Gravity Waves Nonlinear Interaction And Heavy Rain

Based on the dynamics equations describing the atmosphere, we gained two groups of three-wave resonance interaction coupling equations of gravitywaves at the quasi-resonance wave vectors: K₊K2+K3=0 andω₁ +ω₂+ω₃ = △ω (△ω as deviation frequency). One of them is streamlinefield three-wave quasi-resonance equation and especially the other includes the temperature wave-wave interactions. The solution of the first group equations may be given explicitly as elliptic functions, and receives the conservation formula and rough establishes the energy period of about 10 hours of streamline field.The numerical experiment of the three-wave resonance interaction is done use the second group equations, the result shows: (1) For the different initial amplitudes, the obvious periods of low-frequency appeared in the three-wave resonance interaction with time. The main periods of low-frequency are 4h, 10-15h, 25h and 40-5 Oh with the period of 40 minutes. (2) The low-frequency fluctuation periods and the initial amplitudes have close relationship in the resonance interaction. (3)For the same initial amplitudes, the periods are becoming short, the three waves are gradually becoming instability, and the time of strong interaction is shorting with increasing of wave numbers. The periods of low-frequency become long when the horizontal wave numbers are increasing and the vertical wave numbers are decreasing. (4)The energy period of streamline field and the temperature waves have close relationship in the resonance interaction. (5) Nonlinear gravity wave-wave interactions could lead to the new waves of low-frequency and may be the dynamics mechanism to explain the great disaster weather such as sustained storm rainfall.