Linear Stability Of Rossby Wave

In this thesis, the equations of a two-layer model of linear baroclinic Rossby wave in the β-plane approximation are established, we set up a simple model for the stability of baroclinic Rossby wave and find its control parameters p andq. And the stability theory of ordinary differential equations is used to analysis the model、 discuss the stability of it and solve the scope of phase velocity c of the stability and instability of baroclinic Rossby wave.The thesis main content is as follows:The first chapter introduces the research status and research methods of the stability of baroclinic Rossby wave.The second chapter introduces the model of the β-plane approximation to solve the problem of the large scale geophysical fluid、the equations of stable quasi-geostrophic baroclinic Rossby wave of a two-layer and stability theory of ordinary differential equation.The third chapter includes four main parts:(1)βis a function of latitude y, The linear stability of the Rossby wave is discussed by using the two simplest layer model. The wave is instability at high altitudes, and we obtain limiting range of the phase velocity c.(2)The topographical effect hy is a linear function of latitude y, The linear stability of the Rossby wave is discussed by using the two layer model of linear underlying surface, if h> 0, it makes wave instability, and if h< 0, it is conducive to maintain stability.(3)The topographical effect h(y)is a nonlinear function of latitude y, The linear stability of the Rossby wave is discussed by using the two layer model of the sine function underlying surface, if h’(y)>0,the southern slope, it makes wave instability, and if h’(y)< O,the north slope, it is conducive to maintain stability.(4)The work of this paper is summarized, and the future research direction is also discussed.