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1.
Recently, prominent jet-like features of the ocean circulation, called striations, with a meridional scale of O(300–500 ;km) and extending for thousands of kilometers in length, have been detected in satellite and in situ observations and in high-resolution numerical models. In this paper, we study quasi-stationary striations, which are best seen in the multi-year time-averaged velocity fields. Using 1993–2002 mean dynamic ocean topography, satellite altimeter observations, and output of the Ocean General Circulation Model for the Earth Simulator, the dynamics of the quasi-stationary striations in the eastern parts of the subtropical North and South Pacific are examined by assessing individual terms in the time-averaged equations of relative and potential vorticity. While non-linear effects are found to be essential in the dynamics of the striations, rejecting some linear hypotheses forwarded in the earlier studies, the relevance of the Rhines mechanism is not confirmed. Eddy flux does not act as a relative vorticity source for the striations. Using the potential vorticity (PV) diagnostics, we show that the time-mean PV is not conserved along the time-mean streamlines, and on the scale of the striations these changes in PV are largely induced by the eddy flux of layer thickness. The fact that eddy fluxes contribute to the striations’ time-mean PV budget suggests that the striations are not a kinematical artifact of time-averaging of westward-propagating eddies.  相似文献   

2.
Second order potential vorticity and its potential applications   总被引：1，自引：0，他引：1  
A new invariant, the second order potential vorticity (SPV), is derived in this paper. SPV is the dot product of vorticity and the potential vorticity (PV) gradient, and is proven conservative for a compressible, adiabatic and frictionless atmosphere. Research shows that the new invariant may be used to indicate the evolution of PV, because SPV includes all the information that determines PV evolution: the wind field, and the PV gradient. Furthermore, SPV is capable of diagnosing heavy precipitation because of the strong signals it presents in areas of heavy rainfall. SPV also shows great potential as a comprehensive conserved quantity for indicating the dynamical tropopause and baroclinic instability.  相似文献   

3.
Abstract

Applying a mixing-length calculation to potential vorticity rather than to momentum a new type of lateral friction appears in the oceanic mass transport equations. This friction is evaluated for the special case of horizontally homogeneous, quasi-geostrophic turbulence. The main effect is a westward force arising from the so-called β-term. This produces an additional southward interior transport and a strengthening of the western boundary current. A turbulent exchange coefficient KH = 108 em2s?1 is sufficient to give a Gulf Stream transport twice that obtained by the classical Sverdrup model.  相似文献   

4.
Abstract

The equations for a relativistic perfect fluid result from the requirement that the total mass-energy be stationary with respect to variations δxα(a, b, c, s) in the space-time location of the fluid particle identified by Lagrangian labels (a, b, c) at the point s on its world-line. By considering variations of the Lagrangian labels that leave the specific volume and entropy unchanged, we obtain a general covariant statement of vorticity conservation. The conservation laws for circulation, potential vorticity, and helicity are simple corollaries. This Noether-theorem derivation shows that the vorticity laws have no analogues in particle mechanics, where the corresponding particle labels cannot be continuously vaned.  相似文献   

5.
Abstract

The acceptability of zero potential vorticity models as approximations for natural systems of small, but finite, potential vorticity is studied for bounded frontal flows of arbitrary profile. It is demonstrated that all (infinitely) long-wave solutions of the zero potential vorticity front are asymptotic limits for some (not necessarily long-wave) solutions of the small potential vorticity front. In contrast, for downstream-varying solutions there is no simple way of demonstrating this property. These findings suggest that the use of zero potential vorticity models should be carefully examined in other, non-frontal, problems as well. Finally we show that the longwave solutions of the zero potential vorticity flow are at most neutral (quasi-stable).  相似文献   

6.
Abstract

Vorticity, although not the primary variable of fluid dynamics, is an important derived variable playing both mathematical and physical roles in the solution and understanding of problems. The following treatment discusses the generation of vorticity at rigid boundaries and its subsequent decay. It is intended to provide a consistent and very broadly applicable framework within which a wide range of questions can be answered explicitly. The rate of generation of vorticity is shown to be the relative tangential acceleration of fluid and boundary without taking viscosity into account and the generating mechanism therefore involves the tangential pressure gradient within the fluid and the external acceleration of the boundary only. The mechanism is inviscid in nature and independent of the no-slip condition at the boundary, although viscous diffusion acts immediately after generation to spread vorticity outward from boundaries. Vorticity diffuses neither out of boundaries nor into them, and the only means of decay is by cross-diffusive annihilation within the fluid.  相似文献   

