共查询到20条相似文献，搜索用时 15 毫秒
1.
By employing Arnol’d’s method (energy-Casimir), this paper has studied the nonlinear stability of the two-layer generalized Phillips’ model for which the top and bottom surfaces are either rigid or free, and obtained some nonlinear stability criteria. In addition, some linear stability criteria are obtained by normal mode method. The re-sults reveal the influences of the free surface parameter on the stability of atmospheric and oceanic motions 相似文献
2.
Variational principle of instability of atmospheric motions 总被引：2，自引：0，他引：2
Zeng Qingcun 《大气科学进展》1989,6(2):137-172
Problems of instability of rotating atmospheric motions are investigated by using nonlinear governing equations and the variational principle. The method suggested in this paper is universal for obtaining criteria of instability in all models with all possible basic flows. For example, the model can be barotropic or baroclinic, layer or continuous, quasi-geostrophic or primitive equations; the basic flow can be zonal or nonzonal, steady or unsteady.Although the basic flows possess a great deal of variety, they all are the stationary points in the functional space determined by an appropriate invariant functional. The basic flow is an unsteady one if the conservation of angular momentum is included in the associated functional.The second variation, linear or nonlinear, gives the criteria of instability. Especially, the general criteria of instability for unsteady basic flow, orographically disturbed flow as well as nongeostrophic flow are first obtained by the method described in this paper.It is also shown that the difference between the criteria of instability obtained by the linear theory and our variational principle clearly indicates the importance of using nonlinear governing equations.In the appendix the theory is extended to cases such as in a β-plane where the fluid does not possess finite total energy, hence the variational principle can not be directly applied. However, a generalized Liapounoff norm can still be obtained on the basis of variational consideration. 相似文献
3.
Lu Weisong 《Acta Meteorologica Sinica》1989,3(1):90-97
Based on a non-frictional and non-divergent nonlinear barotropic vorticity equation and its solutions oftravelling waves,the criteria for linear and nonlinear barotropic instability are gained respectively at an equilibriumpoint of the equation on a phase plane.The linear and nonlinear analytical solutions to instability waves arealso found.The computational results show that if their amplitudes are equal at the initial time,the amplitudeincrements of nonlinear instable barotropic wave are always less than those of linear instable barotropic wave.The nonlinear effects can slow down the exponential growth of linear instability.The time needed for makingthe amplitude double that of initial time by instabilities,is about 6h for linear instability and about 18h fornonlinear instability,the latter is in agreement with the observations in the real atmosphere. 相似文献
4.
Variational Principle of Instability of Atmospheric Motions 总被引：6，自引：4，他引：2
Problems of instability of rotating atmospheric motions are investigated by using nonlinear governing equations and the variational principle. The method suggested in this paper is universal for obtaining criteria of instability in all models with all possible basic flows. For example, the model can be barotropic or baroclinic, layer or continuous, quasi-geostrophic or primitive equations; the basic flow can be zonal or nonzonal, steady or unsteady.Although the basic flows possess a great deal of variety, they all are the stationary points in the functional space determined by an appropriate invariant functional. The basic flow is an unsteady one if the conservation of angular momentum is included in the associated functional.The second variation, linear or nonlinear, gives the criteria of instability. Especially, the general criteria of instability for unsteady basic flow, orographically disturbed flow as well as nongeostrophic flow are first obtained by the method described in this paper.It is also sh 相似文献
5.
Arnol’d’s Second Nonlinear Stability Theorem for General Multilayer Quasi-geostrophic Model 总被引：1，自引：0，他引：1
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
6.
Nonlinear stability criteria for quasi-geostrophic zonally symmetric flow are improved by establishing an optimal Poincar′e inequality. The inequality is derived by a variational calculation considering the additional invariant of zonal momentum. When applied to the Eady model in a periodic channel with finite zonal length, the improved nonlinear stability criterion is identical to the linear normal-mode stability criterion provided the channel meridional width is no greater than 0.8605· · · times its channel length (which is the geophysically relevant case). 相似文献
7.
