NONLINEAR WAVES IN GEOPHYSICAL FLUID

In this paper, beginning with the shallow-water equations describing the geophysical fluid motion and by a method expanding the nonlinear terms in Taylor series near the equilibrium point, we find the analytic solutions of the finite amplitude nonlinear inertio-surface gravity waves and Rossby waves. We point out that (ⅰ) the finite amplitude nonlinear inertio-surface gravity waves and Rossby waves Satisfy all the KdV equations; (ⅱ) the solutions are all the enoidal functions, i. e. the enoidal waves which include the linear waves and form the solitary waves under certain conditions; (ⅲ) the dispersive relation including both the wave number and the amplitude is established; (ⅳ) the rotating transform method is given, and the two-dimensional nonlinear problem can be reduced to the one-dimensional one.     

SOLITARY INTERNAL GRAVITY INERTIAL WAVE IN A STRATIFIED ATMOSPHERE AND NONLINEAR PROCESSES FOR THE FORMATION OF SQUALL LINES

In this paper the KdV equation is derived from the three dimensional primitive equations for a class of finite amplitude waves in a stratified basic flow. The solitary wave solution is given for a simple case where a constant and uniformly stratified basic flow is confined in a region bounded by solid walls with rectangular cross section. The properties of the solitary wave solution can give a possible explanation for the preferential occurrence of a squall line or storm cell train at the left side of a low level jet and the concurrent fluctuation in the low level jet. For more general cases, i. e. sheared basic flow and nonuniform stratification, the qualitative response of the wave amplitude to the symmetric baroclinic stability of the basic flow is analysed. The results indicate that the vertical circulation in a solitary wave will possibly be dramatically intensified in a local area where the stability is weak or negative.     

WAVE ACTION CONSERVATION EQUATION FOR PLANETARY WAVE IN A SPHERICAL ATMOSPHERE AND WAVE GUIDES OF STATIONARY PLANETARY WAVE PROPAGATIONS SHOWN BY PROPAGATIONS SHOWN BY WAVE ACTION FLUX

It is pointed in this paper that the influence of the component of nongeostrophic windon the potential vorticity transportation in the north-south direction must be considered inthe energy propagations of stationary planetary waves. Then, the wave action conservationequation for planetary waves is demonstrated and the wave action flux, i.e. Eliassen-Palmflux, is obtained in a spherical atmosphere. It is also demonstrated by WKBJ method in this paper that the distribution of E-R fluxvector due to planetary wave is parallel to the local group velocity of waves. Stationary planetary waves responding to an idealized forcing mechanism are computed bymeans of a multi-level model. It is verified by the distributions of E-P flux vector thatthere are two wave guides in the stationary planetary wave propagations in a spherical at-mosphere in winter, i.e. there should be another wave guide pointing from the troposphere atmiddle latitudes toward the upper troposphere at low latitudes in addition to the polar wavegu     

ON OTHER WAVE GUIDE IN STATIONARY PLANETARY WAVE PROPAGATIONS IN WINTER NORTHERN HEMISPHERE

In this paper, the refractive index squared of stationary planetary waves in the isothermalatmosphere is computed theoretically. It has been discovered that there should be the otherwave guide pointing from the lower troposphere in middle and high latitudes toward the uppertroposphere in low latitudes in addition to the polar wave guide in the vertical and lateral pro-pagations of stationary planetary waves in winter. The vertical and lateral propagations of stationary planetary waves responding to an idealiz-ed forcing mechanism, for example, an idealized topography or stationary heat sources overthe Northern Hemisphere have been investigated by means of a quasigeostrophic, steady-state,34-level model with Rayleigh friction, Newtonian cooling effect and the horizontal kinematicthermal diffusivity included in a spherical coordinate system. The computed results have veri-fied that there actually is the other wave guide in the stationary planetary wave propagationsin winter. The vertical distributions of     

ON NONLINEAR GRAVITY TRAVELLING WAVE

In this paper, a two--layer model with dispersive and dissipative effects but without Co-?iolis effect is investigated. It is proved that in the model, under certain parameter condi-tions, there exists monotone travelling wave as well as oscillation travelling wave in additionto the nonlinear periodic solution and solitary wave. The conditions for their existence areprovided. It is particularly pointed out that the pattern of the oscillation travelling wave issimilar to that of the pressure upwelling wave of a squall line which passes certain region.     

