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1.
Abstract

The instability of a current with a geostrophic surface density front is investigated by means of a reduced gravity model having a velocity profile with nearly uniform potential vorticity. It is shown that currents are unstable when the mean potential vorticity decreases toward the surface front at the critical point of the frontal trapped waves investigated by Paldor (1983). This instability is identical with that demonstrated by Killworth (1983) in the longwave limit.

The cross-stream component of mass flux and the rates of energy conversions among the five energy forms defined by Orlanski (1968) are also calculated. The main results are as follows, (a) The mass flux toward the surface front is positive near the front and negative around the critical point. The positive mass flux near the front does not vanish at the position of the undisturbed surface front, so that the mean position of the front moves outward and the region of the strong current spreads. (b) The potential energy of the mean flow integrated over the fluid is released through the work done by the force of the pressure gradient of the mean flow on the fluid, and is converted into the kinetic energy of the mean flow. (c) In the critical layer, the mean flow is rapidly accelerated with the growth of the unstable wave. This acceleration is caused by the rapid phase shift of the unstable wave in the critical layer.  相似文献   

2.
Abstract

The stability of a single layer, geostrophic front of zero potential vorticity bounded by a vertical coast (wall) is investigated by means of a Rayleigh integral. It is proved that the flow of the density-driven current is stable at all wavenumbers provided the mean velocity of basic flow exceeds fL (where f is the Coriolis parameter and L is the distance between the wall and the free streamline). The frequency of the stable long waves is either zero or super-inertial.  相似文献   

3.
Abstract

The stability of a plane parallel shear flow with the profile U(z) = tanh z is considered in a rotating system with the axis of rotation in the z-direction. The establishment of the basic flow requires a baroclinic state, but baroclinic effects are suppressed in the stability analysis by assuming a limit of high thermal conductivity. It is shown that the strongest growing disturbance changes from a purely transverse form in the limit of vanishing rotation rate to a nearly longitudinal form as the angular velocity of rotation increases. An analytical solution of the stability equation is obtained for vanishing growth rates of the transverse form of the instability. But, in general, the solution of the problem requires numerical integrations which demonstrate that the preferred direction of the wave vector of the instability is towards the left of the direction of the mean flow.  相似文献   

4.
Abstract

Supercritically unstable density fronts near a vertical wall in a rotating, two-layer fluid were created on a laboratory turntable by withdrawing the outer wall of an annulus with a narrow gap, and allowing buoyant fluid from within the annulus to collapse toward a state of quasi-geostrophic balance. The resulting “coastal” current has a nearly uniform potential vorticity and is bounded by a front on which ageostrophic, wave-like disturbances grow. If the current width is comparable to the Rossby radius of deformation, the dominant length scale of disturbances is proportional to the width of the current. On the other hand, if the upper layer is much wider than the Rossby radius, then the observed length scale is a constant multiple of the Rossby radius. If the vertical boundary is omitted in the experiments, so that we are left with a circular anticyclonic vortex, the observed length scales and large-amplitude behaviour of disturbances are identical to those for the boundary currents, indicating that the wall has no significant influence on the flow.

At very large amplitude the growing waves lead to the formation of cyclone-anticyclone vortex pairs. For very wide currents, both the mean flow and the disturbances are first confined to a region within a few Rossby radii of the front. However, both the mean flow and the turbulent eddy motions slowly propagate into the previously stationary upper layer until, eventually, the whole of the upper layer is turbulent.  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

The linear, normal mode instability of barotropic circular vortices with zero circulation is examined in the f-plane quasigeostrophic equations. Equivalents of Rayleigh's and Fjortoft's criteria and the semicircle theorem for parallel shear flow are given, and the energy equation shows the instability to be barotropic. A new result is that the fastest growing perturbation is often an internal instability, having a finite vertical scale, but may also be an external instability, having no vertical structure. For parallel shear flow the fastest growing perturbation is always an external instability; this is Squire's theorem. Whether the fastest growing perturbation is internal or external depends upon the profile: for mean flow streamfunction profiles which monotonically decrease with radius, the instability is internal for less steep profiles with a broad velocity extremum and external for steep profiles with a narrow velocity extremum. Finite amplitude, numerical model calculations show that this linear instability analysis is not valid very far into the finite amplitude range, and that a barotropic vortex, whose fastest growing perturbation is internal, is vertically fragmented by the instability.  相似文献   

7.
Abstract

The long time response to an arbitrary unstable disturbance in a two layer model on an f-plane is sought. It has been found that depending on the ratio of the shear to the average speed of the mean flow two types of baroclinic instabilities exist: convective and absolute. When the system supports convective instabilities the long time response to an initial pulse excitation decreases with time at a fixed point in space. When such a system is excited by a wave maker the steady state frequency of response of the system corresponds to a spatially amplifying wave oscillating with the frequency of the wave maker. If the dispersion relation yields a saddle point of the frequency in the wave number complex plane with positive imaginary part of the frequency the system supports absolute instabilities. The response of the system at any point in space excited by an arbitrary signal grows exponentially with time at a rate determined by the properties of the system at the saddle point. This response is different from that of unstable normal modes. It is conjectured that absolute instability may be responsible for local cyclogenesis activity in certain geographical regions.  相似文献   

