Stably stratified turbulence in the presence of large-scale forcing.
Stably stratified turbulence in the presence of large-scale forcing.
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存在大规模强迫的情况下稳定的分层湍流。
DOI：
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发表时间：
2014
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通讯作者：
A. Pouquet
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作者：
C. Rorai;P. Mininni;A. Pouquet
本文对雷诺数Re = 25000和弗劳德数Fr = 0.1和Fr = 0.03的分层湍流进行了两次高分辨率直接数值模拟。流场是在大尺度下强迫的，并在2048（3）点的各向同性网格上离散化。分层使流动各向异性，并引入两个额外的特征尺度相对于均匀各向同性湍流：浮力尺度，L（B），和Ozmidov尺度，Oz（oz）。前者与流沿重力方向发展的层数有关，后者被认为是各向同性恢复的尺度。L（B）和λ（oz）的值取决于弗劳德数，它们的绝对和相对振幅以不容易预测的方式影响傅立叶模式之间的能量再分配。通过对比这两个模拟流的行为，我们发现了一些令人惊讶的相似之处：经过初始瞬变，两个流的动力学和潜在的拟能和能量耗散率的值演变。这是由于雷诺数在两种流动中都足够大，以便解析Ozmidov尺度。当适当的尺寸，能量耗散率是兼容的大气观测。在大尺度上出现了进一步的相似之处：势能和总能量之间的比率（0.01）是由流动自发选择的，并且慢模式在两个区域中单调增长，导致总能量随时间缓慢增加。轴对称的总能量谱显示了各种各样的谱斜率作为一个函数之间的角度强加的分层和波矢量。在平行于重力的方向上计算的一维能量谱是平坦的，从强迫到浮力尺度。在中等尺度下，Fr = 0.03的运行会产生一个λ k（-3）平行谱，而对于较弱的分层，饱和谱没有足够的尺度来产生，而是观察到一个与柯尔莫哥洛夫尺度相容的幂律。最后，螺旋度谱在L（B）之前是平坦的，正如在夜间行星边界层中所观察到的那样。
We perform two high-resolution direct numerical simulations of stratified turbulence for Reynolds number equal to Re≈25000 and Froude number, respectively, of Fr≈0.1 and Fr≈0.03. The flows are forced at large scale and discretized on an isotropic grid of 2048(3) points. Stratification makes the flow anisotropic and introduces two extra characteristic scales with respect to homogeneous isotropic turbulence: the buoyancy scale, L(B), and the Ozmidov scale, ℓ(oz). The former is related to the number of layers that the flow develops in the direction of gravity, and the latter is regarded as the scale at which isotropy is recovered. The values of L(B) and ℓ(oz) depend on the Froude number, and their absolute and relative amplitudes affect the repartition of energy among Fourier modes in ways that are not easy to predict. By contrasting the behavior of the two simulated flows we identify some surprising similarities: After an initial transient the two flows evolve towards comparable values of the kinetic and potential enstrophy and energy dissipation rate. This is the result of the Reynolds number being large enough in both flows for the Ozmidov scale to be resolved. When properly dimensionalized, the energy dissipation rate is compatible with atmospheric observations. Further similarities emerge at large scales: The same ratio between potential and total energy (≈0.1) is spontaneously selected by the flows, and slow modes grow monotonically in both regimes, causing a slow increase of the total energy in time. The axisymmetric total energy spectrum shows a wide variety of spectral slopes as a function of the angle between the imposed stratification and the wave vector. One-dimensional energy spectra computed in the direction parallel to gravity are flat from the forcing up to buoyancy scale. At intermediate scales a ∼k(-3) parallel spectrum develops for the Fr≈0.03 run, whereas for weaker stratification, the saturation spectrum does not have enough scales to develop and instead one observes a power law compatible with Kolmogorov scaling. Finally, the spectrum of helicity is flat until L(B), as observed in the nocturnal planetary boundary layer.