Department of Physics, Indian Institute of Technology, Kanpur 208016, India.
Department of Energy and Process Engineering, Norwegian University of Science and Technology, Trondheim NO-7491, Norway.
Phys Rev E. 2019 Nov;100(5-1):053101. doi: 10.1103/PhysRevE.100.053101.
In this paper, using Pao's conjecture [Y.-H. Pao, Phys. Fluids 8, 1063 (1965)10.1063/1.1761356], we derive expressions for the spectra and fluxes of kinetic energy and enstrophy for two-dimensional (2D) forced turbulence that extend beyond the inertial range. In these expressions, the fluxes and the spectra contain additional factors of the exponential form. To validate these model predictions, we perform numerical simulations of 2D turbulence with external force applied at wavenumber band (k_{f},k_{f}+1) in the intermediate range. The numerical results match with the model predictions, except for the energy and enstrophy fluxes for k<k_{f}, where the fluxes exhibit significant fluctuations. We show that these fluctuations arise due to the unsteady nature of the flow at small wavenumbers. For k<k_{f}, the shell-to-shell energy transfers computed using numerical data show forward energy transfers among the neighboring shells, but backward energy transfers among other shells.
在本文中，我们利用 Pao 的猜想[Y.-H. Pao, Phys. Fluids 8, 1063 (1965)10.1063/1.1761356]，推导出了二维（2D）强迫湍流的动能和旋度谱和通量的表达式，这些表达式超出了惯性范围。在这些表达式中，通量和谱包含了指数形式的额外因子。为了验证这些模型预测，我们对在中间范围内波数带（k_{f}，k_{f}+1）施加外力的二维湍流进行了数值模拟。数值结果与模型预测相符，除了 k<k_{f}处的能量和旋度通量，在该处通量表现出显著的波动。我们表明，这些波动是由于小波数下流动的非稳态性质引起的。对于 k<k_{f}，使用数值数据计算的壳层到壳层的能量传递显示了相邻壳层之间的正向能量传递，但其他壳层之间的反向能量传递。
