湍流传递对临界特性的影响
Effects of turbulent transfer on the critical behaviour
摘要：
本文用场论重整化群研究了两个系统在湍流混合作用下的临界行为。由平衡模型A描述的第一系统对应于非保守序参量的弛豫动力学。第二类是强非平衡反应扩散系统，称为Gribov过程或定向渗流过程。湍流混合由具有随机搅拌力的随机纳维-斯托克斯方程和相关器\propto δ（t-t '）p^{4-d-y}模拟，其中p是波数，d是空间维数，y是任意指数。它示出，取决于y和d之间的关系，系统表现出各种类型的临界行为。除了已知的制度（原始系统没有混合和被动平流标量场），存在新的强非平衡普适类建立，并计算相应的临界尺寸的双重展开在y和ε=4-d（一圈近似）的一阶。
英文摘要：
Critical behaviour of two systems, subjected to the turbulent mixing, is studied by means of the field theoretic renormalization group. The first system, described by the equilibrium model A, corresponds to relaxational dynamics of a non-conserved order parameter. The second one is the strongly nonequilibrium reaction-diffusion system, known as Gribov process or directed percolation process. The turbulent mixing is modelled by the stochastic Navier-Stokes equation with random stirring force with the correlator \propto δ(t-t') p^{4-d-y}, where p is the wave number, d is the space dimension and y the arbitrary exponent. It is shown that, depending on the relation between y and d, the systems exhibit various types of critical behaviour. In addition to known regimes (original systems without mixing and passively advected scalar field), existence of new strongly nonequilibrium universality classes is established, and the corresponding critical dimensions are calculated to the first order of the double expansion in y and ε=4-d (one-loop approximation).
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