Abstract

Using the field theoretic renormalization group technique the simultaneous influence of compressibility and finite time correlations of the non-solenoidal Gaussian velocity field on the advection of a passive scalar field is studied within the generalized Kraichnan model up to the second-order approximation in the corresponding perturbative expansion. The renormalization of the model is performed and explicit forms of the renormalization functions are found. All possible infrared stable fixed points of the model, which drive the corresponding scaling regimes of the model, are identified and their regions of the infrared stability in the model parametric space are discussed in detail. The attention is mainly paid to the properties of the most interesting scaling regime with the presence of the finite-time correlations of the velocity field. It is shown that, apart from two specific values of the parameter that drives the compressibility of the system, there exists a gap in the parametric space between regions where the model with the frozen velocity field and the model with finite-time correlations of the velocity field are stable.

Graphical abstract

中文翻译：

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可压缩性对具有有限时间相关性的Kraichnan模型的缩放比例的影响：两环RG分析

摘要

使用场理论重归一化群技术，研究了广义电磁Kraichnan模型中非电磁场高斯速度场的可压缩性和有限时间相关性对被动标量场对流的同时影响，直到相应扰动下的二阶逼近。扩张。执行模型的重归一化，并找到重归一化函数的显式形式。确定了驱动模型的相应缩放比例的所有可能的模型红外稳定点，并详细讨论了模型参数空间中红外稳定的区域。注意力主要集中在速度场的有限时间相关性存在的情况下，最有趣的缩放比例的性质。

图形概要