Lower Bounds of Decay Rates for Solution to the Single-Layer Quasi-Geostrophic Model

In this paper, we study the long-time behavior of solutions of the single-layer quasi-geostrophic model arising from geophysical fluid dynamics. We obtain the lower bound of the decay estimate of the solution. Utilizing the Fourier splitting method, under suitable assumptions on the initial data, for any multi-index α, we show that the solution Ψ satisfies .

Nonlinear Stability of Zonally Symmetric Quasi-geostrophic Flow

By using the conservation laws and the method of variational principle, an improved Arnol′d′s second nonlinear stability theorem for the two-dimensional multilayer quasi-geostrophic model in periodic channel is obtained.

A BAROTROPIC QUASI-GEOSTROPHIC MODEL WITH LARGE-SCALE TOPOGRAPHY, FRICTION AND HEATING

Based on the barotropic equations including large-scale topography, friction and heat factor, a barotropic quasi-geostrophic model with large-scale topography, friction and heating is obtained by means of scale analysis and small parameter method. It is shown that this equation is a basic one, which is used to study the influence of the Tibetan Plateau on the large-scale flow in the atmosphere. If the friction and heating effect of large-scale topography are neglected, this model will degenerate to the general barotropic quasi-geostrophic one.

On the Variation of Divergent Flow： An Eddy-flux Form Equation Based on the Quasi-geostrophic Balance and Its Application

Based on basic equations in isobaric coordinates and the quasi-geostrophic balance,an eddy-flux form budget equation of the divergent wind has been derived. This newly derived budget equation has evident physical significance. It can show the intensity of a weather system,the variation of its flow pattern,and the feedback effects from smaller-scale systems(eddy flows). The usefulness of this new budget equation is examined by calculating budgets for the strong divergent-wind centers associated with the South Asian high,and the strong divergence centers over the Tibetan Plateau,during summer(June–August) 2010. The results indicate that the South Asian high significantly interacts with eddy flows. Compared with effects from the mean flow(background circulation),the eddy flows’ feedback influences are of greater importance in determining the flow pattern of the South Asian high. Although the positive divergence centers over the Tibetan Plateau intensify through different mechanisms,certain similarities are also obvious. First,the effects from mean flow are dominant in the rapid intensification process of the positive divergence center. Second,an intense offsetting mechanism exists between the effects associated with the eddy flows’ horizontal component and the effects related to the eddy flows’ convection activities,which weakens the total effects of the eddy flows significantly. Finally,compared with the effects associated with the convection activities of the mean flow,the accumulated effects of the eddy flows’ convection activities may be more favorable for the enhancement of the positive-divergence centers.

Criteria for the Nonlinear Stability of Three-Dimensional Quasi-Geostrophic Motions

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.

AVERAGING PRINCIPLE FOR QUASI-GEOSTROPHIC MOTIONUNDER RAPIDLY OSCILLATING FORCING

A class of large scale geophysical fluid flows are modelled by the quasi-geostrophic equation. An averaging principle for quasi-geostrophic motion under rapidly oscil-lating ( non-autonomous) forcing was obtained, both on finite but large time intervals and on the entire time axis. This includes comparison estimate, stability estimate, and convergence result between quasi-geostrophic motions and its averaged motions. Furthermore, the existence of almost periodic quasi-geostrophic motions and attractor convergence were also investigated.

The Solitary Waves of the Barotropic Quasi-Geostrophic Model with the Large-scale Orography

Starting from a modified barotropic quasi-geostrophic model equation, considering the actual situation of the large-orography of the Tibetan Plateau, neglecting its slope in x direction, and using the reductive perturbation method, then the solitary waves are obtained. The results show that the orography is essential factor exciting solitary Rossby waves in a flow without shear.

