The generation of initial or inflow synthetic turbulent velocity or scalar fields reproducing statistical characteristics of realistic turbulence is still a challenge. The synthetic eddy method, previously introduced in the context of inflow conditions for large eddy simulations, is based on the assumption that turbulence can be regarded as a superposition of coherent structures. In this paper, a new type of synthetic eddy method is proposed, where the fundamental eddy is constructed by superposing three Hill’s vortices, with their axes orthogonal to each other. A distribution of Hill’s vortices is used to synthesize an anisotropic turbulent velocity field that satisfies the incompressibility condition and match a given Reynolds stress tensor. The amplitudes of the three vortices that form the fundamental eddy are calculated from known Reynolds stress profiles through a transformation from the physical reference frame to the principal-axis reference frame. In this way, divergence-free anisotropic turbulent velocity fields are obtained that can reproduce a given Reynolds stress tensor. The model was tested on both isotropic and anisotropic turbulent velocity fields, in the framework of grid turbulence decay and turbulent channel flow, respectively. The transition from artificial to realistic turbulence in the proximity to the inflow boundary was found to be small in all test cases that were considered.

生成初始或流入合成湍流速度或标量场再现现实湍流的统计特征仍然是一个挑战。先前在大涡模拟的流入条件背景下引入的合成涡流方法基于以下假设：湍流可被视为相干结构的叠加。本文提出了一种新型的合成涡流方法，其基本涡流是由三个希尔涡叠加构成的，它们的轴相互正交。希尔涡的分布用于合成满足不可压缩条件并匹配给定雷诺应力张量的各向异性湍流速度场。通过从物理参考系到主轴参考系的转换，根据已知的雷诺应力分布计算形成基本涡流的三个涡旋的振幅。通过这种方式，可以获得无发散的各向异性湍流速度场，该场可以再现给定的雷诺应力张量。该模型分别在网格湍流衰减和湍流通道流的框架内在各向同性和各向异性湍流速度场上进行了测试。在所有考虑的测试案例中，发现流入边界附近从人工湍流到现实湍流的过渡很小。获得了可以再现给定雷诺应力张量的无发散各向异性湍流速度场。该模型分别在网格湍流衰减和湍流通道流的框架内在各向同性和各向异性湍流速度场上进行了测试。在所有考虑的测试案例中，发现流入边界附近从人工湍流到现实湍流的过渡很小。获得了可以再现给定雷诺应力张量的无发散各向异性湍流速度场。该模型分别在网格湍流衰减和湍流通道流的框架内在各向同性和各向异性湍流速度场上进行了测试。在所有考虑的测试案例中，发现流入边界附近从人工湍流到现实湍流的过渡很小。