Newtonian jerky dynamics is applied to inertial instability analysis to study the nonlinear features of atmospheric motion under the action of variable forces. Theoretical analysis of the Newtonian jerky function is used to clarify the criteria for inertial instability, including the influences of the meridional distributions of absolute vorticity (ζg ) and planetary vorticity (the β effect). The results indicate that the meridional structure of absolute vorticity plays a fundamental role in the dynamic features of inertial motion. Including only the β effect (with the assumption of constant ζg ) does not change the instability criteria or the dynamic features of the flow, but combining the β effect with meridional variations of ζg introduces nonlinearities that significantly influence the instability criteria. Numerical analysis is used to derive time series of position, velocity, and acceleration under different sets of parameters, as well as their trajectories in phase space. The time evolution of kinematic variables indicates that a regular wave-like change in acceleration corresponds to steady wave-like variations in position and velocity, while a rapid growth in acceleration (caused by a rapid intensification in the force acting on the parcel) corresponds to track shifts and abrupt changes in direction. Stable limiting cases under the f-and β-plane approximations yield periodic wave-like solutions, while unstable limiting cases yield exponential growth in all variables. Perturbing the value of absolute vorticity at the initial position (ζ0 ) results in significant changes in the stability and dynamic features of the motion. Enhancement of the nonlinear term may cause chaotic behavior to emerge, suggesting a limit to the predictability of inertial motion. 相似文献
8.
An attempt has been made to apply Arnol’d type nonlinear stability criteria to the diagnostic study of the persistence (stability) or breakdown (instability) of the atmospheric flows. In the case of the blocking high, the cut-off low and the zonal flow, the relationships of the geostrophic stream function versus the po-tential vorticity of the observed atmosphere are analyzed, which indicates that Arnol'd second type nonlinear stability theorem is more relevant to the observed atmosphere than the first one. For both the sta-ble and unstable zonal flows, Arnol’d second type nonlinear stability criteria are applied to the diagnosis. The primary results show that our analyses correspond well to the evolution of the atmospheric motions. The synoptically stable zonal flows satisfy Arnol'd second type nonlinear stability criteria; while the synoptically unstable ones violate the nonlinear stability criteria. 相似文献
9.
The Charney model is reexamined using a new mathematical tool, the multiscale window transform(MWT), and the MWT-based localized multiscale energetics analysis developed by Liang and Robinson to deal with realistic geophysical fluid flow processes. Traditionally, though this model has been taken as a prototype of baroclinic instability, it actually undergoes a mixed one. While baroclinic instability explains the bottom-trapped feature of the perturbation, the second extreme center in the perturbation field can only be explained by a new barotropic instability when the Charney–Green number γ 1, which takes place throughout the fluid column, and is maximized at a height where its baroclinic counterpart stops functioning.The giving way of the baroclinic instability to a barotropic one at this height corresponds well to the rectification of the tilting found on the maps of perturbation velocity and pressure. Also established in this study is the relative importance of barotropic instability to baroclinic instability in terms of γ. When γ 1, barotropic instability is negligible and hence the system can be viewed as purely baroclinic; when γ 1, however, barotropic and baroclinic instabilities are of the same order;in fact, barotropic instability can be even stronger. The implication of these results has been discussed in linking them to real atmospheric processes. 相似文献
10.
Nonlinear stability criterion for plane rotating shear flow under three-dimensional nondivergence disturbances was obtained by using both variational principle and convexity estimate introduced by Arnold (1965) and Holm et al. (1985). The results obtained in this paper show that the effect of Coriolis force plays an important role in the nonlinear stability criterion, and the nonlinear stability property of the basic flow depends on both the distribution of basic states and the way the external disturbance acts on the states. The upper bound of the gradient of the mass density displacement from the equilibrium k2 = is determined by the basic states and one example was given to show the exact upper value of k. The remarks on Blumen's paper were also given at Section 4 of this paper. 相似文献
11.
