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1.
ABSTRACT

Herein we study the general interaction of two vortex patches in a single-layer quasi-geostrophic shallow-water flow. Steadily-rotating equilibrium states are found over a wide parameter space spanning the Rossby deformation length, vortex area ratio, potential vorticity ratio, and gap between their innermost edges. A linear stability analysis is then used to identify the critical gap separating stable and unstable solutions, over the entire range of area and potential vorticity ratios, and for selected values of the Rossby deformation length. A representative set of marginally unstable equilibrium states are then slightly perturbed and evolved by an accurate contour dynamics numerical algorithm to understand the long-term fate of the instabilities. Not all instabilities lead to vortex merger; many in fact are characterised by weak filamentation and a small adjustment of the vortex shapes, without merger. Stronger instabilities lead to material being torn from one vortex and either wrapped around the other or reduced to ever thinning filamentary debris. A portion of the vortex may survive, or it may be completely strained out by the other.  相似文献   

2.
Hydrodynamical Modeling Of Oceanic Vortices   总被引：1，自引：0，他引：1  
Mesoscale coherent vortices are numerous in the ocean.Though they possess various structures in temperature and salinity,they are all long-lived, fairly intense and mostly circular. Thephysical variable which best describes the rotation and the density anomaly associated with coherent vortices is potential vorticity. It is diagnostically related to velocity and pressure, when the vortex is stationary. Stationary vortices can be monopolar (circular or elliptical) or multipolar; their stability analysis shows thattransitions between the various stationary shapes are possible when they become unstable. But stable vortices can also undergo unsteady evolutions when perturbed by environmental effects, likelarge-scale shear or strain fields, -effect or topography. Changes in vortex shapes can also result from vortex interactions. such as the pairing, merger or vertical alignment of two vortices, which depend on their relative polarities and depths. Such interactions transfer energy and enstrophy between scales, and are essential in two-dimensional and in geostrophic turbulence. Finally, in relation with the observations, we describe a few mechanisms of vortex generation.  相似文献   

3.
Abstract

In this paper, starting from the spectral DIA equations obtained by Veltri et al. (1982), describing the spectral dynamical evolution of magnetohydrodynamic (MHD) turbulence in the presence of a background magnetic field B 0, we have derived an approximate form of these equations (shell model) more appropriate for numerical integration at high Reynolds numbers.

We have studied the decay of an initially isotropic state, with an initial imbalance between the energies for the two signs of the cross-helicity. Reynolds numbers up to 105 have been considered.

Numerical results show that the nonlinear energy cascade behaves anisotropically in the k-space, i.e. in the spectra there is a prevalence of the wavevectors perpendicular to B 0 with respect to the parallel wavevectors. This anisotropic effect, which is due to the presence of the background magnetic field, can be understood in terms of the so-called ‘‘Alfvén effect''.

A different source of anisotropy, due to the difference of the energy transfer for the two polarizations perpendicular to k, is recovered, but its effect is found to be mainly concentrated in the injection range.

Only little differences have been found, in the inertial range, in the spectral indices from the Kraichnan 3/2 value, which is valid for an isotropic spectrum. A form for the anisotropic spectrum can be recovered phenomenologically from our results. Values of the spectral indices quite different from the Kraichnan 3 2 value are obtained only when we consider stationary states with different forcing terms for the two modes of Alfvén wave propagation.

The comparison of our results with the observations of the v and B fluctuations in the interplanatery space shows that the anisotropy found in interplanetary fluctuations might be attributed only partially to the result of a nonlinear energy cascade.  相似文献   

4.
Abstract

In this paper we examine the behaviour of oceanic unsteady flow impinging on isolated topography by means of numerical simulation. The ocean model is quasigeostrophic and forced by an oscillatory mean flow. The fluid domain is of the channel type and open-boundary numerical conditions are used to represent downstream and upstream flow.

In certain cases, vortex shedding, either cyclonic or anticyclonic, is observed in the lee of obstacles. Such shedding can be explained as the consequence of both an enhanced process of vorticity dissipation over the topography which locally affects the balance of potential vorticity on the advective timescale, and a periodic dominance of advective effects which sweep the fluid particles trapped on the seamount. For refined resolution and smallest viscosity the model will predict flows in which the shed eddies are coherent structures with closed streamlines.

