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1.
P. Caillol 《地球物理与天体物理流体动力学》2015,109(2):111-144
In a previous paper, Caillol [Geophys. Astrophys. Fluid Dyn., 2014, 108] investigated the steady nonlinear vortical structure of a singular vortex Rossby mode that has survived to a strong critical-layer-like interaction with a linearly stable, columnar, axisymmetric and dry vortex. We presented a general theory for this wave/mean flow interaction through the nonlinear critical layer theory and calculated the mean azimuthal and axial winds induced at the critical radius at the end of this interaction in the final stage. We here apply that theory to rapidly rotating geophysical vortices: tropical cyclones, cold-air mesocyclones and tornadoes. We find that the numerous assumptions invoked in that paper agree well with the reality of those intense vortices. We also find that in spite of a lack of moist-convection modelling, this dry vortex is fairly well accelerated at the critical radius by such a shear wave with a magnitude of order the square root of the damped-wave amplitude. The intensification level strongly depends on the aspect ratio, height of the system: rapid vortex and parent vortex, over core radius. The thinner the vortex is, the sharper the intensification is. This result is in sharp contrast to the numerous numerical simulations on VR wave/vortex interactions that yield a much smaller intensification of order the square of the wave amplitude. This weakly nonlinear approach nevertheless fails to model small vertical wavelength VR wave/vortex interactions for their related asymptotic expansions are divergent and for they yield strongly nonlinear VR waves coupled with evolving critical layers whose extent can no longer be considered as thin. 相似文献
2.
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
3.
We examine the three-dimensional, nonlinear evolution of columnar vortices in a rotating environment. As the initial vorticity distribution, a wavetrain of finite amplitude Kelvin-Helmholtz vortices in shear is employed. Through direct numerical simulation of the Navier-Stokes equations we seek to better understand the process of maturation of the various three-dimensional modes of instability to which such vortical flows are subject, especially those which exist as a consequence of the action of the Coriolis force. In the absence of rotational influence, we thereby demonstrate that the nonlinear evolution of columnar vortices is most strongly controlled by one or the other of two mechanisms. One mechanism of instability is identifiable as a so-called elliptical instability, which promotes the initial bending of vortex tubes in a sinusoidal fashion, while the other is a hyperbolic mode, which is responsible for the development of streamwise vortex streaks in the "braids" between adjacent vortex cores. In the rotating case, anticyclonic vortices are strongly destabilized by weak background rotation, while rapid rotation stabilizes both the cyclones and anticyclones. The strong anticyclones are subject to two distinct forms of instability, namely a Coriolis force modified elliptical instability and an inertial (centrifugal) instability. The former instability is very similar to the nonrotating form of the elliptical instability as it promotes bending of vortex tubes, while the latter instability grows on the edge of the vortex core and generates streaks of vorticity, which surround the vortex core itself. These results of direct numerical simulation fully verify the results of previous linear stability analyses. Taken together, they provide a simple explanation for the broken symmetry that is often observed to be characteristic of the von Karman vortex streets that develop in the atmospheric lee of oceanic islands. 相似文献
4.
M. M. Jalali 《地球物理与天体物理流体动力学》2013,107(6):375-401
ABSTRACTHerein we study the general interaction of two vortex patches in a single-layer quasi-geostrophic shallow-water flow. Steadily-rotating equilibrium states are found over a wide parameter space spanning the Rossby deformation length, vortex area ratio, potential vorticity ratio, and gap between their innermost edges. A linear stability analysis is then used to identify the critical gap separating stable and unstable solutions, over the entire range of area and potential vorticity ratios, and for selected values of the Rossby deformation length. A representative set of marginally unstable equilibrium states are then slightly perturbed and evolved by an accurate contour dynamics numerical algorithm to understand the long-term fate of the instabilities. Not all instabilities lead to vortex merger; many in fact are characterised by weak filamentation and a small adjustment of the vortex shapes, without merger. Stronger instabilities lead to material being torn from one vortex and either wrapped around the other or reduced to ever thinning filamentary debris. A portion of the vortex may survive, or it may be completely strained out by the other. 相似文献
5.
