approaches to the solution of two problems are studied on a specific example. The first concerns the anharmonicity
of Alfvén’s resonances. The displacement of the peak of the resonance curve towards to the north with the reduction of the
amplitude of the pulsations is discovered. Based on the results of measurements, the nonlinear distortion coefficient of the
latitudinal profile is determined. The second problem is connected with the magnetotelluric sounding. Information about the
resonance structure of the Alfvén pulsations is useful for magnetotelluric sounding. This information gives the possibility
of evaluating the accuracy of the sounding with the application of the local impedance relationship and of introducing corrections
if necessary. 相似文献
16.
Hezi Gildor 《地球物理与天体物理流体动力学》2013,107(6):593-599
The solution for the bottom Ekman layer has a somewhat counter intuitive character, which seems to violate the maximum principle: at a certain level the velocity within the Ekman layer is higher than the velocity in the geostrophic layer above. I explain this character by looking at an analogous problem in an inertial frame of reference and show that it is the result of observing the flow from a rotating frame of reference (i.e. within a system that is not in steady state). The flow in the bottom Ekman layer is a superposition of the flow that results from the force exerted on the fluid by the rotating Earth and of the flow that results from the pressure-gradient term. Therefore, at a certain level the speed is higher than the speed of the geostrophic layer above which results from the pressure gradient alone. 相似文献
17.
Abstract A system is considered in which electrically conducting fluid is contained between two rigid horizontal planes and bounded laterally by a circular cylinder. The fluid is permeated by a strong azimuthal magnetic field. The strength of the field increases linearly with distance from the vertical axis of the cylinder, about which the entire system rotates rapidly. An unstable temperature gradient is maintained by heating the fluid from below and cooling from above. When viscosity and inertia are neglected, an arbitrary geostrophic velocity, which is aligned with the applied azimuthal magnetic field and independent of the axial coordinate, can be superimposed on the basic axisymmetric state. In this inviscid limit, the geostrophic velocity which occurs at the onset of convection is such that the net torque on geostrophic cylinders vanishes (Taylor's condition). The mathematical problem which describes the ensuing marginal convection is nonlinear, and was discussed previously for the planar case by Soward (1986). Here new features are isolated which result from the cylindrical geometry. New asymptotic solutions are derived valid when Taylor's condition is relaxed to include viscous effects. 相似文献
18.
A. V. Guglielmi 《Izvestiya Physics of the Solid Earth》2008,44(1):43-49
A review of studies devoted to the problem of exciting magnetic signals in the crust associated with the formation of the major rupture in an earthquake source and with the propagation of seismic waves was given in [Sgrigna et al., 2004]. However, this review contains incorrect citations from original papers and several erroneous statements concerning inertial and inductive mechanisms of conversion of the energy of rock motion into magnetic field energy. These mistakes are analyzed in the present paper. The formal and physical similarity between seismomagnetic waves in the crust and Alfvén waves in the magnetosphere is used in the analysis. A comparative analysis of the inertial and inductive mechanisms of seismomagnetic field generation is performed. The Cherenkov criterion of Alfvén wave generation due to the ionospheric effect of acoustic waves from earthquakes and explosions is derived. Attention is also given to nonlinear phenomena (nonlinearity of a mechanomagnetic conversion in the crust and anharmonicity and self-focusing of Alfvén waves in the magnetosphere). 相似文献
19.
椭圆形柱体地震动水压力的简化分析方法 总被引：1，自引：1，他引：0
首先,文章基于辐射波浪理论,在椭圆坐标系下采用分离变量法推导了水中椭圆形柱体地震动水压力的解析解。之后,采用有限元方法建立了地震作用下水与结构相互作用的动力方程,方程中水体对结构的作用为一满阵的附加质量矩阵。满阵的附加质量矩阵难以在商业有限元中实现,因此提出了集中的附加质量矩阵方法,其中结构柔性引起的附加质量为集中附加质量矩阵和修正系数的乘积,该修正系数与无量纲参数宽深比和长短轴比相关。最后,通过曲线拟合,提出了刚性椭圆柱体动水力的均布附加量简化公式,该简化公式是无量纲参数宽深比和长短轴比的函数。 相似文献
20.
V.A. Osherovich J. Fainberg R.F. Benson R.G. Stone 《Journal of Atmospheric and Solar》1997,59(18):2361-2366
We study cylindrical oscillations of electrons in a plasma where the background magnetic field is parallel to the axis of a cylinder and the ion background is taken to have a constant positive density. Assuming self-similarity, we reduce the problem to two second order nonlinear differential equations, relating fluctuations of electron density and fluctuations of magnetic field. The system studied is shown to have two fundamental frequencies. In the linear domain, these frequencies correspond to the Z and X cold plasma wave cutoff frequencies (R = 0 and L = 0 conditions in the notation of Stix (1992), respectively). Thus they differ by the gyrofrequency. In the nonlinear domain, these frequencies change and resonances at harmonics and at the sum and difference frequencies appear. When the plasma/gyro frequency ratio is close to an integer, our results indicate special resonance conditions which are characterized by an increase of the amplitude and a narrowing of the fundamental resonances. 相似文献