Abstract

The dynamics of passive scalar in swirling turbulent far wakes with varied values of the total excess momentum and angular momentum are described within a second-order mathematical model. The model includes averaged equations of momenta, turbulence energy balance, dissipation rate transfer, averaged concentration, and dispersion of its turbulent fluctuations in the far wake approximation. The closure of the mathematical model is based on Rodi’s algebraic model of the Reynolds stresses. At large distances, a self-similar solution based on numerical experiments is obtained for problems of the dynamics of passive scalar in turbulent wakes behind a self-propelled body and in a momentumless swirling turbulent wake. The group-theoretical analysis of the mathematical model under study is carried out. The model is reduced to a system of ordinary differential equations, which is solved numerically by the shooting method. The resulting solution is compared with the self-similar solution found by direct numerical integration of the differential equations of the model at large distances from the body. Good agreement is obtained. The problem of asymptotic behavior of characteristics of passive admixture in a swirling turbulent wake behind a sphere with nonzero values of the total excess momentum and angular momentum is also considered. With application of the group-theoretical analysis, it is shown that there is no physically meaningful self-similar solution to the equations of passive admixture dynamics.

中文翻译：

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涡流湍流远尾流中无源标量的动力学

摘要

在二阶数学模型中描述了具有不同总超动量和角动量值的涡旋湍流远尾流中的被动标量动力学。该模型包括动量、湍流能量平衡、耗散率传递、平均浓度和其湍流波动在远尾流近似中的分散的平均方程。数学模型的闭合基于雷诺应力的 Rodi 代数模型。针对自航体后方湍流尾流和无动量旋涡湍流尾流中的被动标量动力学问题，基于数值实验得到了远距离自相似解。对所研究的数学模型进行群论分析。该模型被简化为一个常微分方程组，通过射击法进行数值求解。将得到的解与通过在离身体很远的距离处模型的微分方程直接数值积分得到的自相似解进行比较。获得了良好的协议。还考虑了总超动量和角动量非零值的球体后面的涡流湍流尾流中被动混合特性的渐近行为问题。应用群论分析表明，被动混合动力学方程没有物理上有意义的自相似解。将得到的解与通过在离身体很远的距离处模型的微分方程直接数值积分得到的自相似解进行比较。获得了良好的协议。还考虑了总超动量和角动量非零值的球体后面的涡流湍流尾流中被动混合特性的渐近行为问题。应用群论分析表明，被动混合动力学方程没有物理上有意义的自相似解。将得到的解与通过在离身体很远的距离处模型的微分方程直接数值积分得到的自相似解进行比较。获得了良好的协议。还考虑了总超动量和角动量非零值的球体后面的涡流湍流尾流中被动混合特性的渐近行为问题。应用群论分析表明，被动混合动力学方程没有物理上有意义的自相似解。还考虑了总超动量和角动量非零值的球体后面的涡流湍流尾流中被动混合特性的渐近行为问题。应用群论分析表明，被动混合动力学方程没有物理上有意义的自相似解。还考虑了总超动量和角动量非零值的球体后面的涡流湍流尾流中被动混合特性的渐近行为问题。应用群论分析表明，被动混合动力学方程没有物理上有意义的自相似解。