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1.
The characteristics of the disturbances in the atmosphere and oceans and in other stably stratified and rotating fluids are analyzed according to their phase and group velocities. It is shown that both stable stratification and rotation augment the velocity of the sound waves, and that the internal gravity waves and inertial waves are mutually exclusive when the Brunt-Väisälä frequency is different from the Coriolis parameter. It is also shown that both the barotropic and the internal Rossby waves are well separated from the gravity waves and that they can be represented accurately by the quasi-geostrophic potential vorticity equation, even close to the equator, except for the one member withn=0 which is coupled with an eastward propagating gravity wave.  相似文献   

2.
Abstract

A study is made to determine the stability properties of a baroclinic zonal current on which small amplitude three‐dimensional non‐geostrophic disturbances are superimposed. The flow is assumed to be bounded to the north and south by rigid vertical walls and the Rossby number Ro is taken to be small compared to unity. It is then shown that if the perturbation quantities are expanded in power series in Ro the leading or zero order terms in the series correspond to the quasi‐geostrophic solution obtained by Eady (1949) and that the higher order terms represent the “non‐geostrophic” effects neglected by the latter.

It is shown that to the second order in Ro the non‐geostrophic effects decrease the growth rates of those disturbances which are found to be unstable according to Eady's analysis but do not alter their speed of propagation. The results indicate, on the other hand, that to the same order of approximation the stable waves travel at a speed which is different from that given by Eady's solution. The modification of the perturbation wave structure by the non‐geostrophic effects is also investigated. It is found in particular that to the first order in Ro the latter produce a northward tilt with height in the ridge (or trough) lines of the meridional and vertical particle velocity fields away from the lateral boundaries.  相似文献   

3.
Abstract

The generation of stationary Rossby waves by sources of potential vorticity in a westerly flow is examined here in the context of a two-layer, quasi-geostrophic, β-plane model. The response in each layer consists of a combination of a barotropic Rossby wave disturbance that extends far downstream of the source, and a baroclinic disturbance which is evanescent or wave-like in character, depending on the shear and degree of stratification. Contributions from each of these modes in each layer are strongly dependent on the basic flows in each layer; the degree of stratification; and the depths of the two layers. The lower layer response is dominated by an evanescent baroclinic mode when the upper layer westerlies are much larger than those in the lower layer. In this case, weak stationary Rossby waves of large wavelengths are confined to the upper layer and the disturbance in the lower layer is confined to the source region.

Increasing the upper layer flow (with the lower layer flow fixed) increases the Rossby wavelength and decreases the amplitude. Decreasing the lower layer flow (with the upper layer flow fixed) decreases the wavelength and increases the amplitude. Stratification increases the contribution from the barotropic wave-like mode and causes the response to be confined to the lower layer.

The finite amplitude response to westerly flow over two sources of potential vorticity is also considered. In this case stationary Rossby waves induced by both sources interact to reinforce or diminish the downstream wave pattern depending on the separation distance of the sources relative to the Rossby wavelength. For fixed separation distance, enhancement of the downstreatm Rossby waves will only occur for a narrow range of flow variables and stratification.  相似文献   

4.
Zusammenfassung Es wird dargelegt wie man eine beliebig gekrümmte Schichtgrenze aus seismischen Reflexionsmessungen längs einer beliebig gekrümmten Messfläche berechnen kann. Dazu wird vorausgesetzt, dass die Flächez=f(x,y), die die Schichtgrenze darstellt und die Messflächez=(x,y) zusammen eine glatte geschlossene Fläche bilden und, dass das eingeschlossene Material homogen und isotrop ist.
Summary Under the assumption that the measuring surfacez=(x,y) and the reflection horizon of a structurez=f(x,y) have an arbitrary curvature a simple method is developed for calculating the surfacef from seismic reflection data measured along the surface . In addition the general solution is discussed and some special cases are treated.
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5.
Linear Rossby wave dispersion relationships suggest that Jupiter’s Great Red Spot (GRS) is a baroclinic structure embedded in a barotropic shearing zonal flow. Quasi-geostrophic (QG) two-layer simulations support the theory, as long as an infinitely deep zonal flow is assumed. However, once a finite depth of the lower layer is assumed, a self-interaction of the baroclinic eddy component produces a barotropic radiating field, so that the GRS-like eddy can no longer remain compact. Compactness is recovered by explicitly introducing a deep dynamics of the interior for the lower layer, instead of the shallow QG formulation. An implication of the result is a strong coupling of the GRS to a convectively active interior.Paper presented to the NP Symposia of the 1991 Wiesbaden EGS Assembly on “Nonlinear processes in Geophysics”  相似文献   

