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1.
A series of numerical simulations of steady wave flows in a rotating fluid annulus, subject to internal heating and various thermal boundary conditions, is examined to characterise their structures, energetics and potential vorticity transport properties. The last of these characteristics, together with more conventional scaling considerations, indicate the possibility of applying quasi-geostrophic theory to the interior flow in a formulation similar to the inviscid, adiabatic models of Kuo and White.The analytical model of White, describing finite amplitude, neutral baroclinic eddies and mean flows as illustrations of the Charney-Drazin non-acceleration theorem, is then extended to include uniform diabatic heating and the effects of different forms of lateral shear in the background mean zonal flow. Like the solutions discussed by White, those obtained in the present paper consist of steady, internal jet, mean zonal flows, and baroclinic and barotropic Rossby wave components, all having the same three-dimensional wavenumber. Provided the diabatic heating is proportional to the stratification of the background flow, measured by the square of the Brunt-Vaisälä frequency N, the potential vorticity equation remains homogeneous. All the solutions are then characterised by zero net transfer of potential vorticity despite the possibility of non-zero eddy fluxes of heat or momentum and non-trivial Lorenz energy cycles.A series of particular three-component solutions (which, like some of the solutions discussed by White, do not obey conventional lateral boundary conditions) is examined as possible theoretical analogues of the steady waves observed in the numerical simulations of the laboratory flows, and is found to agree encouragingly well in the spatial variations of their mean flows, eddy stream function (pressure) and eddy fluxes of heat and momentum. Potential vorticity fluxes in the numerical simulations are relatively small (though crucially non-zero), supporting the possible analogy with the analytical model and exposing some limitations of the latter in not accounting for weak dissipation and forcing processes present in the laboratory flows.Further implications of the results are discussed, including possible analogies between the laboratory experiments and certain features in planetary atmospheres and oceans.  相似文献   

2.
From a nonlinear quasi-geostrophic barotropic vorticity equation including frictional dissipation,thermal driving and large topography used by Charney in investigation of the multiple flow equilibria and blocking,using the Serrin-Joseph energy method and the variational principle,we found the nonlinear barotropic stability criteria of the zonal basic flow with the total energy,total enstrophy and their linear combination respectively,and compared the criteria with Charney's results.  相似文献   

3.
The quasi-geostrophic response of a stratified stream incident upon isolated finite amplitude topography on a f-plane is examined in the limit of a Boussinesq, incompressible, inviscid fluid. Compact solutions are derived subject to the following stipulations: uniform upstream velocity and stratification, a circular obstacle and an entirely isentropic/isopycnic lower surface.It is shown that for a semi-infinite flow domain the criterion for Taylor cap formation (i.e., a region of closed streamlines) is . However, for the isentropic lower boundary condition the solutions exist (i.e., have physical validity) only if R0F−1 < 0.5. (Here R0 and F refer to the Rossby and Froude numbers defined respectively in terms of the mountain half-width and height.) Also considered are the modifications both to the flow response and to the foregoing existence criterion that are induced by the introduction of an upstream profile comprising two layers of uniform but different stratification. In addition, the relationship of the derived solutions to the results obtained in previous studies is explored, and in particular an outline is given of the impact of adopting the ‘traditional’ simplified lower boundary condition.  相似文献   

4.
The three-dimensional nonlinear quasi-geostrophic potential vorticity equation is reduced to a linear form in the stream function in spherical coordinates for the permanent wave solutions consisting of zonal wavenumbers from 0 to n and rn vertical components with a given degree n. This equation is solved by treating the coefficient of the Coriolis parameter square in the equation as the eigenvalue both for sinusoidal and hyperbolic variations in vertical direction. It is found that these solutions can represent the observed long term flow patterns at the surface and aloft over the globe closely. In addition, the sinusoidal vertical solutions with large eigenvalue G are trapped in low latitude, and the scales of these trapped modes are longer than 10 deg. lat. even for the top layer of the ocean and hence they are much larger than that given by the equatorial β-plane solutions. Therefore such baroclinic disturb-ances in the ocean can easily interact with those in the atmosphere.Solutions of the shallow water potential vorticity equation are treated in a similar manner but with the effective depth H = RT / g taken as limited within a small range for the atmosphere.The propagation of the flow energy of the wave packet consisting of more than one degree is found to be along the great circle around the globe both for barotropic and for baroclinic flows in the atmosphere.  相似文献   

5.
The second author studied the nonlinear stability of N-layer quasi－geostrophic flow subject to perturbations of parameters and initial data, and established the stability criteria for the flow in question, which involve finding out the lowest eigenvalue of an elliptic boundary value problem.In this paper when the domain is a periodic zonal channel, a formula of the lowest eigenvalue is established, which is useful for further studies and practical applications.  相似文献   

