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1.
Abstract

Unstable waves in a western boundary current are investigated in a full three-dimensional, numerical model. A numerical integration is carried out which traces the evolution of a growing wave on an initially uniform current with vertical shear. As indicated in earlier analytic studies based on simpler 2-layer models (Orlanski, 1969) the current is baroclinically unstable for the observed parameter range of the Gulf Stream.

Large meanders of the jet in the western boundary current are noticeable within 10 days. Finite amplitude effects, which can be investigated by the numerical model, reduce the growth rate of the disturbance by nearly an order of magnitude compared to linear theory. Comparison with observations indicate that the meanders of the Florida Current between Miami and Hatteras are probably baroclinically unstable waves.  相似文献   

2.
We present results of various circulation scenarios for the wind-induced three-dimensional currents in Lake Constance, obtained with the aid of a semi-spectral semi-implicit finite difference code developed in Haidvogel et al. and Wang and Hutter. Internal Kelvin and Poincaré-type oscillations are demonstrated in the numerical results, whose periods depend upon the stratification and the geometry of the basin and agree well with measured data. By solving the eigenvalue problem of the linearized shallow water equations in the two-layered stratified Lake Constance, the interpretation of the oscillations as Kelvin and Poincaré-type waves is corroborated.  相似文献   

3.
Summary Satellite pictures have been utilised to detect mountain waves on the lee of the Andes range. The wavelengths as observed in the pictures from the distribution of clouds in parallel bands lie between 20 and 30 km for the five cases examined. The wavelengths have also been computed theoretically for these cases by an analytical method and a quasi-numerical method, using linearised perturbation equations. Wavelengths so computed are in fairly good agreement with the observed wavelengths, Vertical velocities associated with the waves along the different sectors of the Andes have also been computed. Their maximum values are of the order of 1–5 m sec–1. Also, the quasi-stationary character of the waves, as noticed in some of the pictures, is discussed.  相似文献   

4.
Abstract

This is a study of the influence of bottom topography of an ocean basin on the wind‐driven, barotropic ocean circulation. A detailed investigation is made of the role of vorticity transfer to the ocean bottom in the presence of varying topography. It is shown that the wind‐driven gyre over the topography of the North Atlantic has a transport in the western part of the basin only half of that obtained in an ocean of constant depth.  相似文献   

5.
Abstract

The flow in a mechanically driven thin barotropic rotating fluid system is analysed. The linear theory of Baker and Robinson (1969) is modified and extended into the non-linear regime.

An internal parameter, the “local Rossby number”, is indicative of the onset of nonlinear effects. If this parameter is 0(1) then inertial effects are as important as Coriolis accelerations in the interior of the transport-turning western boundary layer and both of its Ekman layers. The inertial effects in the Ekman layers, ignored in previous explorations of non-linear wind driven oceanic circulation, are retained here and calculated using an approximation of the Oseen type. The circulation problem is reduced to a system of scalar equations in only two independent variables; the system is valid for non-small local Rossby number provided only that the approximate total vorticity is positive.

To complete the solution for small Rossby number a boundary condition for the inertially induced transport is needed. It is found by examining the dynamics controlling this additional transport from the western boundary layer as the transport recirculates through the rest of the ocean basin. The strong constraint of total recirculation within the western boundary layer (zero net inertial transport) is derived.

The calculated primary inertial effects are in agreement with the observations of the laboratory model of Baker and Robinson (1969).

The analysis indicates the extent to which three-dimensional non-linear circulation can be reduced to a two dimensional problem.  相似文献   

6.
Abstract

A fifth-order dispersion relation describing the local stability of a differentially rotating flow against small perturbations is derived. Finite viscosity and conductivity and both vertical (parallel to the rotation axis) and radial gradients in density, temperature and pressure are included. A general form is assumed for the equation of state, although this is not exploited in the paper. A number of special cases are studied: with negligible viscosity and conductivity, it is shown that modes can often be separated into two high frequency (modified acoustic), two intermediate frequency (combined inertial and internal waves) and a low frequency mode. In convectively unstable situations the intermediate frequency modes may be replaced by a damped/growing pair of instablities. Various criteria for mode excitation are given. It is shown that viscosity always inhibits instability at very short wavelengths, while non-zero conductivity may destabilize the flow. At intermediate wavelengths viscosity could also play a destabilizing role. A parameter study of the effects of fluctuations in the conductivity shows that it could cause mode excitation under certain circumstances.  相似文献   

7.

