Instability Development in Shear Flow with an Inflection-Free Velocity Profile and Thin Pycnocline

• 作 者: Semyon M. Churilov
• 机 构: InstituteofSolar-TerrestrialPhysicsSBRAS,Irkutsk664033,Russia
• 出 处: The 5th International Conference on Nonlinear Science and Co
• 发表日期: 2014年8期
• 关键词: Shear flow inflection-free velocity profile sharp density stratification nonline

　　In the class of shear flows under study,a major part of instability waves has so close phase velocities that individual critical layers of those waves merge into a common one.Throughout a weakly-nonlinear stage of perturbation development,this is the layer in that the most intensive and diverse wave interactions occur which determine scenario of perturbation evolution.Analysis of these interactions allows us,first,to reveal two stages of the evolution,three-wave one when three-wave interactions dominate,and post-three-wave when numerous nonlinear interactions of different orders come into play,and,second,to determine which of the higher-order interactions are competitive.On this basis,we have found the structure of nonlinear evolution equations,revealed that the nonlinear growth of wave amplitudes is explosive,and calculated growth indexes for both nonlinear stages.It is found that during the three-wave stage the most rapidly growing are low-frequency waves whereas at the next stage the growth of high frequency waves is accelerated,and to the end of the weakly-nonlinear stage all the waves have amplitudes of the same order.The results obtained are illustrated by numerical calculations for some ensembles of waves.