Yong. L. McHall 《Acta Meteorologica Sinica》1992,6(2):213-230
There are some basic problems in previous theoretical studies of baroclinic instability.The derived criticalbaroclinity was considerably lower than the time averaged mean meridional temperature gradient,especially in the lowertroposphere.Also,the linear mechanism of baroclinic disturbance development which is noted restricted by the criticalbaroclinity was not studied sufficiently.The realistic critical baroclinity and disturbance development are discussed inthis study.It will be shown that the critical condition of instability and typical time and space scales of disturbances de-pend on three-dimensional structures of atmosphere and sphericity of the earth,other than the horizontal temperaturegradient alone.The variant behaviour of atmospheric disturbances depends highly on their specific scales that may bedescribed by the same theoretical model.Thus,there would be no substantial differences in the basic instability mecha-nism of many disturbances including the polar lows and explosive cyclones. 相似文献
12.
A conservation law for the Phillips model is derived. Using this law, the nonlinear saturation of purely baroclinic instability caused by the vertical velocity shear of the basic flow in the Phillips model-the case of energy-is studied within the context of Arnold's second stability theorem. Analytic upper bounds on the energy of wavy disturbances are obtained. For one unstable region in the parameter plane, the result here is a second-order correction in ε to Shepherd's; For another unstable region, the analytic upper bound on the energy of wavy disturbances offers an effective constraint on wavy (nonzonal) disturbances φ'i at any time. 相似文献
13.
Numerical simulation of typhoon surges along the east coast of Zhejiang and Jiangsu Provinces 总被引：2，自引：0，他引：2
Using conventional two-dimensional nonlinear storm model, the storm surges caused by the six ty-phoons with different kinds of tracks which hit the coast of Zhejiang and Jiangsu Provinces including Shanghai during the period from 1953 to 1974 are computed numerically. To avoid the nonlinear and linear computational instabilities, a finite-difference scheme with the quadratic conservation (or the semi-momentum) is adopted and a criterion for linear computational stability is derived. The basic parameters used in this computation are: the space step Δs=30km, the time step Δt=200sec, the coefficient of the wind stress = 2.6 "10-> and the coefficient of the bottom friction v&2=2.0x 10-'. The pressure and surface wind distribution for typhoon are assumed to be characterized by Fujita's pressure formula and Uerto's wind model, respectively. 相似文献
14.
Using conventional two-dimensional nonlinear storm model, the storm surges caused by the six typhoons with different kinds of tracks which hit the coast of Zhejiang and Jiangsu Provinces including Shang -hai during the period from 1953 to 1974 are computed numerically. To avoid the nonlinear and linear computational instabilities, a finite-difference scheme with the quadratic conservation (or the semi-momentum) is adopted and a criterion for linear computational stability is derived. The basic parameters used in this computation are: the space step Δs=30 km, the time step Δt=200 sec, the coefficient of the wind stress vc3-2.6×10-3 and the coefficient of the bottom friction vt2=2.0×10-3. The pressure and surface wind distribution for typhoon are assumed to be characterized by Fujita's pressure formula and Ueno's wind model, respectively. 相似文献
15.
Yao Dirong 《大气科学进展》1988,5(1):27-34
The nonlinear discriminant function, when covariance matrixes of each population are not equal to each other, is discussed on the basis of Bayes’ criterion, and by using the stepwise discriminant method, a method for calculating the nonlinear discriminant function is provided, which is called “stepwise nonlinear discriminant analysis”. In addition, an appropriate discriminant analysis model is selected by testing whether the covariance matrixes of each population are equal, which was proposed by Box. The calculations show that, the discrimi-nant effects of this method are superior not only to linear discriminant analysis, but also to nonlinear discrimi-nant analysis in which the stepwise discriminant algorithm is not used when covariance matrixes of each popu-lation are not equal to each other. Satisfactory results have been obtained in applying this method. This is an important improvement on the linear discriminant analysis used in the weather typing prediction at present. 相似文献
16.