The adjustment of sea surface height (SSH) around the coasts of the Japan/East Sea (JES) and the South China Sea (SCS) basins subjected to extratropical Pacific Oceanic low frequency variability is studied using a Kelvin-planetary wave model and a high resolution numerical model. It is found that the modulation of SSH around the coast of Japan is mainly determined by slow adjustment of planetary waves, which radiate from the west coast of Honshu and Hokkaido due to the coastal Kelvin wave. In contrast, the SSH modulation around the cost of the South China Sea basin is mainly determined by the coastal Kelvin wave, which transfers the anomalous SSH into the SCS via the Luzon Strait and out via the Mindoro Strait. The planetary waves radiating from the west coast of Palawan establish a nearly uniform SSH anomaly in the southern part of the SCS, bounded by an eastward jet at the latitude of the Mindoro Strait. Along the western boundary, SSH anomaly decreases almost linearly toward the south, in accordance with the changing local deformation radius. In these two marginal seas, the mean subtropical Pacific gyre circulation enhances SSH modulation induced by extratropical Pacific low frequency variability. Overall, the SSH adjustment in the JES and the SCS predicted by the analytical model agrees well with the numerical model simulation. Application of this model to interaction between these marginal seas and the open ocean is discussed.  相似文献   

8.
The northern and the southern basin of Lake Lugano, Switzerland, are separated by an artificial dam. The flow of the water is not only influenced by the outflow of the northern basin but also by gravitational oscillations (seiches) of both basins. A longperiodic peak around 100 minutes can be explained by a mathematical model. The interaction of the internal waves is a coupled oscillation with a period of 74 hours.   相似文献   

9.
226Ra profiles have been measured in the western Indian Ocean as part of the 1977–1978 Indian Ocean GEOSECS program. These profiles show a general increase in deep and bottom water Ra concentration from the Circumpolar region to the Arabian Sea. A deep Ra maximum which originates in the Arabian Sea and in the Somali basin at about 3000 m depth spreads southward into the Mascarene basin and remains discernible in the Madagascar and Crozet basins. In the western Indian Ocean, the cold Antarctic Bottom Water spreads northward under the possibly southward-flowing deep water, forming a clear benthic front along the Crozet basin across the Southwest Indian Ridge into the Madagascar and Mascarene basins. The Antarctic Bottom Water continues to spread farther north to the Somali basin through the Amirante Passage at 10°S as a western boundary current. The benthic front and other characteristic features in the western Indian Ocean are quite similar to those observed in the western Pacific where the benthic front as a distinctive feature was first described by Craig et al. [15]. Across the Mid-Indian Ridge toward the Ceylon abyssal plain near the triple junction, Ra profiles display a layered structure, reflecting the topographic effect of the mid-ocean ridge system on the mixing and circulation of the deep and bottom waters. Both Ra and Si show a deep maximum north of the Madagascar basin. Linear relationships between these two elements are observed in the deep and bottom water with slopes increasing northward. This suggests a preferential input of Ra over Si from the bottom sediments of the Arabian Sea and also from the flank sediments of the Somali basin.  相似文献   

10.
Abstract

A simple first order perturbation procedure is used to obtain an equation for divergent planetary waves when the period is much greater than the pendulum day. For unbounded regions the equation is the s2me as one derived by Longuet-Higgins (1965), but in bounded basins it is different. As an example, the eigen frequencies of a rectangular basin are calculated for a number of values of the parameters.