The model suggests a mechanism by which topographically generated eddies may be swept away from a seamount in the ocean.  相似文献   

5.
Abstract

We study a class of vortex dipoles consisting of two patches of uniform potential vorticity in an otherwise quiescent flow on a β-plane. Steadily propagating solutions that are desingularised analogues of point vortex dipoles are found and compared with the point vortex solutions. Like the point vortex dipoles, both rapidly and slowly propagating solutions exist. Numerical simulations show that the slow solutions are unstable and break up under the influence of weak external perturbations. The fast solutions are more robust. The minimum dipole strength necessary for the existence of a steadily propagating solution is less than that found for point vortex dipoles.  相似文献   

6.
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7.
ABSTRACT

Reservoirs are of necessity always built on the basis of incomplete hydrological information which introduces uncertainty into their design and operation. Since the advent of the electronic digital computer attempts have been made to reduce the uncertainty in hydrological design and reservoir management by the use of synthetic hydrology and simulation. It has been found by simulation that the expected benefits from a proposed reservoir system are often a function of the stochastic process selected for the synthetic hydrology, as well as depending upon the magnitude, and choice of driving parameters (commonly, the mean, variance, lag one serial correlation and Hurst's ‘h’). It is suggested that hydrological records are often two short and most statistical tests too weak for the hydrologist to be able to pick ‘the correct’ synthetic hydrological world with any reasonable degree of certainty. However, it would appear that for many problems and places that there is sufficient hydrological data for the hydrologist to assign probabilities to various prior distributions, and to optimize reservoir management and design by Bayesian decision theory.  相似文献   

8.
Abstract

Accretion discs in astrophysics are fundamental for converting gravitational binding energy into observed electromagnetic radiation. We study the behavior of waves in a two dimensional supersonic Keplerian flow inside a given gravitational potential. We present the effects of shearing and rotation on short waves, and the numerical study of the dynamical stability of such flows with respect to various perturbations. We show that a large class of dynamical effects, due to pressure and associated to short time scales, may be excited.  相似文献   

9.
Turbulent magnetofluids appear in various geophysical and astrophysical contexts, in phenomena associated with planets, stars, galaxies and the universe itself. In many cases, large-scale magnetic fields are observed, though a better knowledge of magnetofluid turbulence is needed to more fully understand the dynamo processes that produce them. One approach is to develop the statistical mechanics of ideal (i.e. non-dissipative), incompressible, homogeneous magnetohydrodynamic (MHD) turbulence, known as “absolute equilibrium ensemble” theory, as far as possible by studying model systems with the goal of finding those aspects that survive the introduction of viscosity and resistivity. Here, we review the progress that has been made in this direction. We examine both three-dimensional (3-D) and two-dimensional (2-D) model systems based on discrete Fourier representations. The basic equations are those of incompressible MHD and may include the effects of rotation and/or a mean magnetic field B o. Statistical predictions are that Fourier coefficients of the velocity and magnetic field are zero-mean random variables. However, this is not the case, in general, for we observe non-ergodic behavior in very long time computer simulations of ideal turbulence: low wavenumber Fourier modes that have relatively large means and small standard deviations, i.e. coherent structure. In particular, ergodicity appears strongly broken when B o?=?0 and weakly broken when B o?≠?0. Broken ergodicity in MHD turbulence is explained by an eigenanalysis of modal covariance matrices. This produces a set of modal eigenvalues inversely proportional to the expected energy of their associated eigenvariables. A large disparity in eigenvalues within the same mode (identified by wavevector k ) can occur at low values of wavenumber k?=?| k |, especially when B o?=?0. This disparity breaks the ergodicity of eigenvariables with smallest eigenvalues (largest energies). This leads to coherent structure in models of ideal homogeneous MHD turbulence, which can occur at lowest values of wavenumber k for 3-D cases, and at either lowest or highest k for ideal 2-D magnetofluids. These ideal results appear relevant for unforced, decaying MHD turbulence, so that broken ergodicity effects in MHD turbulence survive dissipation. In comparison, we will also examine ideal hydrodynamic (HD) turbulence, which, in the 3-D case, will be seen to differ fundamentally from ideal MHD turbulence in that coherent structure due to broken ergodicity can only occur at maximum k in numerical simulations. However, a nonzero viscosity eliminates this ideal 3-D HD structure, so that unforced, decaying 3-D HD turbulence is expected to be ergodic. In summary, broken ergodicity in MHD turbulence leads to energetic, large-scale, quasistationary magnetic fields (coherent structures) in numerical models of bounded, turbulent magnetofluids. Thus, broken ergodicity provides a large-scale dynamo mechanism within computer models of homogeneous MHD turbulence. These results may help us to better understand the origin of global magnetic fields in astrophysical and geophysical objects.  相似文献   