Charles A. Lin 《地球物理与天体物理流体动力学》2013,107(4):227-259
Abstract A high vertical resolution model is used to examine the instability of a baroclinic zonal flow and a finite amplitude topographically forced wave. Two families of unstable modes are found, consisting of zonally propagating most unstable modes, and stationary unstable modes. The former have time scale and spatial structure similar to baroclinic synoptic disturbances, but are localized in space due to interaction with the zonally asymmetric forcing. These modes transport heat efficiently in both the zonal and meridional directions. The second family of stationary unstable modes has characteristics of modes of low frequency variability of the atmosphere. They have time scales of 10 days and longer, and are of planetary scale with an equivalent barotropic vertical structure. The horizontal structure resembles blocking flows. They are maintained by available potential energy of the basic wave, and have large zonal heat fluxes. The results for both families of modes are interpreted in terms of an interaction between forcing and baroclinic instability to create favoured regions for eddy development. Applications to baroclinic planetary waves are also considered. 相似文献
6.
Abstract The linear stability of a non-divergent barotropic parallel shear flow in a zonal and a non-zonal channel on the β plane was examined numerically. When the channel is non-zonal, the governing equation is slightly modified from the Orr-Sommerfeld equation. Numerical solutions were obtained by solving the discretized linear perturbation equation as an eigenvalue problem of a matrix. When the channel is zonal and lateral viscosity is neglected the problem is reduced to the ordinary barotropic instability problem described by Kuo's (1949) equation. The discrepancy between the stability properties of westward and eastward flows, which have been indicated by earlier studies, was reconfirmed. It has also been suggested that the unstable modes are closely related to the continuous modes discretized by a finite differential approximation. When the channel is non-zonal, the properties of unstable modes were quite different from those of the zonal problem in that: (1) The phase speed of the unstable modes can exceed the maximum value of the basic flow speed; (2) The unstable modes are not accompanied by their conjugate mode; and (3) The basic flow without an inflection point can be unstable. The dispersion relation and the spatial structure of the unstable modes suggested that, irrespective of the orientation of the channel, they have close relation to the neutral modes (Rossby channel modes) which are the solutions in the absence of a basic shear flow. The features mentioned above are not dependent on whether or not the flow velocity at the boundary is zero. 相似文献
7.
Ballooning disturbances in a finite-pressure plasma in a curvilinear magnetic field are described by the system of coupled equations for the Alfvén and slow magnetosonic modes. In contrast to most previous works that locally analyzed the stability of small-scale disturbances using the dispersion relationship, a global analysis outside a WKB approximation but within a simple cylindrical geometry, when magnetic field lines are circles with constant curvature, is performed in the present work. This model is relatively simple; nevertheless, it has the singularities necessary for the formation of the ballooning mode: field curvature and non-uniform thermal plasma pressure. If the disturbance finite radial extent is taken into account, the instability threshold increases as compared to a WKB approximation. The simplified model used in this work made it possible to consider the pattern of unstable disturbances at arbitrary values of the azimuthal wavenumber (k y ). Azimuthally large-scale disturbances can also be unstable, although the increment increases with decreasing azimuthal scale and reaches saturation when the scales are of the order of the pressure nonuniformity dimension. 相似文献
8.
Masoud Rostami 《地球物理与天体物理流体动力学》2017,111(1):1-31
Analysis of the influence of condensation and related latent heat release upon developing barotropic and baroclinic instabilities of large-scale low Rossby-number shielded vortices on the f-plane is performed within the moist-convective rotating shallow water model, in its barotropic (one-layer) and baroclinic (two-layer) versions. Numerical simulations with a high-resolution well-balanced finite-volume code, using a relaxation parameterisation for condensation, are made. Evolution of the instability in four different environments, with humidity (i) behaving as passive scalar, (ii) subject to condensation beyond a saturation threshold, (iii) subject to condensation and evaporation, with three different parameterisations of the latter, are inter-compared. The simulations are initialised with unstable modes determined from the detailed linear stability analysis in the “dry” version of the model. In a configuration corresponding to low-level mid-latitude atmospheric vortices, it is shown that the known scenario of evolution of barotropically unstable vortices, consisting in formation of a pair of dipoles (dipolar breakdown) is substantially modified by condensation and related moist convection, especially in the presence of surface evaporation. No enhancement of the instability due to precipitation was detected in this case. Cyclone-anticyclone asymmetry with respect to sensitivity to the moist effects is evidenced. It is shown that inertia-gravity wave emission during the vortex evolution is enhanced by the moist effects. In the baroclinic configuration corresponding to idealised cut-off lows in the atmosphere, it is shown that the azimuthal structure of the leading unstable mode is sensitive to the details of stratification. Scenarios of evolution are completely different for different azimuthal structures, one leading to dipolar breaking, and another to tripole formation. The effects of moisture considerably enhance the perturbations in the lower layer, especially in the tripole formation scenario. 相似文献
9.