8.
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   

9.
The North Pacific Subtropical Counter Current (STCC) is a weak zonal current comprising of a weak eastward flow near the surface (with speeds of less than 0.1 m/s and a thickness of approximately 50–100 m) and westward flow (the North Equatorial Current) beneath. Previous studies (e.g., Qiu J Phys Oceanogr 29: 2471–2486, 1999) have shown that the STCC is baroclinically unstable. Therefore, despite its weak mean speeds, nonlinear STCC eddies with diameters ~300 km or larger and rotational speeds exceeding the eddy propagation speeds develop (Samelson J Phys Oceanogr 27: 2645–2662, 1997; Chelton et al. Prog Oceanogr 91: 167–216, 2011). In this study, the authors present numerical experiments to describe and explain the instability and eddy-generation processes of the STCC and the seasonal variation. Emphasis is on finite-amplitude eddies which are analyzed based on the parameter of Okubo (Deep-Sea Res 17: 445–454, 1970) and Weiss (Physica D 48: 273–294, 1991). The temperature and salinity distribution in March and April offer the favorable condition for eddies to grow, while September and October are unfavorable seasons for the generation of eddies. STCC is maintained not only by subsurface front but also by the sea surface temperature (SST) front. The seasonal variation of the vertical shear is dominated by the seasonal surface STCC velocity. The SST front enhances the instability and lead to the faster growth of STCC eddies in winter and spring. The near-surface processes are therefore crucial for the STCC system.  相似文献   

10.
Abstract

A Rayleigh integral is used to prove that an unbounded geostrophic front of uniform potential vorticity is stable with respect to small perturbations of arbitrary wavelength. The ageostrophic theory developed in this study yields a stable, near-inertial, long trapped mode. Recent oceanic observations of the increase in the energy of the inertial peak in the vicinity of fronts support the existence of this inertial trapped mode. In addition the theory yields a geostrophic mode which is expected to become unstable when the potential vorticity is not uniform.  相似文献   

11.
Abstract

The process of wave steepening in Long's model of steady, two-dimensional stably stratified flow over orography is examined. Under conditions of the long-wave approximation, and constant values of the background static stability and basic flow, Long's equation is cast into the form of a nonlinear advection equation. Spectral properties of this latter equation, which could be useful for the interpretation of data analyses under mountain wave conditions, are presented. The principal features, that apply at the onset of convective instability (density constant with height), are:

i) a power spectrum for available potential energy that exhibits a minus eight-thirds decay, in terms of the vertical wavenumber k z -;

ii) a rate of energy transfer across the spectrum that is inversely proportional to the wavenumber for large k z -;

iii) an equipartition between the kinetic energy of the horizontal motion and the available potential energy, under the longwave approximation, although all the disturbance energy is kinetic at the point where convective instability is initiated. It is also shown that features i) and ii) apply to more general conditions that are appropriate to Long's model, not just the long-wave approximation. Application to fully turbulent flow or to conditions at the onset of shearing instability are not considered to be warranted, since the development only applies to conditions at the onset of convective instability.  相似文献   

12.
Abstract

In part I of this study (Fearn, 1983b), instabilities of a conducting fluid driven by a toroidal magnetic field B were investigated. As well as confirming the results of a local stability analysis by Acheson (1983), a new resistive mode of instability was found. Here we investigate this mode in more detail and show that instability exists when B(s) has a zero at some radius s=s c. Then (in the limit of small resistivity) the instability is concentrated in a critical layer centered on s c . The importance of the region where B is small casts some doubt on the validity of the simplifications made to the momentum equation in I. Calculations were therefore repeated using the full momentum equation. These demonstrate that the neglect of viscous and inertial terms when the mean field is strong does not lead to spurious results even when there are regions where B is small.  相似文献   

13.
ABSTRACT

The instability of ideal non-divergent zonal flows on the sphere is determined numerically by the instability criterion of Arnold (Ann. Inst. Fourier 1966, 16, 319) for the sectional curvature. Zonal flows are unstable for all perturbations besides for a small set which are in approximate resonance. The planetary rotation is stable and the presence of rotation reduces the instability of perturbations.  相似文献   