A Simple Quasi-Geostrophic Coupled Ocean-Atmosphere Model

The quasi-geostrophic atmospheric and oceanic equations of momentum and thermodynamics with dissipation factors are used to create a simple coupled ocean-atmosphere model describing the large-scale shallow-water motion. We discuss the ocean-atmosphere coupling effect in mid-high and low latitudes separately and analyze characteristics of which the oscillatory periods of coupled low-frequency modes (ocean mode) vary with the coupling frequency and latitudinal number. This can interpret the correlation between low-frequency oscillation and ocean-atmosphere interaction. Then from the dispersion curves of atmosphere and ocean, we reveal effect of the coupling strength on the propagation of Rossby waves. The convection mechanism between the two modes is also discussed in view of the slowly varying wave train.The results show that Newtonian cooling and Rayleigh friction play a stable rule in oceanic Rossby waves, the period of coupled low-frequency mode grows with the increment of the coupling frequency. The larger the latitudinal number is, the more rapidly it grows. When the coupling frequency tends to critical value, the oceanic Rossby waves become static. When the ocean-atmosphere coupling strength grows to some degree, the propagation of oceanic Rossby waves will become opposite to its original direction. One part of the oceanic Rossby waves is converted into atmospheric Rossby waves, the energy conversion coefficient is also solved out.

RESEARCH ANNOUNCEMENTS——Random Attractors for a Dissipative Quasi-geostrophic Dynamical System Under Stochastic Forcing

We consider the two-dimensional stochastic quasi-geostrophic equation ■=1/(R_e)△~2■-r/2△■+f(x,y,t)(1.1) on a regular bounded open domain D ■,where ■ is the stream function,F Froude Number (F≈O(1)),R_e Reynolds number(R_e■10~2),β_0 a positive constant(β_0≈O(10^(-1)),r the Ekman dissipation constant(r≈o(1)),the external forcing term f(x,y,t)=-(dW)/(dt)(the definition of W will be given later)a Gaussian random field,white noise in time,subject to the

A Semi-Lagrangian Type Solver for Two-Dimensional Quasi-Geostrophic Model on a Sphere

In this paper, we propose a numerical method based on semi-Lagrangian approach for solving quasi-geostrophic (QG) equations on a sphere. Using potential vorticity and stream-function as prognostic variables, two-order centered difference is suggested on the latitude-longitude grid. In our proposed numerical scheme, advection terms are expressed in a Lagrangian frame of reference to circumvent the CFL restriction. The pole singularity associated with the latitude-longitude grid is eliminated by a smoothing technique for the initial flow. Error analysis is provided for the numerical scheme.

二维色散Quasi-Geostrophic方程组的整体适定性

本文研究一类二维色散 quasi-geostrophic 方程组初值问题的整体适定性。 通过引进一类高低频具有不同正则性指标的混合型 Besov 空间,并通过建立相应的色散半群在其上的一致有界性估计,证明了该二维色散 quasi-geostrophic 方程组关于混合型临界 Besov 空间中一致小初值的整体适定性。

GLOBAL REGULARITY FOR MODIFIED CRITICAL DISSIPATIVE QUASI-GEOSTROPHIC EQUATIONS

We consider the n-dimensional modified quasi-geostrophic（SQG） equations δtθ ＋ u·△↓θ＋kΛ^αθ=0, u = Λ^α-1R^⊥θ with κ 〉 0, α∈（0, 1] and θ0∈ W^1,∞（R^n）. In this paper, we establish a different proof for the global regularity of this system. The original proof was given by Constantin, Iyer, and Wu, who employed the approach of Besov space techniques to study the global existence and regularity of strong solutions to modified critical SQG equations for two dimensional case.The proof provided in this paper is based on the nonlinear maximum principle as well as the approach in Constantin and Vicol.

The Effect of Topography on Quasi-Geostrophic Frontogenesis

This paper improves Bannon's work on the quasi-geostrophic frontogenesis in a horizontal deformation field. By setting the lower boundary condition for the equation of potential temperature on the realistic topography instead of on z = 0, a general solution for the temperature field is derived after applying conformal mapping to the equation for the potential temperature, the vertical velocity and divergence field are also calculated. The general characteristics for the frontogenetic process still are frontolytic for warm front and frontogenetic for cold front in downstream of a mountain and the reverse is true upstream of a mountain, but more fine spatial structure of the temperature field and frontogenetic characteristics than Bannon's are obtained near surface because of the treatment of lower boundary condition. It is concluded that the frontogenetic characteristics are related to the translating speed of the deformation field with respect to the topography.

