The random uniform shear layer: An explicit example of turbulent diffusion with broad tail probability distributions
The random uniform shear layer: An explicit example of turbulent diffusion with broad tail probability distributions
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随机均匀剪切层：具有宽尾概率分布的湍流扩散的明确示例
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发表时间：
1993
期刊：
影响因子：
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通讯作者：
A. Majda
中科院分区：
文献类型：
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作者：
A. Majda
最近的实验和计算观察表明，扩散被动标量的大规模不稳定性的发生，表现为比高斯概率分布函数更宽。在这里，开发了一系列明确的精确可解的例子，通过简单的公式来证明在任何正时间的大尺度不稳定性的影响，而无需任何唯象近似。精确的解决方案涉及对流扩散与速度场，涉及均匀剪切流扰动的随机波动均匀剪切流。通过精确的量子力学类比，这些模型中标量的高阶统计量可以通过量子谐振子的公式精确求解。这些显式公式还表明，归一化标量的大时间渐近极限概率分布函数可以比高斯或高斯更宽，这取决于平均流和脉动速度场的相对强度。最近的实验和计算观察表明，扩散被动标量的大尺度不稳定性的发生，表现为比高斯更宽的概率分布函数。在这里，开发了一系列明确的精确可解的例子，通过简单的公式来证明在任何正时间的大尺度不稳定性的影响，而无需任何唯象近似。精确的解决方案涉及对流扩散与速度场，涉及均匀剪切流扰动的随机波动均匀剪切流。通过精确的量子力学类比，这些模型中标量的高阶统计量可以通过量子谐振子的公式精确求解。这些明确的公式还表明，大的时间渐近极限概率分布函数的归一化标量可以比高斯或高斯依赖于相对强度的…
Recent experimental and computational observations demonstrate the occurrence of large‐scale intermittency for diffusing passive scalars, as manifested by broader than Gaussian probability distribution functions. Here, a family of explicit exactly solvable examples is developed which demonstrates these effects of large‐scale intermittency at any positive time through simple formulas for the higher flatness factors without any phenomenological approximations. The exact solutions involve advection–diffusion with velocity fields involving a uniform shear flow perturbed by a random fluctuating uniform shear flow. Through an exact quantum mechanical analogy, the higher‐order statistics for the scalar in these models are solved exactly by formulas for the quantum‐harmonic oscillator. These explicit formulas also demonstrate that the large time asymptotic limiting probability distribution function for the normalized scalar can be either broader than Gaussian or Gaussian depending on the relative strength of the mean flow and the fluctuating velocity field.Recent experimental and computational observations demonstrate the occurrence of large‐scale intermittency for diffusing passive scalars, as manifested by broader than Gaussian probability distribution functions. Here, a family of explicit exactly solvable examples is developed which demonstrates these effects of large‐scale intermittency at any positive time through simple formulas for the higher flatness factors without any phenomenological approximations. The exact solutions involve advection–diffusion with velocity fields involving a uniform shear flow perturbed by a random fluctuating uniform shear flow. Through an exact quantum mechanical analogy, the higher‐order statistics for the scalar in these models are solved exactly by formulas for the quantum‐harmonic oscillator. These explicit formulas also demonstrate that the large time asymptotic limiting probability distribution function for the normalized scalar can be either broader than Gaussian or Gaussian depending on the relative strength of the ...