The Existence Of The Coupled Nonlinear Schr(?)dinger Equations About The Interaction With Nonlinear Gravity Waves And The Numerical Study

It is found that many severe weathers is related with the action of the gravitational waves of great amplify. So many people think that gravitational wave is the important burst mechanism of the happening of many severe weathers. Thus it is significative to study interaction of the gravitational wave , the existence of the solutions and the numerical format for mesoscale meteorology.In this paper, the interaction with the nonlinear gravitational waves in the baroclinic atmosphere, which is one of the causes of outbreak weather, is studied. There are four parts in this thesis:First, based the dynamics equations describing the fact atmosphere, we gained the mode of the nonlinear gravitational waves. By the use of WKB method that the interaction between two wave packets is governed by coupled nonlinear Schrodinger equations:And the coefficients of the equations, which are relevant with the distributing of basic flow ,can be confirmed by the original dates.Second, for the coupled nonlinear Schrodinger equations, adopted the method of integral estimate ,we prove that the condition of the existence for the solutions are:M = const > 0.(2)the initial conditions satisfy Third, we give the format of four-point implicit scheme for the coupled nonlinear Schrodinger equations:If the conditions satisfy , and 0 , the format of four-point implicit scheme is proved to be stable.Furthermore the error is Fourth, we discuss the distributing of the basic flow at perpendicular, which is influenced the coefficients of the equations. Here, we discuss the once shear and second shear of the distributing. It is showed by numerical calculation that the waves amplify becomes great and thewidth of waves becomes narrow after the collision or chase of two solitary gravitational waves .The results indicate that the nonlinear interaction between the gravitational waves may be one of the causes for outbreak of severe convective weather. Furthermore, by comparing once shear with second shear, we find that it is easier to breaking up or energy dispersion for the solitary gravitational waves by the nonlinear action when the distributing of basic flow is once shear. Moreover it is easier to the outbreak of weather. These show that it is easier to inspire the severe convective weather by the action of nonlinear gravity waves in the condition of the existence of high-level jet.