6.
A theory is presented both for spectral energy transfer and for the transfer of spectral components of pseudo-potential enstrophy in a homogeneous quasi-geostrophic turbulent field which is rendered anisotropic by the distortion caused by a random collection of vortices superimposed on the principal motions. The fluid is, thus, subjected to an almost irrotational distortion. The random vortices cause straining effects on turbulent velocity and temperature fluctuations and modify the energy spectrum in the spectral ranges of interest. The strain imposed by the distortion is assumed to be homogeneous. For three-dimensional quasi-geostrophic turbulence that conserves pseudo-potential enstrophy as well as energy, this theory predicts –8/3 and –4 power inertial-range energy spectra.The predictions favourably corroborate the observed spectrum of energy in the atmosphere in the region of hemispheric wave-numbers 10–16 with a –8/3 slope and at higher wave-numbers with –4 slope on a log-log energy-wave-number diagram. The transfer rates of pseudo-potential enstrophy in the range 10n16 and of energy in the rangen>16 are identically zero, while the transfer of energy in the first range is from higher to lower wave-numbers and that of the pseudo-potential enstrophy in the second range is from lower to higher wave-numbers.As compared with the earlier two-dimensional turbulence theory of Kraichnan and the quasigeostrophic turbulence theory of Charney, the present theory predicts more realistic shapes of the energy spectra of atmospheric motions at scales shorter than the baroclinic excitation scales.  相似文献   

7.
Nonlinear permanent form solutions have been found for the barotropic, quasi-geostrophic divergenceless vorticity equation describing large scale, rotating flows over zonal relief. In the linear limit these solutions are topographic Rossby waves. The analytical procedure is an expansion in two small dimensionless parameters, an amplitude parameter (the Rossby number) and the aspect ratio between North-South (cross-relief) and East-West length scales. Permanent form solutions exist when these two parameters, and the related effects of dispersion and nonlinearity, mutually balance. By the same expansion procedure, an analytical linearized stability theory has been formulated which proves the neutral stability of these solutions to infinitesimal, two-dimensional perturbations.  相似文献   

8.
The barotropic, quasi-geostrophic vorticity equation describing large scale, rotating flows over zonal relief supports nonlinear permanent form solutions, namely nonlinear topographic Rossby waves. Through an analytical theory, these solutions have been shown to be neutrally stable to infinitesimal perturbations.Numerical algorithms, which necessarily truncate the infinite number of degrees of freedom of any continuum model to a finite number, are capable of reproducing the numerical equivalent of these form-preserving solutions. Moreover, these numerical solutions are shown to preserve their shape throughout the numerical experiment not only in the limit of small amplitude, but also for high amplitude (Rossby number → O(1)).Through numerical simulation, the stability analysis is carried far beyond the analytical limit of infinitesimal perturbations. The solutions maintain their stability in agreement with the analytical theory, up to perturbations having intensities almost of the same order as the solutions themselves. For higher-amplitude perturbations, the solutions break up and typical turbulent behavior ensues. The passage from wave-like to turbulent behavior, upon surpassing a critical perturbation value, can be observed in the sudden loss of phase locking of the permanent solution Fourier modes.  相似文献   

9.
When a broad ocean current encounters a large-scale topographic feature, standing Rossby wave patterns can be generated. Short Rossby waves with a scale Li = √ Q/β (Q is the speed of the approaching flow; β is the meridional gradient of f) are generated east of the topography. If the zonal scale of the topography, L, is planetary, long standing Rossby waves can be generated west of the topography, when the current has a meridional component. The long waves focus the disturbance zonally and produce alternating regions of intensified or reduced zonal flow. The meridional scale that characterizes these zonal bands is the intermediate scales, L = Li2/3L1/3. When the meridional topographic scale is comparable to L, the amplitude of the long-wave disturbance is dominant. Using multiple-scale methods to exploit the scale gap between the planetary, intermediate and Rossby wave scales, the topographically induced pressure and velocity fields due to a zonal ridge are obtained. When the planetary-scale flow field is directed poleward, a westward counterflow can occur along the poleward flank of the ridge. The meridional scales of these topographically induced flows are comparable to those observed along the Indian-Antarctic Ridge by Callahan (1971).  相似文献   