14.
Abstract

Wetting front instability (fingered flow) accelerates solute transport through the unsaturated zone to the groundwater table. Whether fingers widen or dissipate close to the groundwater is unclear. Water flow in a two-dimensional artificial capillary fringe below a dry layer exhibiting fingered flow was investigated. The flow diverged strongly in the wet soil, suggesting that fingers dissipate. Expressions for the finger radius in dry and wet soil were combined and adapted to a soil hydraulic property parameterization popular in numerical modelling. The modified equation provided finger radii for soils in humid and arid climates. The fingers in the arid soil were excessively wide. The finger radii were used to model solute transport, assuming fingers dissipated in the subsoil. Modelling was cumbersome for the arid climate. One shower may often be insufficient to trigger fingering in arid regions with short, heavy showers. In soils with shallow groundwater, the diverging subsoil flow determines solute leaching.  相似文献   

15.
Abstract

The two-dimensional (horizontal) shear instability of a differentially rotating star is examined. A solar-type rotation law is investigated. and it is found that for equatorial accelerations there is instability when there is a difference of 29% between the angular velocity of the equator and the poles.  相似文献   

16.
Abstract

Experiments have been performed in a cylindrical annulus with horizontal temperature gradients imposed upon the horizontal boundaries and in which the vertical depth was smaller than the width of the annulus. Qualitative observations were made by the use of small, suspended, reflective flakes in the liquid (water).

Four basic regimes of flow were observed: (1) axisymmetric flow, (2) deep cellular convection, (3) boundary layer convective rolls, and (4) baroclinic waves. In some cases there was a mix of baroclinic and convective instabilities present. As a “mean” interior Richardson number was decreased from a value greater than unity to one less than zero, axisymmetric baroclinic instability of the Solberg type was never observed. Rather, the transition was from non-axisymmetric baroclinic waves, to a mix of baroclinic and convective instability, to irregular cellular convection.  相似文献   

17.
Abstract

Saltwater intrusion is a naturally occurring phenomenon that is exacerbated significantly by excessive groundwater exploitation in coastal aquifers. In order to determine the extent of saltwater intrusion in a karstified coastal aquifer in Crete, Greece, a three-dimensional, density-dependent groundwater flow and transport model was developed and compared to the more traditional sharp-interface approach. The karstified medium was modelled using a combination of the equivalent porous medium approach (for lower-order fractures) and a discrete fracture approach (for the main fractures/faults). The model takes into consideration the geomorphologic characteristics of the karstic system, such as the depth and orientation of the fault network, and the diffusion phenomena associated with the variable densities of freshwater and saltwater—parameters that create a complex system, inducing uncertainty in the model. The model results showed that the orientation of the fractures, the pumping activity and the fluid density effects drive the seawater intrusion front asymmetrically inland.

Editor Z.W. Kundzewicz

Citation Dokou, Z. and Karatzas, G.P., 2012. Saltwater intrusion estimation in a karstified coastal system using density-dependent modelling and comparison with the sharp-interface approach. Hydrological Sciences Journal, 57 (5), 985–999.  相似文献   

18.
Two rock samples with different structures and materials were deformed under a biaxial loading system, and multipoint strain measurements were performed for each sample. The distribution of strain anomalies during the deformation and the instability process were analyzed by using C v value put forward by WANG Xiao-qing and CHEN Xue-zhong, et al, a parameter to describe the heterogeneous distribution of earthquake precursors, so as to examine the method of C v value and to explore its physical meaning experimentally. The result shows that the change of C v value is correlated to the change of deformation characteristics and is an effective parameter to describe the heterogeneity of precursor distribution. C v value increases firstly and then decreases before the instability, and the instability occurs when C v value decreases to the level before increasing. This indicates that C v value may be a useful parameter for earthquake prediction. Foundation item: Chinese Joint Earthquake Sciences Foundation (9507435).  相似文献   

19.
《水文科学杂志》2013,58(3):455-472
Abstract

The purpose of this study was to assess the degree of preferential flow in an unsaturated soil column using two different models: the dual-porosity model, MACRO, and the kinematic wave approach (KWA) based on boundary-layer flow theory. The soil column experiments consisted of six infiltrations with intensities varying from 15 to 101 mm h?1. Bromide solution was also infiltrated at an intensity of 79 mm h?1 and a concentration of 80 mg l?1. Both MACRO and the KWA indicated the absence of pure preferential flow. The KWA indicated intermediate flow with dispersion of the wetting front with depth, whereas MACRO indicated flow dominated by the diffusion of capillary potential. These results shed light on the transition between flows dominated by momentum dissipation and by diffusion of capillary potential. The absence of pure macropore flow in the structured sandy soil is mainly due to efficient lateral mass exchange in this material.  相似文献   

20.
Abstract

It is shown that the inclusion of the nonlinear terms in the equations of motion of a coupled density front of zero potential vorticity results in wave solutions which merely propagate with time. The linear theory, on the other hand, predicts an exponential temporal growth. The nonlinear equation admits steady solutions representing standing waves whereas if the nonlinear terms are omitted no steady solutions exist. The general initial value problem is difficult to solve numerically since the linear problem is ill posed.

In addition we prove that the general similarity solution of the nonlinear equation tends to zero for large times, at any point in space, regardless of the initial condition.  相似文献   

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