7.
Abstract

We consider the mixing of passive tracers and vorticity by temporally fluctuating large scale flows in two dimensions. In analyzing this problem, we employ modern developments stemming from properties of Hamiltonian chaos in the particle trajectories; these developments generally come under the heading “chaotic advection” or “Lagrangian turbulence.” A review of the salient properties of this kind of mixing, and the mathematics used to analyze it, is presented in the context of passive tracer mixing by a vacillating barotropic Rossby wave. We then take up the characterization of subtler aspects of the mixing. It is shown the chaotic advection produces very nonlocal mixing which cannot be represented by eddy diffusivity. Also, the power spectrum of the tracer field is found to be k ? l at shortwaves—precisely as for mixing by homogeneous, isotropic two dimensional turbulence,—even though the physics of the present case is very different. We have produced two independent arguments accounting for this behavior.

We then examine integrations of the unforced barotropic vorticity equation with initial conditions chosen to give a large scale streamline geometry similar to that analyzed in the passive case. It is found that vorticity mixing proceeds along lines similar to passive tracer mixing. Broad regions of homogenized vorticity ultimately surround the separatrices of the large scale streamline pattern, with vorticity gradients limited to nonchaotic regions (regions of tori) in the corresponding passive problem.

Vorticity in the chaotic zone takes the form of an arrangement of strands which become progressively finer in scale and progressively more densely packed; this process transfers enstrophy to small scales. Although the enstrophy cascade is entirely controlled by the large scale wave, the shortwave enstrophy spectrum ultimately takes on the classical k ? l form. If one accepts that the enstrophy cascade is indeed mediated by chaotic advection, this is the expected behavior. The extreme form of nonlocality (in wavenumber space) manifest in this example casts some doubt on the traditional picture of enstrophy cascade in the Atmosphere, which is based on homogeneous two dimensional turbulence theory. We advance the conjecture that these transfers are in large measure attributable to large scale, low frequency, planetary waves.

Upscale energy transfers amplifying the large scale wave do indeed occur in the course of the above-described process. However, the energy transfer is complete long before vorticity mixing has gotten very far, and therefore has little to do with chaotic advection. In this sense, the vorticity involved in the enstrophy cascade is “fossil vorticity,” which has already given up its energy to the large scale.

We conclude with some speculations concerning statistical mechanics of two dimensional flow, prompted by our finding that flows with identical initial energy and enstrophy can culminate in very different final states. We also outline prospects for further applications of chaotic mixing in atmospheric problems.  相似文献   

8.
Summary It is shown that the general nonlinear potential vorticity equation for viscous and conductive fluid in a rotating system can be expressed in terms of the geostrophic stream function for the horizontal velocity alone, provided that the motions are hydrostatic and quasi-geostrophic and the Richardson number is much larger than unity. The form of this equation is identical with that obtained from an asymptotic expansion for a small Rossby number.  相似文献   

9.
Summary A simple equation showing the influence of orography on the local change of vorticity is obtained on the basis of the complete vorticity equation. The real velocity is divided into two components: one produced by ascending over the mountain and the other independent of the orography. The component of the velocity induced by the obstacle is given by a model. This idea is applied to the south-western air-stream ascending over the Alps and positive local change of vorticity is obtaied over the Gulf of Genoa. In that way the decrease of pressure and the generation of cyclonic circulation in the Gulf of Genoa, which begins before the cold air comes over Mediterranean, can be explained.  相似文献   

10.
We present a new development in fluid theory, incorporating into it the velocity and spin fields; special attention is given to the structure of transport.The theory includes asymmetric molecular stresses and independent rotation velocity, i.e., spin. Our approach is based on our former studies on the asymmetric continuum theory with the balance and constitutive laws for displacement velocity and independent rotation motion, and points out the role of a related characteristic length unit. It is assumed that the vorticity caused by velocities can induce a spin transport counterpart. Thus, under certain conditions, an additional transport term due to rotational velocity fields may be incorporated to the velocity transport, which may lead to the vortex fields included directly into the theory.  相似文献   

