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Updated: Jun 5, 2026

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
Published on: February 22, 2018
Structure functions of fully developed hydrodynamic turbulence: an analytical approach
K P Zybin1, V A Sirota, A S Ilyin
1P.N.Lebedev Physical Institute, Leninskij pr.53, 119991 Moscow, Russia. zybin@lpi.ru
Abstract:
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.
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