Multiplicative cascades have been used in turbulence to generate fields with multifractal statistics and long-range correlations. Examples of continuous and causal stochastic processes which generate such a random field have been carefully discussed in the literature. Here a causal lognormal stochastic process is built to represent the dynamics of pseudo-dissipation in a Lagrangian trajectory. It is introduced as the solution of a stochastic differential equation, driven by a source of noise which has sudden jumps at periodic intervals, its period being the dissipative time scale of the flow. This random field has scale invariance for a continuum of scales, and displays discontinuous jumps in time, with a smooth time evolution below the Kolmogorov scale. Its multifractal and correlation properties are demonstrated numerically.

中文翻译：

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湍流伪耗散的散粒噪声多重分形模型

乘法级联已用于湍流以生成具有多重分形统计和长程相关性的场。产生这种随机场的连续和因果随机过程的例子已经在文献中仔细讨论过。这里建立了一个因果对数正态随机过程来表示拉格朗日轨迹中伪耗散的动态。它作为随机微分方程的解被引入，由噪声源驱动，该噪声源以周期性间隔突然跳跃，其周期是流的耗散时间尺度。该随机场具有尺度连续体的尺度不变性，并显示不连续的时间跳跃，在 Kolmogorov 尺度以下具有平滑的时间演化。它的多重分形和相关性属性被数值证明。