The energy density of planetary waves is also considered with results which correct those of Buchwald (1972) in the case of bounded basins.  相似文献   

11.
T waves (seismic water waves), which were generated by deep-focused earthquakes, have been found by an array of sensitive ocean-bottom seismographic observations depolyed on the western Pacific basin. The points of generation of T waves have been exactly located by use of the accurate velocity of water waves which were known from explosions. The positions obtained are at the bottom of deep-sea trenches; however, the positions are slightly (10–35 km) ocean-side of the trench. T waves have been known to be generated by seismic waves which were transmitted from the focus to the trench bottom along the descending lithosphere. The intensity of the observed T waves implies that the Q value along the descending lithosphere is more than 4000. The positions of T-wave generation are consistent with the 8.2- to 8.6-km/s stratified structure of the oceanic lithosphere. T waves from shallow earthquakes beneath the lower continental slope are also clearly observed by bottom seismography.  相似文献   

12.
The present article displays the results of theoretical investigation of the planetary ultra-low-frequency (ULF) electromagnetic wave structure, generation and propagation dynamics in the dissipative ionosphere. These waves are stipulated by a spatial inhomogeneous geomagnetic field. The waves propagate in different ionospheric layers along the parallels to the east as well as to the west and their frequencies vary in the range of (10–10−6) s−1 with a wavelength of order 103 km. The fast disturbances are associated with oscillations of the ionospheric electrons frozen in the geomagnetic field. The large-scale waves are weakly damped. They generate the geomagnetic field adding up to several tens of nanotesla (nT) near the Earth's surface. It is prescribed that the planetary ULF electromagnetic waves preceding their nonlinear interaction with the local shear winds can self-localize in the form of nonlinear long-living solitary vortices, moving along the latitude circles westward as well as eastward with a velocity different from the phase velocity of the corresponding linear waves. The vortex structures transfer the trapped particles of medium, as well as energy and heat. That is why such nonlinear vortex structures can be the structural elements of the ionospheric strong macro-turbulences.  相似文献   

13.
The southwestern (SW) coast of Africa (Namibia and Angola) features long sandy beaches and a wave climate dominated by energetic swells from the Southsouthwest (SSW), therefore approaching the coast with a very high obliquity. Satellite images reveal that along that coast there are many shoreline sand waves with wavelengths ranging from 2 to 8 km. A more detailed study, including a Fourier analysis of the shoreline position, yields the wavelengths (among this range) with the highest spectral density concentration. Also, it becomes apparent that at least some of the sand waves are dynamically active rather than being controlled by the geological setting. A morphodynamic model is used to test the hypothesis that these sand waves could emerge as free morphodynamic instabilities of the coastline due to the obliquity in wave incidence. It is found that the period of the incident water waves, Tp, is crucial to establish the tendency to stability or instability, instability increasing for decreasing period, whilst there is some discrepancy in the observed periods. Model results for Tp = 7–8 s clearly show the tendency for the coast to develop free sand waves at about 4 km wavelength within a few years, which migrate to the north at rates of 0.2–0.6 km yr?1. For larger Tp or steeper profiles, the coast is stable but sand waves originated by other mechanisms can propagate downdrift with little decay.  相似文献   