10.
Measurements of the temperature and zonal velocity fields which develop in a rotating annulus of fluid with an upper surface, differentially heated from the inner to outer cylinder, are described for the lower symmetric regime (small radial temperature differences). The temperature field is essentially conductive for moderate to large rotation rates, Ω (>1.0 sec−1). The zonal velocity field is poorly approximated by the thermal wind equation.Measurements of the transition to waves from the lower symmetric regime at very large rotation rates are presented for positive and negative radial temperature differences. They suggest that the centrifugal buoyancy force and the free surface curvature may be important factors for the lower symmetric-wave transition at large Ω. By varying the stratification of the fluid over a range of 103 independently of the radial temperature difference, ΔrwT, it is conclusively shown that several theories are correct in predicting that the lower symmetric transition is independent of the stratification at small ΔrwT > 0 for large enough Ω.  相似文献   

11.
强迫和耗散作用下大气运动的非线性正压不稳定   总被引：2，自引：0，他引：2  
本文从Charney研究多平衡态的包含摩擦耗散、热力强迫和大地形的非线性准地转正压涡度方程出发,应用Serrin-Joseph的能量方法,利用变分原理,分别用总能景和总位涡拟能导得纬向基流的非线性正压稳定性判据。   相似文献   

12.
Arnol’d’s second nonlinear stability criterion for motions governed by a general multilayer quasi-geostiophic model is established. The model allows arbitrary density jumps and layer thickness, and at the top and the bottom of the fluid, the boundary condition is either free or rigid. The criterion is obtained by the establishment of the upper bounds of disturbance energy and potential enstrophy in terms of the initial disturbance field.  相似文献   

13.
The linear baroclinic instabilities of a basic geostrophic shear flow in a stratified, thermally active ocean are considered, including the β-effect. It is shown that the internal heat production, even if it introduces only minor changes into the geostrophic balance, may deeply modify the stability properties of the stationary solutions. If density, geostrophic basic flow, and heat production are all regarded as arbitrary functions of depth only, and if a linear nonzonal assumption is made about the geostrophic pressure field, it can be shown how the geostrophic equilibrium is altered and how the internal heating affects both the directions of propagation and the growth rates of quasi-geostrophic disturbances. A semicircle theorem valid for every direction of propagation is proved, by generalizing well-known results obtained for adiabatic geostrophic flows.Finally, it is found that the modified instability can be described adequately by a directional Richardson number related to the perturbed stationary geostrophic flow.  相似文献   

14.
The effects of topography on baroclinic wave flows are studied experimentally in a thermally driven rotating annulus of fluid.Fourier analysis and complex principal component (CPC) analysis of the experimental data show that, due to topographic forcing, the flow is bimodal rather than a single mode. Under suitable imposed experimental parameters, near thermal Rossby number ROT = 0.1 and Taylor number Ta = 2.2 × 107, the large-scale topography produces low-frequency oscillation in the flow and rather long-lived flow pattern resembling blocking in the atmospheric cir-culation. The ‘blocking’ phenomenon is caused by the resonance of travelling waves and the quasi-stationary waves forced by topography.The large-scale topography transforms wavenumber-homogeneous flows into wavenumber-dispersed flows, and the dispersed flows possess lower wavenumbers.  相似文献   

15.
摩擦耗散大气中切变流的非线性稳定性   总被引：2，自引：2，他引：2  
陆维松 《气象学报》1989,47(4):412-423
本文从包含摩擦耗散的非线性准地转方程组和包含摩擦耗散与大地形作用的非线性浅水波方程组出发,使用了Serrin-Joseph的能量方法,利用变分原理,分别用总能量和总位涡拟能导得这两个方程组的切变基流的非线性稳定性判据。  相似文献   

