A simple barotropic potential vorticity equation with the influence of dissipation is applied to investigate the nonlinear Rossby wave in a shear flow in the tropical atmophere. By the reduetive perturbation method, w...A simple barotropic potential vorticity equation with the influence of dissipation is applied to investigate the nonlinear Rossby wave in a shear flow in the tropical atmophere. By the reduetive perturbation method, we derive the rotational KdV （rKdV for short） equation. And then, with the help of Jaeobi elliptie functions, we obtain various periodic structures for these Rossby waves. It is shown that dissipation is very important for these periodic structures of rational form.展开更多
In this paper, a conservative difference scheme for the Rosenau-Korteweg de Vries (RKdV) equation in 2D is proposed. The system satisfies the conservative laws in energy and mass. Existence and uniqueness of its diffe...In this paper, a conservative difference scheme for the Rosenau-Korteweg de Vries (RKdV) equation in 2D is proposed. The system satisfies the conservative laws in energy and mass. Existence and uniqueness of its difference solution have been shown. The order of O(τ^2 +/h^4) in the discrete L^∞-norm with time step τ and mesh size h is obtained. Some important lemmas are proposed to prove the high order convergence. We prove that the present scheme is unconditionally stable. Numerical results are also given in order to check the properties of analytical solution.展开更多
基金The project supports by National Natural Science Foundation of China under Grant No. 40233033
文摘A simple barotropic potential vorticity equation with the influence of dissipation is applied to investigate the nonlinear Rossby wave in a shear flow in the tropical atmophere. By the reduetive perturbation method, we derive the rotational KdV （rKdV for short） equation. And then, with the help of Jaeobi elliptie functions, we obtain various periodic structures for these Rossby waves. It is shown that dissipation is very important for these periodic structures of rational form.
基金National Natural Science Foundation of China (No. 11801116)Fundamental Research Funds for the Central Universities (No. HEUCF181104)Special Funds of Science and Technology Innovation Talents of Harbin (No. 2017RAQXJ099).
文摘In this paper, a conservative difference scheme for the Rosenau-Korteweg de Vries (RKdV) equation in 2D is proposed. The system satisfies the conservative laws in energy and mass. Existence and uniqueness of its difference solution have been shown. The order of O(τ^2 +/h^4) in the discrete L^∞-norm with time step τ and mesh size h is obtained. Some important lemmas are proposed to prove the high order convergence. We prove that the present scheme is unconditionally stable. Numerical results are also given in order to check the properties of analytical solution.