14.
Summary The time-dependent primitive equations for a shallow homogeneous ocean with a free surface are solved for a bounded basin on the sphere, driven by a steady zonal wind stress and subject to lateral viscous dissipation. These are the vertically integrated equations for a free-surface model, and are integrated to 60 days from an initial state of rest by an explicit centered-difference method with zero-slip lateral boundary conditions. In a series of comparative numerical solutions it is shown that at least a 2-deg resolution is needed to resolve the western boundary currents adequately and to avoid undue distortion of the transient (Rossby waves. The -plane formulation is shown to be an adequate approximation for the mean circulation in the lower and middle latitudes, but noticeably intensifies the transports poleward of about 50 deg and both slows and distorts the transients in the central basin. The influence of the (southern) zonal boundary on the transport solutions is confined to the southernmost gyre, except in the region of the western boundary currents where its influence spreads to the northern edge of the basin by 30 days. The total boundary current transport is shown to be approximately proportional to the zonal width of the basin and independent of the basin's (uniform) depth, while the elevation of the free water surface is inversely proportional to the basin depth, in accordance with linear theory. The introduction of bottom friction has a marked damping effect on the transient Rossby waves, and also reduces the maximum boundary-current transport. The solutions throughout are approximately geostrophic and are only slightly nonlinear.The root-mean-square (rms) transport variability during the period 30 to 60 days is concentrated in the southwest portion of the basin through the reflection of the transient Rossby waves from the western shore and has a maximum corresponding to an rms current variability of about 3 cm sec–1. The transport variabilities are about 10 percent of the mean zonal transport and more than 100 percent of the mean meridional transport over a considerable region of the western basin (outside the western boundary current regime). Some 99 percent of the total kinetic energy is associated with the zonal mean and standing zonal waves, which are also responsible for the bulk of the meridional transport of zonal angular momentum. Although the transient Rossby waves systematically produce a momentum flux convergence at the latitude of the maximum eastward current, much in the manner of their atmospheric counterparts, this is only a relatively small contribution to the zonal oceanic momentum balance; the bulk of the mean zonal stress is here balanced by a nearly stationary net pressure torque exerted against the meridional boundaries by the wind-raised water. In an ocean without such boundaries the role of the transient circulations may be somewhat more important.  相似文献   

15.
Abstract

In order to show that aperiodic magnetic cycles, with Maunder minima, can occur naturally in nonlinear hydromagnetic dynamos, we have investigated a simple nonlinear model of an oscillatory stellar dynamo. The parametrized mean field equations in plane geometry have a Hopf bifurcation when the dynamo number D=1, leading to Parker's dynamo waves. Including the nonlinear interaction between the magnetic field and the velocity shear results in a system of seven coupled nonlinear differential equations. For D>1 there is an exact nonlinear solution, corresponding to periodic dynamo waves. In the regime described by a fifth order system of equations this solution remains stable for all D and the velocity shear is progressively reduced by the Lorentz force. In a regime described by a sixth order system, the solution becomes unstable and successive transitions lead to chaotic behaviour. Oscillations are aperiodic and modulated to give episodes of reduced activity.  相似文献   

16.

Thermal instabilities in the form of oscillatory magnetoconvection representing diffusively modified Alfvén waves in an electrically-conducting Bénard fluid layer of rigid walls in the presence of a vertical magnetic field are investigated. Emphasis of the article is on the transition from a nearly undamped Alfvén wave to diffusively modified Alfvén waves, and on the effect of physically realisable magnetic field boundary conditions on magnetoconvection. It is found that the extra magnetic dissipation in the magnetic Hartmann boundary layers can enhance oscillatory magnetoconvection in the form of strongly modified Alfvén waves. Oscillatory magnetoconvection produced solely by the Alfvén wave mechanism can be the most unstable mode even in the presence of a strong viscous effect. This article also represents the first study on the effect of an electrically conducting wall on magnetoconvection which is associated with a nonlinear eigenvalue problem. We find that the electrically perfectly conducting condition does not yield a good approximation for magnetoconvection with an electrically highly conducting wall. The size of oscillation frequency with an electrically highly conducting wall can be more than a factor of 2 larger than that obtained using the perfectly conducting condition.  相似文献   

17.
v--vThe phenomenon of "Lg blockage," where Lg is strongly attenuated by crustal heterogeneities, poses a serious problem to CTBT monitoring because Lg is an important seismic phase for discrimination. This paper examines blockage in three continental regions where the Lg blockages may be caused by large, enclosed sedimentary basins along the propagation path. The Barents Sea Basin blocks Lg propagation across the Barents Sea from the Russian nuclear test sites at Novaya Zemlya to Scandinavian stations. Also, "early Lg" waves are observed in Sn codas on NORSAR, NORESS, and ARCESS recordings of Novaya Zemlya explosions where direct Lg is blocked. Early Lg waves may have resulted from Sn-to-Lg mode conversion at the contact between the Barents Basin and the Kola Peninsula. The Northern and Southern Caspian Sea Basins also block Lg waves from PNEs and earthquakes, perhaps due to thick, low-velocity, low-Q sediments replacing the granitic layer rocks in the crust. Lg blockage has also been observed in the Western Mediterranean/Levantine Basin due to low-Q sediments and crustal thinning. A "basin capture" model is proposed to explain Lg blockage in sedimentary basins. In this model, shear waves that reverberate in the crust and constitute the Lg wave train are captured, delayed, and attenuated by thick, low-velocity sediments that replace the "granitic" layer rocks of the upper crust along part of the propagation path. Sn waves, which propagate below the basin, would not be blocked and in fact, the blocked Lg waves may be diverted downward into Sn waves by the low velocity sediments in the basin.  相似文献   