10.
The meanders of a baroclinic coastal current in the Northwestern Mediterranean Sea have already been reported in the literature. These meanders can be surrounded by vortices. Such vortices have been observed in the western part of the Gulf of Lions but the location and the mechanism of their formation are poorly documented. In this paper, we use the current measurements of a one-year experiment, which was conducted in the eastern part of the Gulf of Lions to detect and characterize the vortex activity. A vortex detection algorithm based on few velocity data was developed. Current measurements were available at the sea surface (HF radars) and in the water column from 50 to 140 m depth (four current meter moorings). SST images and hydrologic data were also used. Results focus on observations that are coherent 50 m and at the surface. Vortices are anticyclonic, of submesoscale size and present maximal velocities of 30–50 cm/s. The drift speed of the vortices is comparable to but less than the velocity of the Northern Current. These observations enable to estimate the minimum vortex occurrence in this area. The presence of vortex structures is strongly correlated with a specific sequence of wind patterns.  相似文献   

11.
《水文科学杂志》2013,58(4):883-892
Abstract

Contour benches are earthen structures constructed across cultivated slopes, at intervals down the slope, largely used in semi-arid zones. The results of an experiment to monitor water and sediment balance inside a contour bench terrace system are presented. The study site, located in the El-Gouazine watershed (central Tunisia), includes two terraced plots of approximately 3000 m2, one of which was left fallow for several years, while the other was tilled. The characteristics of rainfall—runoff processes and erosion inside both terraced plots during a two-year period (2004–2006) are described. Ploughing reduced runoff by 75%. Erosion was monitored following runoff episodes that produced observable deposits in the bench channel. After ploughing, erosion was reduced by 44% between July 2004 and July 2005 and by 50% between October 2005 and July 2006. However, erosion per millimetre of runoff was about twice as great on the tilled soil as on the fallow. Even though ploughing weakens the soil, it seems to reduce erosion by increasing infiltration. For the studied rain events, ploughing used in combination with contour bench terraces seems to have limited erosion and enhanced the effectiveness of contour bench terrace management.  相似文献   

12.
Abstract

A vortex-tube geometry of the cascade of energy to small-scale eddies, in the inertial range of fully-developed turbulence, is proposed. The model is a special case of the beta model of Frisch, Sulem and Nelkin (1978). We require that the cascade conserve the principal invariants of inviscid, incompressible flow, namely volume, topological knottedness, circulation, and, at discrete times marking the termination of steps in the cascade, energy. The process terminates in a finite time, as in any beta model, leaving behind a self-similar network of “inactive” tubes. We associate a self-similar scaling dimension D with the structure, equal to the Hausdorff dimension of the set of “active” tubes at the termination of the cascade. Because circulation Λ plays a key role in the analysis of the cascade, we refer to these vortex-tube geometries as “gamma models”. The viewpoint throughout is entirely deterministic.

We describe two examples of gamma models. In the ring geometry, an eddy is a vortex ring, and the cascade produces “rings upon rings”, so we allow cutting and fusing of tubes while conserving total helicity. In the preferred helical model, no cutting is needed, and the cascade produces an infinite progression of braided “coils upon coils”. We suggest that latter geometry as a candidate for the topology of a singularity of the inviscid limit of a Navier-Stokes flow, when modeled by discrete vortex tubes.

A crucial ingredient of a gamma model, not explicitly present in a beta model, is the possibility of “splitting” a vortex tube into sub-tubes carrying smaller circulation. We suggest a dynamical basis for this process, as an instability of tubes whose cores violate the Rayleigh criterion.

The parameters describing a gamma model are not uniquely determined by our study, but there is a “simplest” helical gamma model, involving minimal splitting and distortion of tubes. The dimension D of the structure is 13/5, with a scale factor Λ = 2?5/4. This value of D agrees with that suggested by Hentschel and Procaccia (1982), by analogy with established results for certain branched polymers.  相似文献   

13.
Abstract

Various interactions between small numbers (two and four) of baroclinic, geostrophic point vortices in a two-layer system are studied with attention to the qualitative changes in behavior which occur as size of the deformation radius is varied.

