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The Evolutionary Characteristic and Interaction of Nonlinear Vortex Rossby Waves

Author: HaoYongMei
Tutor: ZhouWeiCan
School: Nanjing University of Information Engineering
Course: Applied Mathematics
Keywords: The nonlinear vortex Rossby wave schr (o Of ¨) dinge Equation Stability Numeric format Spiral cloud band
CLC: P433
Type: Master's thesis
Year: 2006
Downloads: 66
Quote: 1
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Abstract


This thesis is based on the principles of atmospheric dynamics of mesoscale dynamics equation reductive perturbation atmosphere within the nonlinear vortex Rossby waves and their interaction evolution equations , equations of theoretical study and practical atmosphere Beijing solving nonlinear vortex Rossby wave phase velocity value 10 0 m / s, measured shift with spiral cloud with the same speed , which is why many scholars from the vortex Rossby wave to find typhoon the spiral cloud with the formation , to maintain the theory explained . Study nonlinear vortex Rossby wave evolution equations , the existence of solutions , periodic wave solutions and their stability and numerical format not only has theoretical significance , but also has important practical value . Through research, the results showed that : 1 . Single nonlinear evolution of the vortex Rossby wave satisfy the nonlinear Schr ( ? ) Dinger equation : ( αA / of αT is ) α ( the α 2 < / sup > A / αμ 2 < / sup > ) β | A | 2 A = 0 nonlinear evolution equations in the vortex Rossby wave interactions satisfy the coupled nonlinear Schr (?) dinger group : ( ? ) 2 . coupled nonlinear Schr (?) dinger equations satisfy the conditions : (1) the q j < / sub> ( S 1 < / sub> the S 2 < / sub>) ∈ C 2 , (S j ∈ [0, ∞)) for real-valued function , and | the q j ( S < sub> 1 , S 2 ) | ≤ M (S 1 S 2 ), M = const gt; 0 (2 ) A j0 ∈ H 2 is equations exist; nonlinear Schr ( ? ) dinger equation and the cycle fluctuations solutions and their stability the research has been stable and unstable criterion . Coupled nonlinear Schr ( ? ) Dinger equations given a four-point implicit format : the iB j ( ? ) < / Sub> B jμ the α j ( ?) β j q j (| B 1 | 2 , | B 2 | 2 ) B j (c gj * / 4α j ) = 0 B j | Sh = 0, B j | T = 0 = e ( i (c gj < / sub> * / 2α j ) μ) A j0

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CLC: > Astronomy,Earth Sciences > Atmospheric science (meteorology ) > Dynamic meteorology > Atmospheric dynamics
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