11.
We employ time sequences of images observed with a G-band filter (λ4305Å) by the Solar Optical Telescope (SOT) on board of Hinode spacecraft at different latitude along solar central meridian to study vorticity of granular flows in quiet Sun areas during deep minimum of solar activity. Using a feature correlation tracking (FCT) technique, we calculate the vorticity of granular-scale flows. Assuming the known pattern of vertical flows (upward in granules and downward in intergranular lanes), we infer the sign of kinetic helicity of these flows. We show that the kinetic helicity of granular flows and intergranular vortices exhibits a weak hemispheric preference, which is in agreement with the action of the Coriolis force. This slight hemispheric sign asymmetry, however, is not statistically significant given large scatter in the average vorticity. The sign of the current helicity density of network magnetic fields computed using full disk vector magnetograms from the Synoptic Optical Long-term Investigations of the Sun (SOLIS) does not show any hemispheric preference. The combination of these two findings suggests that the photospheric dynamo operating on the scale of granular flows is non-helical in nature.  相似文献   

12.
Shielded vortices consist of a core of potential vorticity (PV) of a given sign surrounded (or shielded) by a layer of opposite-signed PV. Such vortices have specific properties and have been the focus of numerous studies, first in two dimensional geometries (where PV is just the vertical component of the vorticity vector) and in geophysical applications (mostly in layered models). The present paper focuses on three-dimensional, spheroidal shielded vortices. In particular, we focus on vortical structures whose overall volume-integrated PV is zero. We restrict attention to vortices of piecewise uniform PV in the present research. We first revisit the problem within the quasi-geostrophic model, then we extend the results to the non-hydrostatic regime. We show that the stability of the structure depends on the ratio of PV between the inner core and the outer shield. In particular it depends on the polarity of the core and of the wavenumber of the azimuthal mode perturbed.  相似文献   

13.
Summary The concept of potential vorticity is employed to demonstrate the quintessential interplay of an embient rotation with the forced or free stirring of a fluid.  相似文献   

14.
Summary Drawing on the analysis of the linearized vorticity equation it was proved that a moving cyclonal vortex is capable of initiating the development of a new cyclonal vortex in a baroclinic frontal region, characterized by a reduced vertical stability. A necessary condition for this development is the simultaneous presence of convergence in the friction layer.  相似文献   

15.
The large-scale terms in the vorticity equation are evaluated usingKrishnamurti's (1971a, b) summer mean winds at 200 mb for a global belt from 25°S to 45°N. The production of vorticity by the divergent wind field is found to be imbalanced over all of the tropical and subtropical belt. As a result there is a requirement for a sub-grid scale (space or time) mechanism which removes negative vorticity from the regions of strong divergence (Tibetan and Mexican highlands) and removes positive vorticity from the regions of strong convergence (mid-oceanic troughs) at 200 mb during northern summer at a rate of approximately 4×10–10 sec–2. As suggested byHolton andColton (1972), in regions of strong and persistent convection, such as the Tibetan Plateau, deep cumulus clouds can account for this transport. However, the mechanism for removing positive vorticity in the vicinity of the upper tropospheric mid-oceanic troughs is still an intriguing and open question.On leave-of-absence at the National Science Foundation, Climate Dynamics Research Section.  相似文献   

16.
The problem treated here is the dynamics of a bay where water is driven through its opening periodically in time. The basic equations are expressed in the two horizontal coordinates and time and they are obtained by an integration of the Navier-Stokes equations in the vertical coordinate. The equations are nonlinear because of the convective terms in the acceleration. The problem of harbor dynamics provides a natural parameter as the ratio of mass of water entering the bay through the waves to the total mass of water in the bay. This small parameter multiplies the nonlinear terms and thus the problem is ideally suited for a perturbation analysis. The nonlinear terms are responsible for the generation of secondary flows and are particularly important near resonant frequences. The analysis further indicates the existence of a time independent flow analogous to acoustic streaming, known from solutions of the Navier-Stokes equations. The question of vorticity is studied and is seen that: a constant dissipation coefficient precludes the generation of vorticity even for the nonlinear case: and that only a weak (second order) vorticity can exist in the case of a variable dissipation term expressed through the Chezy coefficient. The study suggests also a semi analytic-numerical scheme with savings of 0(102) for irregular geometries through the separation of the various order harmonics as opposed to the usual integration in time.  相似文献   

