Analytic Studies On The Interactions Between Nonlinear Kelvin And Rossby Waves

In this paper, we have investigated the nonlinear Kelvin and Rossby waves of theatmosphere in low latitudes. It is found by use of the WKB method that the wave packet isgoverned by nonlinear Landau equation, this equation was used to describe turbulence initially. Itis shown by numerical calculations that the amplitude of the waves changes rapidly and the widthof waves becomes narrow after the collision of the two waves. The results indicate that thenonlinear interaction between Kelvin and Rossby waves may be one of the causes for the outbreak of severe convective weather. Thus it is significative to study the interaction equations,theexistence of the solutions and the stability of the numerical format. There are mainly four parts inthe thesis:First, the nonlinear Kelvin wave is governed by nonlinear Landau equation:Second, the interaction between the nonlinear Kelvin and Rossby wave packets governed bycoupled nonlinear Landau equations:Third, for the coupled nonlinear Landau equations, we prove that the conditions of theexistence for the solutions are:(1)σ₂₁≥0,σ₃₁≥0,c_gj^*>0, andβ(x)≥0 is a real function with a period of L;(2)q(s) is real function, q(s)∈c¹,q(s)≥0,s∈[0,∞) ;λ_j(x)(j=1,2) is a real boundedfunction with a period of L;(3)the initial conditions satisfy A_j0(x)∈H²ã€‚Fourth, we give the format of four-point scheme for the coupled nonlinear equations:If the conditions satisfy:A_j0∈H¹,0≤b≤|c_gj^*|≤M,0≤q_j(s₁,s₂)≤R(s₁+s₂),s_j∈[0,+∞]The format of four-point implicit scheme is proved to be stable, furthermore the error is: O(Ï„+h²)...