In 1959 Batchelor predicted that the stationary statistics of passive scalars advected in fluids with small diffusivity k should display a power spectrum along an inertial range contained in the viscous-convective range of the fluid model. This prediction has been extensively tested, both experimentally and numerically, and is a core prediction of passive scalar turbulence.

中文翻译：

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固定雷诺数下随机流体力学中被动标量湍流的 Batchelor 谱

1959 年，Batchelor 预测，在具有小扩散率k的流体中平流的被动标量的平稳统计应该显示沿着包含在流体模型的粘性对流范围内的惯性范围的功率谱。该预测已经通过实验和数值进行了广泛的测试，并且是被动标量湍流的核心预测。