Zybin K P, Sirota V A
P. N. Lebedev Physical Institute of RAS, Leninskij Prospekt, Moscow, Russia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2012 May;85(5 Pt 2):056317. doi: 10.1103/PhysRevE.85.056317. Epub 2012 May 30.
We develop a theory of turbulence based on the inviscid Navier-Stokes equation. We get a simple but exact stochastic solution (vortex filament model) which allows us to obtain a power law for velocity structure functions in the inertial range. Combining the model with the multifractal conjecture, we calculate the scaling exponents without using the extended self-similarity approach. The results obtained are shown to be in very good agreement with numerical simulations and experimental data. The role of more general stochastic solutions of the Navier-Stokes equation is discussed.
我们基于无粘性的纳维-斯托克斯方程发展了一种湍流理论。我们得到了一个简单但精确的随机解（涡丝模型），这使我们能够获得惯性范围内速度结构函数的幂律。将该模型与多重分形猜想相结合，我们无需使用扩展自相似性方法就能计算标度指数。结果表明与数值模拟和实验数据非常吻合。我们还讨论了纳维-斯托克斯方程更一般随机解的作用。