6.
正压大气模式下,采用摄动方法和时空伸长变换推导了具有β效应、地形效应和耗散的mKdV-Burgers方程,得到Rossby孤立波振幅的演变满足带有β效应,地形与耗散的mKdV-Burgersm方程的结论.说明β效应、地形效应是诱导Rossby孤立波的重要因素.  相似文献   

7.
Geostrophic dynamics in the horizontally differential super-rotation of Venus are examined using fA (the Coriolis parameter defined by the angular velocity of a basic flow in an inertial frame) and Γ (the differential rotation parameter defined by the latitudinal gradient of the angular velocity) under the conditions that vertical shear of the basic field is not considered and the intrinsic phase velocity has a magnitude comparable to that of an eddy horizontal flow. The geostrophic and quasi-geostrophic approximations are valid in the regions of weakly differential and rigid-body super-rotations; however, they are invalid in the regions of strongly differential super-rotation even when the Rossby number R O is sufficiently smaller than unity for synoptic eddies. In a general circulation model of a Venus-like atmosphere, the horizontal divergence that results from the strong differential cannot be ignored over a wide range within latitudes ±60° and below 60?km elevation because of large Γ/fA (≥1/2).  相似文献   

8.
Abstract

Isallobaric effect of a slowly varying quasi-geostrophic flow represented by propagating waves may give rise to a mean steady topographic drag component which turns out to be the principal one when viscous effects are negligibly small. This drag component decreases, in contrast to the quasi-geostrophic component, when statistical properties of the topography become isotropic. When the phase velocity of the incident wave is much larger (smaller) than the phase speed of Rossby waves, the isallobaric drag becomes independent (dependent) on the sign of that velocity.  相似文献   

9.
We discuss the form-drag instability for a quasi-geostrophic channel flow. We first study the characteristics of this instability in a barotropic flow, considering in detail the influence of the meridional scale and discussing which structure of the perturbation zonal flow must be chosen in order to describe properly this instability.We then consider a continuous quasi-geostrophic channel model in which the topography enters only through the bottom boundary condition, and we discuss how in this case the effects of the form-drag are felt by the mean zonal flow through the ageostrophic mean meridional circulation. Because the meridional structure of the perturbation zonal flow cannot simply be extended from the barotropic to the continuous case, we show how to modify it properly.We then study the baroclinic model in the particular case of constant (in the vertical) basic-state zonal flow and show how this case closely resembles the barotropic, demonstrating the barotropic nature of the form-drag instability.Symbols t is the partial derivative with respect tot. - x is the partial derivative with respect tox. - y is the partial derivative with respect toy. - represents the geostrophic stream function. - u is the eastward component of the geostrophic wind. - v is the northward component of the geostrophic wind. - u a is the eastward component of the ageostrophic wind. - v a is the northward component of the ageostrophic wind. - w is the vertical component of the wind. - f is the Coriolis parameter=2 sin f o+y. - f o is the Coriolis parameter evaluated at mid-latitude. - N is the Brunt-Vaisala frequency. - [A] is the zonal (x) average ofA at constantp andy. - <A> is the horizontal (x andy) average ofA at constantp  相似文献   

10.
Depth variable vertical eddy diffusion coefficients for heat (K z) were calculated from continuously measured temperature profiles in Überlinger See (western part of Lake Constance). The temperatures were averaged over vertical intervals of 10 m yielding 14 discrete values (maximum depth of Überlinger See: 147 m). A linear fit from 10 June to 29 September 1987 was used to smooth the significant temperature fluctuations caused by internal seiches of Lake Constance.Assuming horizontal homogeneity for the smoothed data the Gradient-Flux-Method was applied to compute vertical diffusion coefficientsK z at different depths using the depth variable volumes and surfaces of the 14 layers. The resulting mean diffusion coefficients for the period from June to September are 0.04 cm2/s near the thermocline and up to 0.8 cm2/s in deeper strata (accuracy: ± 50%). It is shown that horizontal mixing between Überlinger See and Obersee (main lake) alters the computation ofK z by less than 50%.A relationship betweenK z and stability (Brunt-Väisälä) frequencyN is found which corresponds well to the theory of internal wave induced turbulence.Combining the diffusion coefficients with measured phosphorus profiles, a phosphorus flux from the hypolimnion to the epilimnion of (0.7 ± 0.4) mg P m–2 d–1 was calculated, corresponding to about 20% of the average external loading per area of Lake Constance in 1986.  相似文献   