A particularly interesting interaction, which illustrates the richness of baroclinic vortex dynamics, is a collision between two hetons. (A heton is a vortex pair in which the constituent vortices have opposite signs and are in opposite layers. The “breadth” of a heton is the distance between its constituent vortices. A translating heton transports heat.) When two hetons, which initially have different breadths, collide, the result is either an exchange of partners, or a “slip-through” collision in which the initial structures are preserved. It is shown here that the outcome is always an exchange, provided the deformation radius is sufficiently small. This strongly contrasts with a collision between pairs of classical, one-layer vortices in which no exchange occurs if the initial ratio of the breadths is sufficiently extreme.

Finally the transport of passive fluid by a translating baroclinic pair is investigated. A pair of vortices in the top layer transports no lower layer fluid if the distance between the vortices is less than 1.72 deformation radii. By contrast, the size of the region trapped by a heton increases without bound as the spacing between the vortices increases.  相似文献   

14.
Abstract

We have used techniques of nonlinear dynamics to compare a special model for the reversals of the Earth's magnetic field with the observational data. Although this model is rather simple, there is no essential difference to the data by means of well-known characteristics, such as correlation function and probability distribution. Applying methods of symbolic dynamics we have found that the considered model is not able to describe the dynamical properties of the observed process. These significant differences are expressed by algorithmic complexity and Renyi information.  相似文献   

15.

We examine the three-dimensional, nonlinear evolution of columnar vortices in a rotating environment. As the initial vorticity distribution, a wavetrain of finite amplitude Kelvin-Helmholtz vortices in shear is employed. Through direct numerical simulation of the Navier-Stokes equations we seek to better understand the process of maturation of the various three-dimensional modes of instability to which such vortical flows are subject, especially those which exist as a consequence of the action of the Coriolis force. In the absence of rotational influence, we thereby demonstrate that the nonlinear evolution of columnar vortices is most strongly controlled by one or the other of two mechanisms. One mechanism of instability is identifiable as a so-called elliptical instability, which promotes the initial bending of vortex tubes in a sinusoidal fashion, while the other is a hyperbolic mode, which is responsible for the development of streamwise vortex streaks in the "braids" between adjacent vortex cores. In the rotating case, anticyclonic vortices are strongly destabilized by weak background rotation, while rapid rotation stabilizes both the cyclones and anticyclones. The strong anticyclones are subject to two distinct forms of instability, namely a Coriolis force modified elliptical instability and an inertial (centrifugal) instability. The former instability is very similar to the nonrotating form of the elliptical instability as it promotes bending of vortex tubes, while the latter instability grows on the edge of the vortex core and generates streaks of vorticity, which surround the vortex core itself. These results of direct numerical simulation fully verify the results of previous linear stability analyses. Taken together, they provide a simple explanation for the broken symmetry that is often observed to be characteristic of the von Karman vortex streets that develop in the atmospheric lee of oceanic islands.  相似文献   

16.

Results from a new series of experiments on the geophysically important issue of spontaneous emission of internal gravity waves during unsteady interactions of vortical structures are presented. Vortex dipoles are a common element of a quasi-two-dimensional turbulent flow. Vortex dipoles perform translational motion and can collide with other vortices. During collision events the flow is unsteady and unbalanced and a further adjustment process associated with these events can therefore result in the spontaneous emission of gravity waves. Our laboratory experiments demonstrate that gravity waves are emitted when two translating vortex dipoles interact (collide) in a layered fluid, in accord with the current theoretical results. The emission was evident both in a two-layer system and in a fluid with a linear distribution of density with depth. The waves were generated during the period of deceleration of the secondary dipoles which constitute a vortex quadrupole emerging immediately after the collision of the primary dipoles.  相似文献   

