The unified ideal model of mean motion resonance of artificial satellites due to geopotential perturbations

From Kaula's Earth gravitational potential written in classical orbital elements, the unified ideal model of mean motion resonance of artificial satellites due to geopotential perturbations is developed in this paper first, through a suitable sequence of canonical transformations constructed by implicit functions. This unified ideal orbital resonance model is valid for all the commensurabilities between the rotational angular velocity of the Earth and the angular velocities of mean orbital motion of artificial satellites with arbitrary inclination and small eccentricity, and can be also transformed into Garfinkel's general expression of ideal resonance problem. Then 1/1 resonance of the 24-hour satellite with arbitrary inclination and small eccentricity is analyzed under the effect of harmonics of J2 and J 22 of the geopotential, based on the unified ideal model of mean motion resonance. The analytical expressions of the libration period and libration half width of the 1/1 resonance of the 24-hour satellite with arbitrary inclination and small eccentricity are presented.

REYNOLDS EXCHANGE IN THE ATMOSPHERIC MULTI-SCALE MOTIONS

In this paper the system of Reynolds equations of the multi-scaled atmospheric motions is set up based on the con- cept of decomposing the meteorological elements into multi-scale disturbances.It is proved to be true that the Reynolds exchange term in the averaged motion is equal to the sum of averaged nonlinear terms in all sub-averaged motions.In order to avoid the higher order closure in Eulerian approaches,a new K-theory based on the multi-scaled Reynolds equations is given in which the subscale motions are described by Langevin equation as the air particles are moving in the Eulerian average background.From the new K-theory are derived the momentum,heat and mass exchange coefficients as the functions of statistical variables such as variances and Lagrangian time scales of velocity,temperature and other meteorological elements in disturbances.The new K-theory also expounds the causes for the differences be- tween the exchange coefficients of one element and another and gives the ambient conditions in which the buoyancy and/or Coriolis force Will build the chaotic disturbances into the orderly gradient of mean values of the corresponding elements.In consequence the K-theory can be used to explain some of negative viscosity phenomena in atmospheric mo- tions.

A Front-Tracking Method for Motion by Mean Curvature with Surfactant

In this paper,we present a finite difference method to track a network of curves whose motion is determined by mean curvature.To study the effect of inhomogeneous surface tension on the evolution of the network of curves,we include surfactant which can diffuse along the curves.The governing equations consist of one parabolic equation for the curve motion coupled with a convection-diffusion equation for the surfactant concentration along each curve.Our numerical method is based on a direct discretization of the governing equations which conserves the total surfactant mass in the curve network.Numerical experiments are carried out to examine the effects of inhomogeneous surface tension on the motion of the network,including the von Neumann law for cell growth in two space dimensions.

THE OSCILLATION OF CERTAIN ZONAL MEAN CHARACTERISTICS OF MOTION ON A SPHERIC EARTH'S ATMOSPHERE——PART 2:ANISOTROPIC QUASI-EDDY MOTION

This paper is an extension of the author's paper (Xie,1982) to the spherical earth.It is found that the simi- lar results are obtained under the assumption of isotropic distribution of horizontal kinetic energy along the zonal and meridional directions.It points out the limitation of the results already obtained and paves the path for the approach of anisotropie semi-eddy or quasi-eddy motion of the atmosphere.