11.
Large-scale zonal flow driven across submarine topography establishes standing Rossby waves. In the presence of stratification, the wave pattern can be represented by barotropic and baroclinic Rossby waves of mixed planetary topographic nature, which are locked to the topography. In the balance of momentum, the wave pattern manifests itself as topographic formstress. This wave-induced formstress has the net effect of braking the flow and reducing the zonal transport. Locally, it may lead to acceleration, and the parts induced by the barotropic and baroclinic waves may have opposing effects. This flow regime occurs in the circumpolar flow around Antarctica. The different roles that the wave-induced formstress plays in homogeneous and stratified flows through a zonal channel are analyzed with the BARBI (BARotropic-Baroclinic-Interaction ocean model, Olbers and Eden, J Phys Oceanogr 33:2719–2737, 2003) model. It is used in complete form and in a low-order version to clarify the different regimes. It is shown that the barotropic formstress arises by topographic locking due to viscous friction and the baroclinic one due to eddy-induced density advection. For the sinusoidal topography used in this study, the transport obeys a law in which friction and wave-induced formstress act as additive resistances, and windstress, the effect of Ekman pumping on the density stratification, and the buoyancy forcing (diapycnal mixing of the stratified water column) of the potential energy stored in the stratification act as additive forcing functions. The dependence of the resistance on the system parameters (lateral viscosity ε, lateral diffusivity κ of eddy density advection, Rossby radius λ, and topography height δ) as well as the dependence of transport on the forcing functions are determined. While the current intensity in a channel with homogeneous density decreases from the viscous flat bottom case in an inverse quadratic law ~δ –2 with increasing topography height and always depends on ε, a stratified system runs into a saturated state in which the transport becomes independent of δ and ε and is determined by the density diffusivity κ rather than the viscosity: κ/λ 2 acts as a vertical eddy viscosity, and the transport is λ 2/κ times the applied forcing. Critical values for the topographic heights in these regimes are identified.  相似文献   

12.
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   

13.
Abstract

The low Rossby number flow in a rotating cylinder with an inclined bottom, of small slope, is examined when part of the lid of the container is rotating at a slightly different rate. The resulting flow is calculated numerically by solving the governing equations for the two-dimensional geostrophic motion which approximates the flow in most of the fluid including the inertially-modified E ¼ -layers. The presence of ageostrophic regions, on the container walls and beneath the velocity discontinuity on the lid, is accounted for in the governing equations and their boundary conditions. This study supplements previous work on this configuration, in which the zero Rossby number flow was calculated and experimental results were presented, by enabling a direct comparison to be made between the results of the low Rossby number theory and the experiments. The numerical results for a range of Rossby and Ekman numbers compare well with those from the experiments despite a severe limitation on the size of the Rossby number arising from the analysis in the ageostrophic part of the detached shear layer.  相似文献   

14.
The temporal variations in mean zonal wind, horizontal temperature gradient at 30 mb and Total Ozone in Antarctic Spring (1 Sept.–30 Nov.) for nine seasons (1979–1987) were examined. The ozone hole filling commenced when the zonal flow decelerated to 50–58 m.sec–1 at 30 mb. Our calculation of Rossby critical wave number with vertical shear suited for Antarctic Spring indicated that flow is preconditioned for vertical propagation of Rossby critical wave number two at this range of zonal flow. This preconditioning can be attributed to the diabatic heating in the Antarctic Spring since no sudden minor warmings/coolings have occurred during the period.  相似文献   

15.
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   

16.
Abstract

Geostrophic flow in the theory of a shallow rotating fluid is exactly analogous to the drift approximation in a strongly magnetized electrostatic plasma. This analogy is developed and exhibited in detailed to derive equations for the slow nearly geostrophic motion. The key ingredient in the theory is the isolation, to whatever order in Rossby number desired, of the fast motion near the inertial frequency. One of the remaining degrees of freedom represents a new approximate constant of the motion for nearly geostrophic flow. This is the analogue of the familiar magnetic moment adiabatic invariant in the plasma problem.