TRANSPORTATION THEORY OF MULTIPLE SCATTERING AND ITS APPLICATION TO SEISMIC CODA WAVES OF IMPULSE SOURCE

The energy distribution of elastic waves in an infinite elastic medium with uniformly and randomly distributed scatterers has been researched. The scattering process is assumed to be isotropic and without conversions between wave types. We get the equation on the distribution of energe density in time and space covering single as well as multiple scattering. Taking physical symmetry of the field into account, it can be simplified. In the case of small earthquakes, the energy source of elastic waves can be assumed as a short pulse emitted isotropically at t=0. The first-order approximate solution in the 3-dimensional space can be obtained, and it is equivalent to Sato's solution for single scattering. In the 2-dimensional space the complete analytical solution has been derived by the mathematical inductance which leads to a conclusion that the codas of surface waves can give the Q-factor related to intrinsic absorption. The equation obtained in this paper is more general.     

Simulation of Viscoelastic Fluid Flows in Expansion Geometry Using Finite Volume Approach简

The simulation results on viscoelastic fluid flows in sudden expansion geometry with different expansion ratios are presented. Oldroyd-B, linear Phan-Thien-Tanner （L-PTT） and Finitely Extensible Nonlinear Elastic （FENE-P） based constitutive equations were applied in two-dimensional Cartesian coordinates. The governing equations in transient and fully developed regions were solved using open source software called OpenFOAM. The flow patterns, including velocity profiles, shear stresses and first normal stress differences in some horizontal and vertical sections are illustrated. In addition, effects of the fluid type, flow dynamics and expansion ratio on the flow and vortex patterns in transient and fully developed regions are presented and discussed. The presented results show that existences of vortices cause the inverse velocity and negative stresses in expansion regions of the channel which increase with increment of expansion ratio and Weissenberg number （We）. Furthermore, some dead spaces can be observed at channel expansion regions close to the wall which are also increased. The results also show that at low We numbers all fluids show close behavior while at high We numbers the FENE-P fluid behavior shows high divergence from that of the two other fluids.     

Stress-induced polymer deformation in shear flows

By means of dynamic Monte Carlo simulation of bulk lattice polymers in Couette shear flow, it was demonstrated that in addition to velocity gradient the constant driving forces acting as the activation aspect of shear stresses can also raise polymer deformation. Moreover, enhancing driving forces in a flow without any velocity gradient can reproduce nonNewtonian fluid behaviors of long-chain polymers. The simulations of Poiseuille shear flow with a gradient of shear stresses show that, the velocity gradient dominates small deformation in the flow layers of low shear stresses, while the shear stress dominates large deformation in the flow layers of high shear stresses. This result implies that the stress-induced deformation could be mainly responsible for the occurrence of non-Newtonian fluid behaviors of real polymers at high shear rates.     

PERIODIC, SOLITARY AND DISCONTINUOUS PERIODIC SOLUTION OF NONLINEAR WAVES IN THE ATMOSPHERE AND THEIR EXISTENCE (Ⅰ)——ON THE PSEUDO-ENERGY, THE PSEUDO-ENERGY INFLUENCE FUNCTION AND THEIR USE

In this paper various non-dispersion solutions of nonlinear waves in the atmosphere are discussed. We turn the nonlinear partial differential equations into the nonlinear ordinary differential equations after the phase angle function has been introduced. The nature around the equilibrium points and singular points of these ordinary differential equations is discussed and various analytic expressions of the nondispersion solutions are obtained. In part (Ⅰ), two problems are dealt with mainly. (ⅰ) The relation between pseudo-energy and the pseudo-energy influence function and nonlinear waves is discussed. Through the discussion of the pseudo-energy influence function, we can determine the existential condition of the periodic solution, the solitary wave solution, the discontinuous periodic solution and the discontinuous solitary wave solution. We also indicate that if there exists an external source, which occasions infinitely small changes in the pseudo-energy influence function, the nonlinear solitary     

