LINEAR AND NONLINEAR BAROTROPIC INSTABILITY

Based on a non-frictional and non-divergent nonlinear barotropic vorticity equation and its solutions oftravelling waves,the criteria for linear and nonlinear barotropic instability are gained respectively at an equilibriumpoint of the equation on a phase plane.The linear and nonlinear analytical solutions to instability waves arealso found.The computational results show that if their amplitudes are equal at the initial time,the amplitudeincrements of nonlinear instable barotropic wave are always less than those of linear instable barotropic wave.The nonlinear effects can slow down the exponential growth of linear instability.The time needed for makingthe amplitude double that of initial time by instabilities,is about 6h for linear instability and about 18h fornonlinear instability,the latter is in agreement with the observations in the real atmosphere.

LINEAR AND NONLINEAR BAROTROPIC INSTABILITY

Based on a non-frictional and non-divergent nonlinear barotropic vorticity equation and its solutions of travelling waves,the criteria for linear and nonlinear barotropic instability are gained respectively at an equilibrium point of the equation on a phase plane.The linear and nonlinear analytical solutions to instability waves are also found.The computational results show that if their amplitudes are equal at the initial time,the amplitude increments of nonlinear instable barotropic wave are always less than those of linear instable barotropic wave.The nonlinear effects can slow down the exponential growth of linear instability.The time needed for making the amplitude double that of initial time by instabilities,is about 6h for linear instability and about 18h for nonlinear instability,the latter is in agreement with the observations in the real atmosphere.