The procedure is a Rossby number expansion of the Hamiltonian for the fluid expressed in Lagrangian, rather than Eulerian variables. The fundamental Poisson brackets of the theory are not expanded so desirable properties such as energy conservation are maintained throughout.  相似文献   

17.
We examine the equilibrium form, properties, stability and nonlinear evolution of steadily-rotating simply-connected vortex patches in the single-layer quasi-geostrophic model of geophysical fluid dynamics. This model, valid for rotating shallow-water flow in the limit of small Rossby and Froude numbers, has an intrinsic length scale L D called the “Rossby deformation length” relating the strength of the stratification to that of the background rotation. Here, we generate steadily-rotating vortex equilibria for a wide range of γ?=?L/L D , where L is the typical horizontal length scale of the vortex. We vary both γ (over the range 0.02?≤?γ?≤?10) and the vortex aspect ratio λ (over the range 0?<?λ?<?1). We find two modes of instability arising at sufficiently small aspect ratio λ?<?λ c (γ): an asymmetric (dominantly wave 3) mode at small γ (or large L D ) and a symmetric (dominantly wave 4) mode at large γ (or small L D ). At marginal stability, the asymmetric mode dominates for γ???3, while the symmetric mode dominates for γ???3. The nonlinear evolution of weakly-perturbed unstable equilibria results in major structural changes, in most cases producing two dominant vortex patches and thin, quasi-passive filaments. Overall, the nonlinear evolution can be classified into three principal types: (1) vacillations for a limited range of aspect ratios λ when 5?≤?γ?≤?6, (2) filamentation and a single-dominant vortex for γ???1, and (3) vortex splitting – asymmetric for 1???γ???4 and symmetric for γ???4.  相似文献   

18.
The specific features of the amplification and mutual transformation of wave modes in a linear regime have been revealed based on an analysis of the numerical solution to the set of equations describing the interaction of the magnetized Rossby wave and the inertial wave with the spatially inhomogeneous zonal wind (shear flow) in the ionospheric D, E, and F regions. It has been established that the presence of the geomagnetic field and Hall and Pedersen currents in the ionosphere improves the interaction and energy exchange between the waves and shear flow.  相似文献   

