Zybin K P, Sirota V A, Ilyin A S
P.N.Lebedev Physical Institute, Leninskij pr.53, 119991 Moscow, Russia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Nov;82(5 Pt 2):056324. doi: 10.1103/PhysRevE.82.056324. Epub 2010 Nov 29.
We develop a theory of turbulence based on the inviscid Navier-Stokes equation, without using dimensional or phenomenological considerations. The theory allows us to obtain the scaling law and to calculate the scaling exponents of the Lagrangian and Eulerian velocity structure functions in the inertial range. The obtained results are shown to be in very good agreement with numerical simulations and experimental data. The introduction of stochasticity into the equations is discussed in detail. The main equation of the theory obtained directly from the Navier-Stokes equation is analyzed by means of continual integration.
我们基于无粘的纳维-斯托克斯方程发展了一种湍流理论，而不使用量纲或唯象学的考虑因素。该理论使我们能够获得标度律，并计算惯性范围内拉格朗日和欧拉速度结构函数的标度指数。结果表明，所得结果与数值模拟和实验数据非常吻合。详细讨论了将随机性引入方程的问题。通过连续积分对直接从纳维-斯托克斯方程得到的该理论的主要方程进行了分析。