17.
A diagnostie method of cumulus parameterization is suggested in which vertical transport of horizontal momentum by cumulus-scale is derived by making use of large-scale vorticity as well as divergence budget equations. Data for composite monsoon depression over India available from our earlier studies used to test the method. As a first approximation, the results are obtained using only the vorticity budget equation.The results show that in the southwest sector of the monsoon depression, which is characterized by maximum cloudiness and precipitation, there is an excess of cyclonic vorticity in the lower troposphere and anticyclonic vorticity in the upper troposphere associated with the large-scale motion. The distribution of eddy vertical transport of horizontal momentum is such that anticyclonic vorticity is generated in the lower troposphere and cyclonic vorticity aloft. Cumulus-scale eddies thus work against the large-scale system and tend to off-set the large-scale imbalance in vorticity.  相似文献   

18.
Abstract

Laboratory experiments and analysis of shallow water equations in a rotating fluid show that channel flow is governed by the ratio of the width of the channel to the Rossby radius of deformation R= √[g&Delta;ρH/ρf 2]. Flows through narrow ocean openings exhibit blocking and clear evidence of hydraulic control. These imply that formulae can be derived for width, volume flux, and velocity scales of the currents. A new version of the constant potential vorticity problem is solved, and it is shown to predict volume flux within 22% of the zero potential vorticity results. Next a systematic method of predicting volume flux through ocean passages is described. Some examples are given from the Denmark Straits overflow and the flow of Antarctic Bottom Water into the western Atlantic Ocean. Two-layer flows and counter-flows with rotation in a narrow passage, the so-called lock exchange flow problem, duplicate flows at a number of important straits and openings to bays. A potential vorticity formulation is reviewed. The flows in the mouths of various bays such as Funka Bay in Hokkaido, Japan, Spencer Gulf in South Australia, and Chesapeake Bay in the United States has R < width of the mouth, and the two currents are separated by a front. The width of the front and the density difference can be predicted with good results.  相似文献   

19.
Before data from satellites can be used with confidence in dynamical studies of the middle atmosphere an assessment of their reliability is necessary. To this end, independently analysed data from different instruments may be compared. In this paper, this is done for the Southern Hemisphere as a prelude to the dynamical studies of the middle atmosphere being fostered by the MASH project of the Middle Atmosphere Program. Data from two infrared radiometers are used: a limb scanner (LIMS) and a nadir sounder (SSU). While there is usually qualitative agreement between basic fields (temperatures, winds), substantial quantitative differences are found, with more pronounced differences in fields of Eliassen-Palm flux divergence and Ertel's potential vorticity.The fidelity of the base-level analysis to which satellite data are tied is important for calculating quantities of relevance to dynamical theory. In the Southern Hemisphere, conventional data are sparse and, through the analysis procedure, this introduces errors into derived fields for the middle atmosphere. The impact of using base-level analyses from different sources is assessed. Large discrepancies are found in fields computed by differentiation.Several techniques are suggested whereby the reliability of fields derived from satellite data may be gauged.  相似文献   

20.
Extreme atmospheric events are intimately related to the statistics of atmospheric turbulent velocities. These, in turn, exhibit multifractal scaling, which is determining the nature of the asymptotic behavior of velocities, and whose parameter evaluation is therefore of great interest currently. We combine singular value decomposition techniques and wavelet transform analysis to generalize the multifractal formalism to vector-valued random fields. The so-called Tensorial Wavelet Transform Modulus Maxima (TWTMM) method is calibrated on synthetic self-similar 2D vector-valued multifractal measures and monofractal 3D vector-valued fractional Brownian fields. We report the results of some application of the TWTMM method to turbulent velocity and vorticity fields generated by direct numerical simulations of the incompressible Navier–Stokes equations. This study reveals the existence of an intimate relationship between the singularity spectra of these two vector fields which are found significantly more intermittent than previously estimated from longitudinal and transverse velocity increment statistics.
Alain ArneodoEmail:
  相似文献   

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