19.
Zusammenfassung In nachstehender Untersuchung wird in umfassender Weise gezeigt, wie sich aus der Karte der Vertikalintensität einer lokalen, für sich allein betrachteten Schwerestörung sämtliche anderen Feldgrössen und Ableitungen berechnen lassen. Es ergibt sich dadurch die Möglichkeit, den Verlauf des störenden Kraftfeldes auch unter der Erdoberfläche zu berechnen und aus einem Kraftlinienbild unmittelbar den Aufbau der Inhomogenitäten im Untergrund zu erkennen.
Summary It is shown that the picture of a local anomaly in gravity (U z ) may give the basement of structural calculations to an extend that was not known till now. FromU z all other terms and derivations of the field of gravity are obtainable such asU, U x ,U y ,U zz ,U zzz , etc. The knowledge of these terms enables us to pursue the lines of gravity under the surface and thus to recognise immediately the characterising features of the structure itself.
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20.
Zusammenfassung Beim Erstarren der Erdkruste verwandelten sich dieBenard'sche Wirbelzellen der Schmelze in festeFelder von durchschnittlich 1200–1400 km, als Elementarbausteine aller späteren Grosstektonik. Orogenese bringt diese Felder immer neu in Reihe, so dass ihre Nähte zu erdumspannenden Gebirgs-Systemen zusammenschliessen. Die erste Erstarrung begann am Pol, und schuf, gegen den Aequator fortschreitend, eine Folge von Gebirgsringen, welche, die jeweils schon erstarrte Polkalotte mit W-E-(äquatorialem) Streichen umgeben (Aequatoriden). Die Kontraktion des Kernes fordert Zusammenschub auch in der zweiten Komponente durch Faltenzüge, die meridional verlaufen (Meridiiden). So entstand ursprüglich einorthogonales Muster des Grundgebirgsbaues.Die Konvektionsströmungen der ältesten Orogenesen trifteten die bereits erstarrte Sial-schollen zu einem Haufen über der Verschluckungszone zusammen; ebenso das letzte sauere. Differentiat, das sich in der Ruhezeit unter diesen gebildet hatte, und in das der grösste Teil desU-Th-Gehaltes der Urschmelze übergegangen war. Auch dieses konnte, weil leichter als das basische Substratum, nicht in die Verschluckungszone hinabgezogen werden, sondern wurde über dieser, an der Wurzel des werdenden Faltengebirges zusammengestaut. Dadurch wurdenU undTh, ursprünglich über die Fläche gleichmässig verteilt, zusammengefegt, zuerst durch N-S-Zusammenschub in äquatoriale Streifen. Die folgende Meridiiden-Faltung schob dann diese Streifen W-E zusammen zu Haufen, an die Kreuzungen (Scharungen) von Aequatoriden und Meridiiden, wo dadurch derU-Th-Gehalt des Untergrundes vervielfacht wurde. Diese Anreicherung ist Vorbedingung, dass sich Vorkommen vonU-Th-Mineralen überhaupt bilden können. Tatsächlich liegen alle Vorkommen, die an Abbau nur denken lassen 16 an der Zahl, an diesen Grundgebirgsknoten, ja sogar die Einzelfunde vonU-Th-Mineralen liegen allermeist nah an diesen, damit wohl der Menge nach 99% des greifbaren Vorrates. Im ursprünglichen orthogonalen System der Aequatoriden — Meridiiden sind — auf Festland und ausserhalb der erfahrungsgemäss sterilen jungalpidischen Gebirge — 64 solcherGebirgsknoten gegeben. Von diesen sind 16 einigermassen reichlich mitU-Th-Vorkommen garniert, bei weiteren 14 sind wenigstens etlicheU-Th-Minerale gefunden worden, bei den restlichen 34 nicht einmal das. Da mag z. T. Gelegenheit zur letztenlokalen Konzentration gefehlt haben, z. T. mögen aber dort solche Vorkommen zwar vorhanden sein, aber nochnicht aufgefunden. Unsere Theorie gestattet vorauszusagen, in welchen Gegenden die Suche nach U- und Th-Vorkommen und-Lagerstätten Aussicht auf Erfolg hat.
Summary The outermost layer of the molten Earth has been divided into separate cells of vorticose motion. After the solidification each cell becomes a solid «field», 1200×1400 km in width, as a quadri- or multilateral brick for the following tectonic structures. Orogeny puts the fields in a line and the «geosutures», the walls between the neighbouring fields, consequently form long chains of mountains. The solidification begins at the pole and forms successively circles of mountains surrounding the already solidified Polar Calotte (Equatorides). The contraction of the core connected with the orogeny involves also a shortening in W-E-direction and consequently forms chains of N-S-strike (Meridiides). By the crossing of the Equatorides and the Meridiides results an orthogonal pattern of the Archean basement.The convection currents of the oldest orogenies push together the already solidified sheets of Sial above the «Verschluckungszone» and likeweise the acid fraction already differentiated from the substratum and accumulated under the solidified Sial. This fraction contains the bulk ofU andTh, hoarded up in this manner near the «roots» of the growing mountains. Therefore the content ofU andTh, which formerly has been dispersed over the whole surface, is swept together, at first by the folding of the Equatorides to a narrow strip extending W-E. The following folding of the Meridiides has pushed this strip together to a heap near the crossings of Equatorides and Meridiides, where the content ofU andTh in the subsoil has been enormously multiplied in this manner.This enrichement is an indispensable condition for the development of deposits containingU orTh. It is amatter of fact, and to be observed in the map, that all deposits of economic value (16 in number) are situated near the above mentioned crossings of chains. Even solitary occurrences of minerals containingU andTh are mostly found near these «Gebirgsknoten». In their neighbourhood more than 99% of all the visible ore are concentrated. Sixty four of such crossings of chains are determined by the system of the old Equatorides and Meridiides (exception the young Alpine System which is unproductive in any case). Sixteen of these are planted with considerableU orTh-deposits, someU-Th-minerals are found near the other fourteen. Near the remaining thirty four occurrences ofU andTh are unknown, either by lacking of local concentration, or they are not discovered till now.Our Theory enables us topredicte the territories where some new deposits of Uand Thare to be expected.
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