论文标题
用于湍流伪造的射击噪声多重模型
Shot noise multifractal model for turbulent pseudo-dissipation
论文作者
论文摘要
繁殖级联反应已用于湍流中，以生成具有多重统计和远程相关性的场。文献中已经仔细地讨论了产生这种随机场的连续和因果随机过程的例子。在这里，建立了一个因果日对数随机过程，以代表拉格朗日轨迹中伪消失的动力学。它作为随机微分方程的解决方案引入，由噪声源驱动，噪声源是在周期性的间隔中突然跳跃，其周期为流动的耗散时间尺度。这个随机字段具有对量表的连续体的尺度不变性，并且显示不连续的跳跃，其时间的流畅演变低于Kolmogorov量表。其多重分子和相关属性在数值上被证明。
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.