18.
Abstract

It is found that in a rotating stratified fluid bounded by a single rigid wall, edge waves may occur at all frequencies less than or equal to N sin a (a is the angle of the wall from the horizontal and N the Brunt‐Vaisala frequency). These decay exponentially away from the boundary, in a distance of O(S) wavelengths, for α = O(1), or O(S ‐1) wavelengths, for αS ≤ O(1), where S is the ratio of N to the Coriolis parameter f, taken for illustration to be large. The phase and energy both move with a component to the left, facing shallow water. The waves could, for example, appear as an internal tide at the continental rise or as baroclinic meandering of currents over a slope.

The low‐frequency limit, αS ? 1, is studied in detail. To allow for large scales of motion other rigid boundaries and variations in f are included. The edge (actually “bottom") waves then merge with topographic‐planetary waves as the wavelengths increase; the familiar depth‐independent mode is found to be possible in the sea for wavelengths exceeding about 450 km. The ß‐effect introduces modes complementary to that trapped at the bottom, which instead are isolated from it.  相似文献   

19.
Summary From numerical solutions of a wind-driven homogeneous ocean model, anegative lateral eddy viscosity of the order 104 cm2 sec–1 is inferred from the large-scale time-dependent currents in the interior of an enclosed shallow basin. The transient Rossby waves in this region produce a systematic convergence of eddy momentum at the latitude of the maximum average eastward current, and thus effect a transfer of zonal momentum from the large-scale eddies to the mean flow. In this sense they are analogous to the Rossby waves in the atmospheric general circulation, and it is speculated that such waves may help to maintain the mean zonal ocean currents. Although this negative viscosity induced by the large-scale transients is relatively small compared with the prescribed lateral viscosity of 108 cm2 sec–1 and should be given a quite different physical interpretation, it is evidently an important viscous effect for the mean flow in the interior of the basin. The prescribed viscosity, on the other hand, is effective in controlling the model's simulated sub-grid scale dissipation, which occurs almost entirely in the nearby steady boundary currents.  相似文献   

20.
In this article we study the linear instability of the two-dimensional strongly stratified model for global MHD in the diffusive solar tachocline. Gilman and Fox [Gilman, P.A. and Fox, P., Joint instability of the latitudinal differential rotation and toroidal magnetic fields below the solar convection zone. Astrophys. J., 1997, 484, 439–454] showed that for ideal MHD, the observed surface differential rotation becomes more unstable than is predicted by Watson's [Watson, M., Shear instability of differential rotation in stars. Geophys. Astrophys. Fluid Dyn., 1981, 16, 285–298] nonmagnetic analysis. They showed that the solar differential rotation is unstable for essentially all reasonable values of the differential rotation in the presence of an antisymmetric toroidal field. They found that for the broad field case B φ～sinθcosθ, θ being the co-latitude, instability occurs only for the azimuthal m?=?1 mode, and concluded that modes which are symmetric (meridional flow in the same direction) about the equator onset at lower field strengths than the antisymmetric modes. We study the effect of viscosity and magnetic diffusivity in the strongly stably stratified case where diffusion is primarily along the level surfaces. We show that antisymmetric modes are now strongly preferred over symmetric modes, and that diffusion can sometimes be destabilising. Even solid body rotation can be destabilised through the action of magnetic field. In addition, we show that when diffusion is present, instability can occur when the longitudinal wavenumber m?=?2.  相似文献   

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