NONLINEAR GRAVITY INERTIAL WAVE OF TWO DIMENSIONS AND DISCUSSION OF THE POSSIBILITY OF SOLITARY WAVE''''S EXISTENCE

In this paper we discuss the problem of a nonlinear gravity inertial wave of twodimensions and the possibility of solitary wave's existence. First of all, the existingcondition and analytic solution expression of shallow water waves are obtained by theapplication of the qualitative method of O. D. Es. We find that when the problem is de-generated, some physical values produce the nonlinear solitary wave, while other physi-cal values will be unbounded, so we consider that the nonlinear solitary wave for thesystem does not exist. Then we introduce concepts of the generalized energy (i. e. pseu-do-energy): when the pseudo-energy produces the tiny change at acting on a special ex-ternal effect, there will be solitary waves in this system. Finally, we obtain the repre-sentative of the nonlinear solitary wave which is different from KdV equation.     

STABILITY AND EQUATIONS OF AMPLITUDE AND PHASE FOR DISTURBANCES ON ZONAL FLOW IN BAROTROPIC ATMOSPHERE ON SPHERICAL COORDINATES

Using the method of linear disturbances, it is proved that the sufficient and necessarycondition for neutral disturbances is that the isolines of the phase for disturbances are dis-tributed in the meridional direction, in an ideal and inviscid and nondivergent atmosphere onrotating spherical coordinates with a shear zonal parallel flow and the zonal rigid boundaryconditions. From the above conclusion, we can get that the disturbances with tilted treughmay not be neutral, and it must be amplifying or damping. Furthermore, we have derivedthe nonlinear equations of amplitude and phase for disturbances.     

LINEAR AND NONLINEAR STABILITY PROBLEMS FOR THE BAROCLINIC ROSSBY WAVES

In this paper, beginning with two-level quasi-geostrophie equations describing the baroclinic Rossby waves and using the bifurcation theory, a simple model of the stability for the baroclinic Rossby waves is set up. We find the linear and nonlinear control parameters and modify some classical conclusions of the stabilities.     

A DIAGNOSTIC STUDY OF FORMATION AND MAINTENANCE OF BLOCKING SITUATION ON THE NORTHERN HEMISPHERE USING E-P FLUX

In this paper, the variations of the mean flow, the E-P flux and its divergence of planetary waves in the process of the formation, maintenance and collapse of the blocking situation in the second half of February, 1979 are analysed with the transformed Eulerian mean-motion equations.Analysed results show that because the basic flow changes from the easterly into the westerly in the lower troposphere at high latitudes, the planetary wave for wavenumber 2 strongly propagates upwards, and because of the interaction between the upward propagating planetary wave and the basic flow, the westerty is weakened and approaches to the resonant flow of wavenumber 2 in the middle and upper troposphere (then, in the lower and middle Stratosphere). This may cause the anomalous amplification of planetary wave for wavenumber 2, and moreover make the mean flow change from the westerly into the easterly in the lower and middle stratosphere, following the upper troposphere. Therefore, the blocking situation can be formed a     

PERIODIC, SOLITARY AND DISCONTINUOUS PERIODIC SOLUTION OF NONLINEAR WAVES IN THE ATMOSPHERE AND THEIR EXISTENCE (Ⅱ)——ON THE POSSIBILITY OF TAYLOR EXPANSION, M CRITERION AND NONLINEAR WAVE SPEED FORMULAS

In this part, the nonlinear wave speed formulas are discussed. Because the nonlinear wave speed formulas are relative to wave form, we introduce a non-dimensional quantity M, which describes the nonlinear wave pattern and qualitatively determines the nonlinear degree. It is called M criterion. The wave speed formulas of the nonlinear Rossby wave and the nonlinear inertial gravity wave are also discussed. The wave speed of the former decreases with the growth of the amplitude but that of the latter is on the opposite. Furthermore we have also discussed the problems which must be taken note of in applying the Taylor expansion as we solve the approximate solution of nonlinear waves.     