Planetary equatorial waves are studied with the shallow water equations in the presence of a mean zonal thermocline gradient. The interactions between this gradient and waves are represented by three non-linear terms in the equations: one in the wind-forcing formulation in the x-momentum equation, and two for the advection of mass and divergence of the velocity field in the continuity equation. When the mean gradient is imposed but small, these three (linearized) terms will perturb the behavior of the equatorial waves. This paper gives a simple analytic treatment of this problem.The equatorial Kelvin mode is first solved with all three contributions, using a Wentzel-Kramers-Brillouin method. The Kelvin mode shows a spatial or/and temporal growth when the thermocline gradient is negative which is the usual situation in the equatorial Pacific ocean (deep thermocline in the west and shallow in the east). The more robust and efficient contribution comes from the advection term.The single effect of the advection of the mean zonal thermocline gradient is then studied for the Kelvin and planetary Rossby modes. The Kelvin mode remains unstable (damped), while the Rossby modes appear damped (unstable) for a negative (positive) thermocline gradient. 相似文献
10.
11.
Willem V. R. Malkus 《地球物理与天体物理流体动力学》2013,107(1-3):123-134
Abstract Broad band secondary instability of elliptical vortex motion has been proposed as a principal source of shear-flow turbulence. Here experiments on such instability in an elliptical flow with no shear boundary layer are described. This is made possible by the mechanical distortion in the laboratory frame of a rotating fluid-filled elastic cylinder. One percent ellipticity of a 10 cm diameter cylinder rotating once each second can give rise to an exponentially-growing mode stationary in the laboratory frame. In first order this mode is a sub-harmonic parametric Faraday instability. The finite-amplitude equations represent angular momentum transfer on an inertial time scale due to Reynolds stresses. The growth of this mode is not limited by boundary friction but by detuning and centrifugal stabilization. On average, a generalized Richardson number achieves a marginal value through much of the evolved flow. However, the characteristic flow is intermittent with the cycle: rapid growth, stabilizing momentum transfer from the mean flow, interior re-spin up, and then again. Data is presented in which, at large Reynolds numbers, seven percent ellipticity causes a fifty percent reduction in the kinetic energy of the rotating fluid. In the geophysical setting, this tidal instability in the earth's interior could be inhibited by sub-adiabatic temperature gradients. A near adiabatic region greater than 10 km in height would permit the growth of tidally destabilized modes and the release of energy to three-dimensional disturbances. Such disturbances might play a central role in the geodynamo and add significantly to overall tidal dissipation. 相似文献
12.
In this article we address two questions: Why do freely evolving vortices weaken on average, even when the viscosity is very small? Why, in the fluid's interior, away from vertical boundaries and under the influence of Earth's rotation and stable density stratification, do anticyclonic vortices become dominant over cyclonic ones when the Rossby number and deformation radius are finite? The context for answering these questions is a rotating, conservative, Shallow-water model with Asymmetric and Gradient-wind Balance approximations. The controlling mechanisms are vortex weakening under straining deformation (with a weakening that is substantially greater for strong cyclones than strong anticyclones) followed by a partially compensating vortex strengthening during a relaxation phase dominated by Vortex Rossby Waves (VRWs) and their eddy–mean interaction with the vortex. The outcome is a net, strain-induced vortex weakening that is greater for cyclones than anticyclones when the deformation radius is not large compared to the vortex radius and the Rossby number is not small. Furthermore, when the exterior strain flow is sustained, the vortex changes also are sustained: for small Rossby number (i.e., the quasigeostrophic limit, QG), vortices continue to weaken at a relatively modest rate, but for larger Rossby number, cyclones weaken strongly and anticyclones actually strengthen systematically when the deformation radius is comparable to the vortex radius. The sustained vortex changes are associated with strain-induced VRWs on the periphery of the mean vortex. It therefore seems likely that, in a complex flow with many vortices, anticyclonic dominance develops over a sequence of transient mutual straining events due to the greater robustness of anticyclones (and occasionally their net strengthening). 相似文献
13.