Establishment of infinite dimensional Hamiltonian system of multilayer quasi-geostrophic flow & study on its linear stability

A multilayer flow is a stratified fluid composed of a finite number of layers with densities homogeneous within one layer but different from each other. It is an intermediate system between the single-layer barotropic model and the continuously stratified baroclinic model. Since this system can simulate the baroclinic effect simply, it is widely used to study the large-scale dynamic process in atmosphere and ocean. The present paper is concerned with the linear stability of the multilayer quasi-geostrophic flow, and the associated linear stability criteria are established. Firstly, the nonlinear model is turned into the form of a Hamiltonian system, and a basic flow is defined. But it cannot be an extreme point of the Hamiltonian function since the system is an infinite-dimensional one. Therefore, it is necessary to reconstruct a new Hamiltonian function so that the basic flow becomes an extreme point of it. Secondly, the linearized equations of disturbances in the multilayer quasi-geostrophic flow are derived by introducing infinitesimal disturbances superposed on the basic flows. Finally, the properties of the linearized system are discussed, and the linear stability criteria in the sense of Liapunov are derived under two different conditions with respect to certain norms.

Global Well-Posedness and Asymptotic Behavior for the 2D Subcritical Dissipative Quasi-Geostrophic Equation in Critical Fourier-Besov-Morrey Spaces

In this paper,we study the subcritical dissipative quasi-geostrophic equa-tion.By using the Littlewood Paley theory,Fourier analysis and standard techniques we prove that there exists a unique global-in-time solution for small initial data belonging to the critical Fourier-Besov-Morrey spaces FN^(3-2a+(λ-2)/p)_(p,λ,q).Moreover,we show the asymptotic behavior of the global solution v.i.e.||v(t)||FN^(3-2a+(λ-2)/p)_(p,λ,q)decays to zero as time goes to infinity.

二维quasi-geostrophic方程的几何结构和非爆炸性(英文)

讨论了二维quasi-geostrophic方程中的主动标量θ的封闭水平集C的动态演变.当水平集具有某种指定几何性质,那么在水平集上▽⊥θ的大小与Ω(t)可比的假设下,证明了有限时间T内解爆炸的不存在性.最后给出了一个2D QG方程的Lax对表示.

NONLINEAR STABILITY CRITERIA FOR MOTIONS OF MULTILAYER QUASI-GEOSTROPHIC FLOW

Some nonlinear stability criteria for motions of multilayer quasi-geostrophic flow on a beta-plane are obtained by combining Arnold’s method with an accurate estimate method. The criteria can be applied to perturbations of initial data and parameters; rather than the former only. Particularly a criterion corresponding to Arnold’s second theorem is gained, which relies on some precise analyses and estimates.

ON THE MAINTENANCE OF BLOCKING ANTICYCLONES OF NORTHERN HEMISPHERE—PART I:QUASI-GEOSTROPHIC POTENTIAL VORTICITY ANALYSIS

Four observed blocking anticyclones in different regions of the Northern Hemisphere are in- vestigated.Analyses show that there exist distinct differences in the maintenance of the time-mean quasi-geostrophic potential vorticity(PV)low in 300 hPa within blocking areas.In two Pacific blocking cases,the PV advection by time-mean flow tends to flow the PV low to northwestern part of the blocking highs,and thus is beneficial to the maintenance of the blockings'strength.The transfer by transient eddies acts to balance the effect of the time-mean flow.In the Atlantic and Alaska blocking cases,however,the advection of mean flow tends to flow the PV low eastward. The PV transfer by transient eddies acts to flow potential vorticity low to the western part of the blocking ridges and also to balance the time-mean flow's effect.Thus,in the latter two cases,it is the transfer by the transient eddies that acts to maintain the blockings.

Well- posedness for the 2D dissipative quasi-geostrophic equations in the Besov space

In this paper, we consider the initial value problem of the 2D dissipative quasigeostrophic equations. Existence and uniqueness of the solution global in time are proved in the homogenous Besov space Bsp,p∞with small data when1/2 ＜α≤ 1, 2/2α- 1 ＜ p ＜∞, sp = 2/p - (2α - 1).Our proof is based on a new characterization of the homogenous Besov space and Kato's method.

Asymptotic profile of solutions to the two-dimensional dissipative quasi-geostrophic equation

This paper is concerned with the asymptotic behavior of the two-dimensional dissipative quasigeostrophic equation.Based on the spectral decomposition of the Laplacian operator and iterative techniques,we obtain improved L2 decay rates of weak solutions and derive more explicit upper bounds of higher order derivatives of solutions.We also prove the asymptotic stability of the subcritical quasi-geostrophic equation under large initial and external perturbations.