Title: Response maxima in time-modulated turbulence: Direct Numerical Simulations Show Chinese title

Title: 时间调制湍流中的响应峰值：直接数值模拟

Abstract: The response of turbulent flow to time-modulated forcing is studied by direct numerical simulations of the Navier-Stokes equations. The large-scale forcing is modulated via periodic energy input variations at frequency $\omega$. The response is maximal for frequencies in the range of the inverse of the large eddy turnover time, confirming the mean-field predictions of von der Heydt, Grossmann and Lohse (Phys. Rev. E 67, 046308 (2003)). In accordance with the theory the response maximum shows only a small dependence on the Reynolds number and is also quite insensitive to the particular flow-quantity that is monitored, e.g., kinetic energy, dissipation-rate, or Taylor-Reynolds number. At sufficiently high frequencies the amplitude of the kinetic energy response decreases as $1/\omega$. For frequencies beyond the range of maximal response, a significant change in phase-shift relative to the time-modulated forcing is observed. Show Chinese abstract

Abstract: 通过直接数值模拟纳维-斯托克斯方程研究了湍流对时间调制强迫的响应。 大尺度强迫通过在频率$\omega$处周期性能量输入变化进行调制。 在反向大涡旋转时间范围内的频率下，响应达到最大值，证实了 von der Heydt、Grossmann 和 Lohse（Phys. Rev. E 67, 046308 (2003)) 的平均场预测。 根据理论，响应最大值仅对雷诺数有很小的依赖性，并且对所监测的具体流体量也相当不敏感，例如动能、耗散率或泰勒雷诺数。 在足够高的频率下，动能响应的振幅按$1/\omega$减小。 在超过最大响应范围的频率下，观察到了相对于时间调制强迫的相位移的显著变化。