Kessar Mouloud, Plunian Franck, Stepanov Rodion, Balarac Guillaume
Université Grenoble Alpes, CNRS, LEGI, Grenoble, France.
Université Grenoble Alpes, CNRS, ISTerre, Grenoble, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Sep;92(3):031004. doi: 10.1103/PhysRevE.92.031004. Epub 2015 Sep 28.
We solve the Navier-Stokes equations with two simultaneous forcings. One forcing is applied at a given large scale and it injects energy. The other forcing is applied at all scales belonging to the inertial range and it injects helicity. In this way we can vary the degree of turbulence helicity from nonhelical to maximally helical. We find that increasing the rate of helicity injection does not change the energy flux. On the other hand, the level of total energy is strongly increased and the energy spectrum gets steeper. The energy spectrum spans from a Kolmogorov scaling law k^{-5/3} for a nonhelical turbulence, to a non-Kolmogorov scaling law k^{-7/3} for a maximally helical turbulence. In the latter case we find that the characteristic time of the turbulence is not the turnover time but a time based on the helicity injection rate. We also analyze the results in terms of helical modes decomposition. For a maximally helical turbulence one type of helical mode is found to be much more energetic than the other one, by several orders of magnitude. The energy cascade of the most energetic type of helical mode results from the sum of two fluxes. One flux is negative and can be understood in terms of a decimated model. This negative flux, however, is not sufficient to lead an inverse energy cascade. Indeed, the other flux involving the least energetic type of helical mode is positive and the largest. The least energetic type of helical mode is then essential and cannot be neglected.
我们通过两种同时作用的外力来求解纳维-斯托克斯方程。一种外力作用于给定的大尺度，用于注入能量。另一种外力作用于属于惯性范围的所有尺度，用于注入螺旋度。通过这种方式，我们可以使湍流螺旋度的程度从非螺旋状态变化到最大螺旋状态。我们发现增加螺旋度注入率并不会改变能量通量。另一方面，总能量水平会大幅增加，并且能谱会变得更陡。能谱范围从非螺旋湍流的科尔莫戈罗夫标度律(k^{-5/3})，到最大螺旋湍流的非科尔莫戈罗夫标度律(k^{-7/3})。在后一种情况下，我们发现湍流的特征时间不是周转时间，而是基于螺旋度注入率的一个时间。我们还根据螺旋模式分解来分析结果。对于最大螺旋湍流，发现一种类型的螺旋模式比另一种模式的能量高几个数量级。能量最高的那种螺旋模式的能量级串由两个通量之和产生。一个通量为负，可以用一个抽取模型来理解。然而，这个负通量不足以导致能量反向级串。实际上，涉及能量最低的那种螺旋模式的另一个通量为正且是最大的。那么能量最低的那种螺旋模式是至关重要的，不能被忽略。
