The linear Rossby wave frequency expression is expanded at higher accuracy based on the scale difference characteristics of atmospheric long waves in the x and y directions. That the nature of the waves represented by...The linear Rossby wave frequency expression is expanded at higher accuracy based on the scale difference characteristics of atmospheric long waves in the x and y directions. That the nature of the waves represented by the expansion is identical to that of the original ones is demonstrated both in phase velocity C and wave energy dispersion speed C., followed by the derivation of the nonlinear expression describing atmospheric long wave behaviors with the associated approximate analytic solution obtained. Then, for the first time atmospheric' oscillatory Rossby solitary wave with its dispersion relation is obtained by numerical calculation with the aid of physical parameters of the real atmosphere. The solitary wave is found to be very close to such longwave systems as blocking highs and cut-off depressions in the actual atmosphere.展开更多
In this paper, we apply the theory of planar dynamical systems to carry out qualitative analysis for the dynamical system corresponding to B-BBM equation, and obtain global phase portraits under various parameter cond...In this paper, we apply the theory of planar dynamical systems to carry out qualitative analysis for the dynamical system corresponding to B-BBM equation, and obtain global phase portraits under various parameter conditions. Then, the relations between the behaviors of bounded traveling wave solutions and the dissipation coeffiicient μ are investigated. We find that a bounded traveling wave solution appears as a kink profile solitary wave solution when μ is more than the critical value obtained in this paper, while a bounded traveling wave solution appears as a damped oscillatory solution when μ is less than it. Furthermore, we explain the solitary wave solutions obtained in previous literature, and point out their positions in global phase portraits. In the meantime, approximate damped oscillatory solutions are given by means of undetermined coefficients method. Finally, based on integral equations that reflect the relations between the approximate damped oscillatory solutions and the implicit exact damped oscillatory solutions, error estimates for the approximate solutions are presented.展开更多
文摘The linear Rossby wave frequency expression is expanded at higher accuracy based on the scale difference characteristics of atmospheric long waves in the x and y directions. That the nature of the waves represented by the expansion is identical to that of the original ones is demonstrated both in phase velocity C and wave energy dispersion speed C., followed by the derivation of the nonlinear expression describing atmospheric long wave behaviors with the associated approximate analytic solution obtained. Then, for the first time atmospheric' oscillatory Rossby solitary wave with its dispersion relation is obtained by numerical calculation with the aid of physical parameters of the real atmosphere. The solitary wave is found to be very close to such longwave systems as blocking highs and cut-off depressions in the actual atmosphere.
基金supported by Shanghai Leading Academic Discipline Project (No. S30501)Shanghai Natural Science Foundation Project (No. 10ZR1420800)
文摘In this paper, we apply the theory of planar dynamical systems to carry out qualitative analysis for the dynamical system corresponding to B-BBM equation, and obtain global phase portraits under various parameter conditions. Then, the relations between the behaviors of bounded traveling wave solutions and the dissipation coeffiicient μ are investigated. We find that a bounded traveling wave solution appears as a kink profile solitary wave solution when μ is more than the critical value obtained in this paper, while a bounded traveling wave solution appears as a damped oscillatory solution when μ is less than it. Furthermore, we explain the solitary wave solutions obtained in previous literature, and point out their positions in global phase portraits. In the meantime, approximate damped oscillatory solutions are given by means of undetermined coefficients method. Finally, based on integral equations that reflect the relations between the approximate damped oscillatory solutions and the implicit exact damped oscillatory solutions, error estimates for the approximate solutions are presented.
