In this short article,we wish to initiate a probability theory to describe the(in)famous transition to turbulence phenomena.For normal systems,the instability threshold can be predicted because the transition probabil...In this short article,we wish to initiate a probability theory to describe the(in)famous transition to turbulence phenomena.For normal systems,the instability threshold can be predicted because the transition probability jumps from zero to P→1 when the control parameter exceeds the threshold.However,for non-normal systems,such a transition is probabilistic,which depends on the control parameter and initial energy.A low-dimensional reduction idea is proposed to give a detailed description of the transition probability of non-normal systems in the future.We also wish that such an idea could be transplanted for understanding such a transition in more complex flows,e.g.,atmospheric flows,mantle convection,and ocean circulation.展开更多
基金support of Investigation into Turbulence Transport in Spheres under Multiphysics Fields(Grant No.KJZ-YY-NLT0604)the National Natural Science Foundation of China(Grant No.52176065)。
摘要In this short article,we wish to initiate a probability theory to describe the(in)famous transition to turbulence phenomena.For normal systems,the instability threshold can be predicted because the transition probability jumps from zero to P→1 when the control parameter exceeds the threshold.However,for non-normal systems,such a transition is probabilistic,which depends on the control parameter and initial energy.A low-dimensional reduction idea is proposed to give a detailed description of the transition probability of non-normal systems in the future.We also wish that such an idea could be transplanted for understanding such a transition in more complex flows,e.g.,atmospheric flows,mantle convection,and ocean circulation.