Mechanism in Leading to Richardson′s Four-Thirds Law

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  • Mechanism in Leading to Richardson’s Four-Thirds Law
  • Mechanism in Leading to Richardson s Fo

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For the relative diffusion of a pair particles in turbulent flow, the mechanism in leading to Richardson’s four-third law is studied analytically and numerically by using the effective Hamiltonian method. With this analysis, in connection with the Kolmogorov’s spectrum and the scaling law, it is shown that the main contribution to the Richardson’s law comes from a relatively small region of the inertial range, and there is a considerably large contribution from the vortexes whose diameters are larger than the relative distance between a pair of particles. It is also reported that the range of Richardson’s law in the smaller scales in the turbulence with a multi-range spectrum is extended toward large scales beyond a typical length in the smaller scales.

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