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<p>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 <i>P</i> → 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.</p>

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Sketching a Probability Theory of Transition to Turbulence

  • 期刊论文

  • 发表日期：

    2026年2月7日

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  • Zijing Ding,
  • Dazhi Yang,
  • Jin-Han Xie,
  • Hui Li

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.