Experimental study on the influence of seismic subsidence of loess under bidirectional loading modes
《地震研究进展（英文）》2021,1(4):100064
Water content, dry density, void ratio, depth of soil layer, and seismic loading may all exert influence on the seismic subsidence of loess. Many scholars have carried out seismic subsidence tests of loess to simulate the stress on soil using unidirectional (axial) vibration instead of bidirectional vibration. We conduct seismic subsidence tests of loess using two different dynamic stress loading methods, unidirectional and bidirectional dynamic stress. In addition, the effects of different dynamic stress loading modes on the development of seismic subsidence of loess are compared for a case-study in northwestern China. The results show that (1) the increasing ratio of radial stress to axial stress has exerted significant influence on the seismic subsidence coefficient of loess under the loading mode of bidirectional dynamic stress (2) there is a critical ratio of radial stress to axial stress for seismic subsidence of loess, ranging from 0.6 to 0.8; when the ratio of radial load to axial load is greater than the critical value, the effect of bidirectional load on the development of seismic subsidence is more remarkable (3) when the ratio of radial load to axial load is smaller, the seismic subsidence of loess calculated by the existing unidirectional stress loading method is safe for engineering projects. However, if the value exceeds the safety ratio range it is dangerous to conduct safety evaluations using the seismic loess subsidence. The prediction value of seismic subsidence at engineering sites directly affects the later foundation treatment and the safety of the overlying structures. The seismic subsidence calculation and evaluation method in this study may provide a scientific basis for safety evaluations of loess sites in northwestern China. 相似文献
14.
Abstract Inertial waves are excited in a fluid contained in a slightly tilted rotating cylindrical cavity while the fluid is spinning up from rest. The surface of the fluid is free. Since the perturbation frequency is equal to the rotation speed resonance occurs at a critical height to radius aspect ratio of the fluid. Detailed study of a particular inertial wave shows that in solid body rotation this “eigenratio” agrees with predictions from linear inviscid theory to within 0.5%. Measured time dependence of the eigenratio during spin-up from rest is a function of the tilt amplitude and agrees favorably with predictions from a numerical study. Mean flow associated with the inertial wave becomes unstable during spin-up and in the steady state. A boundary for the unstable region is found experimentally. 相似文献
15.
Abstract The normal mode instability of steady Wu-Verkley (1993) wave and modons by Verkley (1984, 1987, 1990) and Neven (1992) is considered. All these flows are solutions to the vorticity equation governing the motion of an ideal incompressible fluid on a rotating sphere. A conservation law for infinitesimal perturbations to each solution is derived and used to obtain a necessary condition for its exponential instability. By these conditions, Fjörtoft's (1953) average spectral number of the amplitude of an unstable mode must be equal to a specific number that depends on the degree of the solution in its inner and outer regions as well as on spectral distribution of the mode energy in these regions. Some properties of the conditions for different types of modons are discussed. The maximum growth (and decay) rate of the modes is estimated, and the orthogonality of the amplitude of each unstable, decaying, or non-stationary mode to the basic solution is shown in the energy inner product. The new instability conditions confine the unstable disturbances of the WV wave and modon to a hypersurface in the perturbation space and allow interpretation of their energy structure. They are also useful both in estimating the maximum growth rate of unstable modes and in testing the numerical algorithms designed for the linear stability study. 相似文献
16.
Experimental studies have been carried out on the dynamic stability of a cantilever cylindrical shell partially filled with liquid, under vertical excitation. Two polyester test cylinders with radius 100 mm, thickness 0.25 mm, and lengths 113 and 227 mm were used. The test cylinder was harmonically excited with constant acceleration- or displacement-amplitude. It was found that not only the parametric principal instability resonance but also the parametric combination involving two natural vibrations, each of which has the same circumferential wave number but different axial mode numbers, could occur. The latter type of vibration apparently has not been previously studied. By varying the dimensionless water height from 0.25 to 1.0 stepwise by 0.25 increments, the instability regions and vibration modes were determined for the two test cylinders. The response waves of shell wall and liquid free surface, and axial and circumferential vibration modes were also observed. 相似文献
17.
J. Shukla 《Pure and Applied Geophysics》1977,115(5-6):1449-1461
Barotropic-Baroclinic instability of horizontally and vertically shearing mean monsoon flow during July is investigated numerically by using a 10-layer quasi-geostrophic model. The most unstable mode has a wavelength of about 3000 km and westward phase speed of about 15 m sec–1. The most dominant energy conversion is from zonal kinetic energy to eddy kinetic energy. The structure of the most unstable mode is such that the maximum amplitude is concentrated at about 150 mb and the amplitude at the lowest layers is negligibly small. Barotropic instability of the zonal flow at 150 mb seems to be the primary excitation mechanism for the most unstable mode which is also similar to the observed westward propagating waves in the upper troposphere during the monsoon season. The results further suggest that Barotropic-Baroclinic instability of the mean monsoon flow cannot explain the occurrence of monsoon depressions which have their maximum amplitude at the lower levels and are rarely detected at 200 mb. 相似文献
18.
