To realize high Reynolds number turbulent flow in a numerical simulation, an artificial energy input is required. In this study, we propose a deterministic forcing method and a stochastic forcing method to maintain the mean turbulence kinetic energy (TKE) and helicity at ideal values. The proposed forcing methods control both the mean TKE and helicity by introducing two tuning parameters: $\alpha$ and $\beta$, where $\alpha$ is the helicity injection rate and $\beta$ is the convergence of target statistical quantities to ideal values. We carried out 24 direct numerical simulations to investigate the effects of the forcing methods, including the tuning parameters, on turbulence. When we controlled the forcing term based on the proposed methods, the temporal correlation between the TKE and energy dissipation rate was artificially suppressed in the deterministic forcing method, and for higher $\beta$ in the stochastic forcing method. No differences were found between the proposed deterministic and stochastic forcing methods in terms of one- and two-point statistics. There are also some common characteristics between the energy and helicity dissipation rates, including the normalized mean energy and helicity dissipation rates, scale-by-scale budgets, and stretched exponential form of probability density functions. The numerical results support the joint cascade scenario of energy and helicity.

中文翻译：

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各向同性螺旋湍流中基于恒能控制的强迫方法

为了在数值模拟中实现高雷诺数湍流，需要人工输入能量。在这项研究中，我们提出了确定性强迫方法和随机强迫方法，以将平均湍流动能（TKE）和螺旋度保持在理想值。所提出的强制方法通过引入两个调整参数来控制平均TKE和螺旋度：$\alpha$ 和 $\beta$， 在哪里 $\alpha$ 是螺旋注入速率，并且 $\beta$是目标统计量到理想值的收敛。我们进行了24个直接数值模拟，以研究强迫方法（包括调整参数）对湍流的影响。当我们基于所提出的方法控制强迫项时，在确定性强迫方法中人为地抑制了TKE和能量耗散率之间的时间相关性，并且对于更高的$\beta$在随机强迫方法中。就一点统计和两点统计而言，拟议的确定性和随机强迫方法之间没有发现差异。能量和螺旋度耗散率之间也有一些共同的特征，包括归一化的平均能量和螺旋度耗散率，按比例缩放的预算以及概率密度函数的扩展指数形式。数值结果支持了能量和螺旋度的联合级联方案。