16.
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17.
A systematic investigation of the effects of various parametrizations of dissipation, e.g. quadratic and linear frictional drag, harmonic lateral viscosity, and harmonic lateral diffusion on inertial flow over a sill and possible hydraulic control is presented. Rotation effects are ignored and the geometry is assumed to vary only slowly with downstream distance so that the flow may be considered one-dimensional. Results are given both for a single-active layer and for two-active layers with a rigid lid.If the parametrization is only a function of the dependent variables and not of their spatial derivatives, then it may be possible to hydraulically control the flow. A general expression is derived for the possible control point and the two gradients there, which are functions of the slope and possibly of flow rate. Specific energy is irreversibly removed from the flow and non-controlled as well as controlled flows can exhibit significant asymmetry in fluid depth over a sill. The upstream specific energy, and hence depth of the lower layer, of the controlled flow is greater than for an ideal fluid. Frictional effects modify the behaviour of long gravity waves, such that they are dispersive and damped with time. The system will only exhibit hydraulic control if these effects are small.For a viscous single layer of fluid, the gradient in surface elevation is always uniquely defined, so classically defined hydraulic control, as such, cannot exist. However, for values of non-dimensional lateral eddy viscosity coefficient, , where q is the flow rate, there is a narrow band of specific energies centred around that for the control solution in an ideal fluid, Ecrit, for which the surface elevation, h is very asymmetric over the sill; the solutions resemble the inviscid, hydraulically controlled solutions. Outside this range, either the fluid depth tends to zero, or the surface elevation is almost uniform over the sill. A ‘control’-type solution exists which has the conjugate values of the inviscid equation up- and downstream of the sill, where the gradient in fluid depth, and hence the viscous term, is zero. For larger values of AM, the band of specific energies is much wider, and the upstream specific energy of the ‘control’-type solution is much lower than that for an inviscid fluid. Long gravity waves are dispersive and damped with time. There is a short-wave cut-off, k2 > h/(4AM2), above which waves are stationary in the flow. Longer waves, k2 h/(4AM2), are critical if , as for an ideal fluid. If these waves can propagate significant distances, then any observed asymmetry in h will be due to inertial and not to viscous effects. The behaviour of unidirectional, two-layer flow is similar. The governing equation for viscous, two-layer exchange flow is singular, and typically excludes the ‘control’-type solutions found for unidirectional flows.Establishing the existence and behaviour of steady inertial flows in the presence of lateral diffusion between layers is more difficult. It significantly alters the single-layer solutions once the non-dimensional coefficient AH is large, i.e. . The flow rate may become zero on the downslope as all the fluid diffuses into the inert, infinitely deep, overlaying layer. The fluid depth is maintained by reverse flow from downstream. In this case, the depth of the active layer tends to zero downstream for all values of specific energy. For two-layer flow, both unidirectional and exchange, the governing equation is such that the lower-layer flow rate and interfacial height return to their upstream values.Motivation for the study is provided by the increasingly fine spatial resolution achievable in large-scale numerical models of the ocean general circulation, and the question of whether they are capable of simulating some form of hydraulic control. Application to modelling oceanic flows over a sill is discussed.  相似文献   

18.
This paper is an extension of the auther's works (1980,1982,1987).Simple anisotropic distribution of horizontal kinetic energy is assumed,i.e.,the zonal kinetic energy is twice that of the meridional kinetic energy.The large-scale atmospheric motion is considered as that consisting of quasi-horizontal eddies and regular flow.The techniques of quasi-eddy,quasi-steady,quasi-geostrophic and quasi-adiabatic approximations are used in order to get the analytical solutions of the system of equations governing the variation of the zonal mean characteristics.The results show that the zonal mean characteristics of the atmospheric motion are a combination of different periods ranging from a few days to a few weeks depending on the components of Chebyshev polynomials of the sine of the latitude.When more general anisotropy of horizontal kinetic energy is assumed,Gegenbauer polynomials appear instead of Chebyshev polynomials.When the distribution of horizontal kinetic energy is isotropic,the polynomials retrograde to Legendre polynomials.  相似文献   

19.
    
Arnol′d′s second nonlinear stability criterion for motions governed by a general multilayer quasi-geostrophic model is established. The model allows arbitrary density jumps and layer thickness, and at the top and the bottom of the fluid, the boundary condition is either free or rigid. The criterion is obtained by the establishment of the upper bounds of disturbance energy and potential enstrophy in terms of the initial disturbance field. Project supported by the State Education Commission of China Project supported by the National Natural Science Foundation of China and LASG, IAP, the Chinese Academy of Sciences  相似文献   

20.
Laboratory experiments are described which provide insight into the interaction of intermediate depth boundary currents (IDBCs) with interrupted sloping topography. Specifically, they contribute to the debate over meddy formation on the Iberian continental slope. The experiments were performed in a rectilinear rotating tank filled initially with a linearly-stratified fluid. A false bottom sloped away from the side-wall along which the current flowed, and was interrupted by a gap of variable length. The effects of varying gap length and rotation rate on the boundary current were observed.In the first of two sets of experiments, the current flowed above the slope, along the vertical sidewall. In the second, the current flowed along the sloping bottom. In the former, current nose speed was consistent with geostrophic predictions, but decreased in the presence of a gap in the topography. Kelvin wave radiation is postulated as a reason for this. The IDBCs exhibited vortical lateral intrusions at values of the Burger number Bu=(N0/Ω)2 at which counterpart flat-bottom studies had been stable, implying that the sloping topography had a de-stabilising effect. Energy measurements and qualitative observations suggest the intrusions were due to mixed barotropic/baroclinic instabilities, the latter dominating at higher rotation rates.In the second configuration, four distinct flows were observed, distinguished by the deformation radius:gap width ratio RD/G*. For a range of values of RD/G*, attached eddies formed at the upstream end of the gap. They remained at this position, unlike those in similar studies of surface boundary currents (Klinger, 1993). Their persistence and ability to move downstream – salient factors for meddy – formation were greater for a finite gap size than a permanent change from sloping to flat bottom.  相似文献   

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