地震作用过程中地震加速度通常呈先增大后减小的特征。利用拟静力法对危岩的稳定性进行分析时,考虑地震过程中地震加速度的变化,对山西太原天龙山危岩体加固工程中的同一危岩体分别以滑塌式和倾倒式破坏模式进行计算,发现地震作用过程中危岩体可能在两种破坏失稳模式之间相互转化。将此问题扩展至一般情况进行计算并讨论,得出如下结论:地震力对危岩体破坏作用的贡献大小不同,通常情况下,地震作用力对危岩的倾覆力矩贡献相对较大;进行稳定性评价时应考虑地震作用过程,以安全系数最先达到1.0的破坏模式作为危岩体的可能破坏模式进行计算;对危岩体进行抗震加固设计时应对加固设计进行多种工况下的校核,保证其在地震作用过程中不同危险状态的稳定性。 相似文献
19.
The tropical cyclones form over the oceanic regions where conventional meteorological observations are not available. This
contributes to a poor initial analysis of the cyclonic vortex and hence inadequate forecast. One way of overcoming the above
problem is to modify the initial analysis by replacing the weak and ill-defined vortex in the initial analysis with a synthetic
vortex having the correct size and intensity at the correct location. In this study we are investigating the effect of inclusion
of a synthetic vortex based on Rankine as well as on Holland wind profiles, using NCAR-AFWA bogussing scheme for the prediction
of four tropical cyclones, which formed over the Bay of Bengal during November 2002 and 2005, December 2005 and over the Arabian
Sea during May 2004, using the MM5 model. Two numerical experiments are designed in this study for each of the above four
cyclones. In the first experiment the model is integrated with a synthetic vortex based on Rankine wind profile while in the
second experiment we utilize the Holland wind profile. For the November 2002 cyclone, in both the experiments the model is
integrated from 10 November 2002 18 UTC to 12 November, 2002 12 UTC with the synthetic vortex inserted at the initial time.
The results of the study for the November 2002 cyclone show that the model simulation with the Holland vortex has produced
a stronger cyclone in terms of minimum sea-level pressure and maximum wind speed. Also, the results for the November 2002
cyclone with the Holland vortex showed a better longitudinal height section of the horizontal wind speed across the center
of the cyclone. The track error of the cyclone for the November 2002 cyclone is less in the model simulation with the Holland
vortex at the initial time and at 24 hours of forecast. The results for the November 2002 cyclone with the Rankine vortex
showed greater vertical wind speed as compared to the Holland vortex. However, for the November 2002 cyclone there were no
significant differences in the spatial distribution of precipitation for both the experiments. In order to provide an adequate
number of case studies for a good statistical sample, the present study is extended for three additional cyclones over the
Indian region. All four cyclones studied here show that the Holland vortex has produced a stronger cyclone in terms of the
minimum sea-level pressure and maximum wind speed. The Holland vortex showed a better vertical structure of wind speed in
the longitudinal height section at 24 hours of forecast for the November 2005 cyclone while the structure was better for the
Rankine vortex for the remaining two cyclones. There were no significant differences in the spatial distribution of precipitation
for the two experiments corresponding to all four cyclones. Some statistical results pertaining to all four cyclones are provided
such as the average track error as well as the average difference between the observed and the model minimum sea-level pressure
and the maximum wind speed. The statistical results corresponding to the average of all the four cyclones are at only a slight
variance with the results corresponding to the November 2002 cyclone. 相似文献
20.
Georges R. Darbre 《地震工程与结构动力学》1984,12(5):703-707
The modal base forces in structures having a straight-line mode of vibration are investigated. Making use of the orthogonality relationship between the different modes, a relation between the modal base shears and base moments is found in all but the straight-line mode. This relation states that the contribution of the inertia forces to the modal overturning moments referred to the centre of rotation of the straight-line mode is identically null. The contributions of the vertical forces and lateral constraints must, however, be accounted for. For the special case of the straight-line mode being proportional to the height of each storey, the centre of rotation coincides with the base of the structure. For the case of the straight-line mode being a uniform displacement, the centre of rotation is at infinity and the contribution of the inertia forces to the modal base shears identically disappears in all but the straight-line mode. 相似文献