17.
A new method for classifying mountain morphology, ‘mountain ordering,’ is proposed, and quantitative expressions for various morphological parameters of two ordered mountains in northern Japan were obtained using this method. Mountain order was defined in terms of the closed contour lines on a topographic map. A set of closed, concentric contour lines defines a first-order mountain. Higher-order mountains can be defined as a set of closed contour lines that contain lower-order mountains and that have only one closed contour line for each elevation; they are identified as m + 1th-order mountains, where m represents the order of the enclosed, lower-order mountains. The geomorphometry for a mountain ordered according to this definition permits the identification of systematic relationships between various morphological parameters. The relationships between mountain order and these morphological parameters follow a form similar to that of Horton's laws, and permit the calculation of the ratios of number, area and height; these parameters are sufficient to express the magnitude of a mountain's dissection. The size–frequency distribution for area and height shows self-similarity for ordered mountains, and determines their fractal dimensions. Furthermore, the relationship between area and height, which has the form of a power function, describes the relief structure of ordered mountains. Copyright © 1999 John Wiley & Sons, Ltd.  相似文献   

18.
Abstract

This paper treats the dynamical conditions that obtain when long straight parallel twisted flux tubes in a highly conducting fluid are packed together in a broad array. It is shown that there is generally no hydrostatic equilibrium. In place of equilibrium there is a dynamical nonequilibrium, leading to neutral point reconnection and progressive coalescence of neighboring tubes (with the same sense of twisting), forming tubes of larger diameter and reduced twist. The magnetic energy in the twisting of each tube declines toward zero, dissipated into small-scale motions of the fluid and thence into heat.

The physical implications are numerous. For instance, it has been suggested that the subsurface magnetic field of the sun is composed of close-packed twisted flux tubes. Any such structures are short lived, at best.

The footpoints of the filamentary magnetic fields above bipolar magnetic regions on the sun are continually shuffled and rotated by the convection, so that the fields are composed of twisted rubes. The twisting and mutual wrapping is converted directly into fluid motion and heat by the dynamical nonequilibrium, so that the work done by the convection of the footpoints goes directly into heating the corona above. This theoretical result is the final step, then, in understanding the assertion by Rosner, Tucker, and Valana, and others, that the observed structure of the visible corona implies that it is heated principally by direct dissipation of the supporting magnetic field. It is the dynamical nonequilibrium that causes the dissipation, in spite of the high electrical conductivity. It would appear that any bipolar magnetic field extending upward from a dense convective layer into a tenuous atmosphere automatically produces heating, and a corona of some sort, in the sun or any other convective star.  相似文献   

19.
ABSTRACT

In this paper, we explore for the first time the interactions of the net downward, time-dependent, γ-pumping overlying an imposed layer of magnetic fluid, in a polytropic atmosphere. Our calculations show that an equipartition of energy, between the magnetic and kinetic components, must be reached for buoyancy-driven magnetic structures to rise into the pumping region. However, structures do not rise unhindered, as in a previous investigation. We show that the evolution and other features of the emerging magnetic flux structures are significantly affected by the temporal variation of the γ-pumping. The rate of emerging structures, the strength of magnetic concentrations and the extent to how far magnetic field can travel were all found to depend on the timescale of the γ-pumping.  相似文献   

20.
The research on climate change in polar regions, especially on the role of polar in the global climate system, has gain unprecedented level of interest. It has been the key scientific issue of the International Polar Year program (IPY, 2007―2008). In this paper, we dealt with the debate upon the breakup time of the stratospheric polar vortex in boreal spring. An observational study of the relation between strato- spheric polar vortex breakup and the extra-tropical circulation was performed. The mean breakup date―when the winter westerly at the core of polar jet turns to summer easterly―is about April 10. The breakup time has large interannual variation with a time span of about 2 months. It also has a long-term trend with the 1990s and 2000s witnessing more and more late breakups of polar vortex. Composite of wind speed at the core of polar jet for the extremely early and late breakup years shows that late years have two periods of westerly weakening while early breakup years have only one. The first weakening in the late years happens in middle January with wind speed dropping sharply from more than 40 m s?1 to about 15 m s?1. This is accompanied with anomalous activities of planetary waves in both strato- sphere and troposphere; while the second weakening in the late breaking years is mainly the results of diabatic heating with very weak wave activities. In early breakup years, the transition from westerly to easterly is rapid with wind speed dropping from more than 30 m s?1 to less than ?10 m s?1 within a month. This evolution is associated with a strong bidirectional dynamical coupling of the stratosphere and troposphere. The circulation anomalies at low troposphere are also analyzed in the extremely early and late breakup years. It shows that there are significant differences between the two kinds of extreme years in the geopotential height and temperature composite analysis, indicating the dynamical cou- pling of stratosphere and troposphere with the evolution of stratospheric polar vortex.  相似文献   

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