The nonlinear discriminant function, when covariance matrixes of each population are not equal to each other, is discussed on the basis of Bayes' criterion, and by using the stepwise discriminant method, a method for calculating the nonlinear discriminant function is provided, which is called "stepwise nonlinear discriminant analysis". In addition, an appropriate discriminant analysis model is selected by testing whether the covariance matrixes of each population are equal, which was proposed by Box. The calculations show that, the discriminant effects of this method are superior not only to linear discriminant analysis, but also to nonlinear discriminant analysis in which the stepwise discriminant algorithm is not used when covariance matrixes of each population are not equal to each other. Satisfactory results have been obtained in applying this method. This is an important improvement on the linear discriminant analysis used in the weather typing prediction at present. 相似文献
17.
Optimal Perturbations Triggering Weather Regime Transitions: Onset of Blocking and Strong Zonal Flow 总被引：1，自引：0，他引：1
In this paper, the approach proposed by Mu and Jiang (2008) to obtain the optimal perturbations for triggering blocking (BL) onset is generalized to seek the optimal perturbations triggering onset of the strong zonal flow (SZF) regime. The BL and SZF regimes are characterized by the same dipole-like anomaly pattern superposed on the climatological flow, but with opposite sign. The results show that this method is also superior at finding the initial optimal perturbations triggering onset of the SZF regime, especially in the medium range. Furthermore, by comparing the two kinds of conditional nonlinear optimal perturbations (CNOPs) trig-gering onset of BL and SZF regimes, we find that in the linear approximation, there is symmetry in the sensitivities for BL and SZF onset, and the perturbations that optimally trigger onset of BL and SZF regimes at times when linear approximation is valid are also characterized by the same spatial pattern but with opposite sign. Whereas when the optimization time is extended to 6 days, the two kinds of CNOPs lose their out-of-phase behavior. The nonlinearity results in an asymmetry between the sensitivity for BL and SZF onset. Additionally, we find that the optimal perturbations have one common property, which is that the second baroclinic mode contributes more to the initial perturbations while the barotropic mode dominates the final structures. 相似文献
18.
Due to uncertainties in initial conditions and parameters,the stability and uncertainty of grassland ecosystem simulations using ecosystem models are issues of concern.Our objective is to determine the types and patterns of initial and parameter perturbations that yield the greatest instability and uncertainty in simulated grassland ecosystems using theoretical models.We used a nonlinear optimization approach,i.e.,a conditional nonlinear optimal perturbation related to initial and parameter perturbations (CNOP) approach,in our work.Numerical results indicated that the CNOP showed a special and nonlinear optimal pattern when the initial state variables and multiple parameters were considered simultaneously.A visibly different complex optimal pattern characterizing the CNOPs was obtained by choosing different combinations of initial state variables and multiple parameters in different physical processes.We propose that the grassland modeled ecosystem caused by the CNOP-type perturbation is unstable and exhibits two aspects:abrupt change and the time needed for the abrupt change from a grassland equilibrium state to a desert equilibrium state when the initial state variables and multiple parameters are considered simultaneously.We compared these findings with results affected by the CNOPs obtained by considering only uncertainties in initial state variables and in a single parameter.The numerical results imply that the nonlinear optimal pattern of initial perturbations and parameter perturbations,especially for more parameters or when special parameters are involved,plays a key role in determining stabilities and uncertainties associated with a simulated or predicted grassland ecosystem. 相似文献
19.
Some more proper criteria for the nonlinear stability of three-dimensional quasi-geostrophic motions are given by combining variational principle with a prior estimates method. The criteria are suitable for perturbations of initial condition as well as parameters in the model. The basic flow can be steady or unsteady. Particularly the difficulty due to the nonlinear boundary condition is completely overcome by the use of our method. 相似文献
20.
By using the symmetric equations of atmospheric dynamics in y-z plane with vertical and horizontal shear of wind, the nonlinear ordinary differential equation is derived with the method of travelling wave.Its stability is discussed by using the theory of nonlinear stability and the KDV equation is solved. The effects of linear CISK, nonlinear CISK, inertial stability and vertical shear of wind on the amplitude and the width of isolated inertial gravitational wave are discussed. In order to understand deeply the formation and development of meso-scale synoptic systems, such as the squall line, MCC, the cold surge of Asia high and typhoon, the factors of development of the isolated inertial gravity wave are analysed. 相似文献