LASER DOPPLER MEASUREMENT OF THE AXIAL VELOCITY DISTRIBUTION IN THE CONVERGENT FLOW OF A POLYMERIC FLUID INTO A RECTANGULAR SLIT

The center line velocity distributions in the convergent flow of a silicone oil as a Newtonian fluid and a solution of silicone rubber ia silicone oil as a non-Newtonian fluid into a rectangular slit of various entrance angles have been measured by means of laser Doppler velocimetry. The non-Newtonian fluid used conformed to the behavior of a power-law fluid at shear rates greater than 20 s~(-1) with a non-Newtonian index n=0.76. The convergent flow studied had a contraction ratio of 12, with slit height of 0.83mm, slit length to height ratio of 18.1, slit width to height ratio of 14.3 and the width to height ratio before entering the slit of 1.19. Flow experiments were done at room temperature with shear rates at the slit wall of (1.7—11)·10~3s~(-1) and generalized Reynolds number 0.21—2.2. No elastic turbulence was observed in front of the slit entrance. The center line velocity gradient along the flow direction was appreciably reduced in the flow cells of small entrance angles. Two new phenomena h     

ON NONLINEAR WAVES IN THE GROWTH PROCESS

Having included the growth mechanism of coupling wind-generated waves into the Stokes' equa-tions, the growth evolution equation of nonlinear wind-generated waves in the wavenumber space andthe governing equation for narrow band spectrum condition in the physical space, the generalized Schro-dinger equations are deduced in this paper. From the discrete type of the growth evolution equa-tion, the analytical expressions of a nonlinear single wave from growing to tending towards equilibriumstate are given in this study. The unstable features of adjacent frequencies of this wave under a quiteseparate condition of evolution time scale and growth time scale are further analyzed.     

NONLINEAR CNOIDAL WAVES AND SOLITARY WAVES IN ATMOSPHERE

In this paper, starting with the equations describing the atmospheric motion and by arelatively simple method, we find that, nearby the mechanical equilibrium point, all thefinite amplitude nonlinear inertia waves, internal gravity waves and Rossby waves in thedispersive atmosphere satisfy the KdV (Korteweg-de Vries) equation, its solution being thecnoidal waves and solitary waves. For the finite amplitude Rossby waves, we find the newdispersive relation which is different from the Rossby formula and contains the amplitudeparameter. It is shown that the larger the amplitude and width, the faster are the wavesfor the finite amplitude inertia waves and internal gravity waves, and the slower are thewaves for the Rossby solitary waves, to which perhaps the polar vortex and the blocking orcut-off systems belong. This treatise gives the nonlinear waves a new way and inspires usto study the nonlinear adjustment process and evolution process and the turbulence structure.     

HEAT FLOW ON THE QINGHAI-XIZANG(TIBETAN) PLATEAU AND THE MODELING OF THE TECTONO-THERMAL EVOLUTION

Thirteen observed heat flow values in combination with relevant geological and geophysical information are employed in the current paper to conduct a model study by means of direct inversion. The modeling demonstrates the tectono-thermal evolution of the Tibetan Plateau during the last 40 Ma since the continent-continent collision. The authors stress the fact that the tectonic deformations of terranes are usually the inducing factors for the deep-seated thermal activities in the crust and upper mantle. On this basis a series of kinematic equations of 3-D deformations of terranes in forms of shortening-thickening-uplifting-erosion-mass sliding were deduced using the principle of plate kinematics. These equations are further used as systematically defined initial and boundary conditions for simulating the integrated processes of tectono-thermal evolution, The results of the model study suggest that there exist sharp differences in the tectono-thermal evolution between the old northern terranes and the new     

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.     

FRICTIONAL DISSIPATION AND NONLINEAR BAROTROPIC INSTABILITY

Based on the nonlinear quasi-geostrophic barotropic vorticity equation with Ekman friction, the criteria for nonlinear barotropic stability of the zonal basic flows are derived using Serrin-Joseph energy approach and through total energy, total enstrophy and their linear combination, separately, in terms of variational principle. Since the new transformation for Euler equation is utilized, the estimation of eigenvalue is more accurate, and the previous results of the author are improved very well.