Nonlinear intermodulation waves of large-scale shallow water equations

According to the general shallow water equations, the nondimensional nonlinear dynamic equations are obtained that can describe large-scale barotropic atmosphere. Using multi-scale method, a nonlinear controlling equation for disturbed height (or pressure) field is deduced. Applying elliptic equation to construct the solutions of the controlling equation, the analytic solutions of the disturbed height field and velocity are obtained, which include the multiply periodic waves and shock (explosive) waves. The solutions of the disturbed height field present periodic waves with different periodicity and wavelength along longitude and latitude, which are modulated by the solitary waves of latitude. The velocity solutions display that in the large-scale air flows exist periodic distribution phenomena of cyclone and anticyclone.